diff options
Diffstat (limited to 'java/com/google/security/wycheproof')
10 files changed, 2994 insertions, 520 deletions
diff --git a/java/com/google/security/wycheproof/testcases/AesGcmTest.java b/java/com/google/security/wycheproof/testcases/AesGcmTest.java index d71b8c2..9f27992 100644 --- a/java/com/google/security/wycheproof/testcases/AesGcmTest.java +++ b/java/com/google/security/wycheproof/testcases/AesGcmTest.java @@ -16,13 +16,18 @@ package com.google.security.wycheproof; +import com.google.security.wycheproof.WycheproofRunner.ExcludedTest; +import com.google.security.wycheproof.WycheproofRunner.ProviderType; +import com.google.security.wycheproof.WycheproofRunner.SlowTest; import java.nio.ByteBuffer; import java.security.AlgorithmParameterGenerator; import java.security.AlgorithmParameters; import java.security.InvalidAlgorithmParameterException; import java.security.InvalidKeyException; import java.security.NoSuchAlgorithmException; +import java.security.SecureRandom; import java.util.ArrayList; +import java.util.Arrays; import javax.crypto.Cipher; import javax.crypto.ShortBufferException; import javax.crypto.spec.GCMParameterSpec; @@ -178,6 +183,41 @@ public class AesGcmTest extends TestCase { } } + /** + * JCE has a dangerous feature: after a doFinal the cipher is typically reinitialized using the + * previous IV. This "feature" can easily break AES-GCM usages, because encrypting twice with + * the same key and IV leaks the authentication key. Hence any reasonable implementation of + * AES-GCM should not allow this. The expected behaviour of OpenJDK can be derived from the tests + * in jdk/test/com/sun/crypto/provider/Cipher/AES/TestGCMKeyAndIvCheck.java. + * OpenJDK does not allow two consecutive initializations for encryption with the same key and IV. + * + * <p>The test here is weaker than the restrictions in OpenJDK. The only requirement here is that + * reusing a Cipher without an explicit init() is caught. + * + * <p>BouncyCastle 1.52 failed this test + * + * <p>Conscrypt failed this test + */ + public void testIvReuse() throws Exception { + for (GcmTestVector test : getTestVectors()) { + Cipher cipher = Cipher.getInstance("AES/GCM/NoPadding"); + cipher.init(Cipher.ENCRYPT_MODE, test.key, test.parameters); + cipher.updateAAD(test.aad); + byte[] ct1 = cipher.doFinal(test.pt); + try { + byte[] ct2 = cipher.doFinal(test.pt); + fail( + "It should not possible to reuse an IV." + + " ct1:" + + TestUtil.bytesToHex(ct1) + + " ct2:" + + TestUtil.bytesToHex(ct2)); + } catch (java.lang.IllegalStateException ex) { + // This is expected. + } + } + } + /** Encryption with ByteBuffers. */ public void testByteBuffer() throws Exception { for (GcmTestVector test : getTestVectors()) { @@ -370,4 +410,62 @@ public class AesGcmTest extends TestCase { byte[] output = cipher.doFinal(input); assertEquals(input.length + 16, output.length); } + + /** + * Test AES-GCM wrapped around counter bug which leaks plaintext and authentication key. Let's + * consider 12-byte IV, counter = IV || 0^31 || 1. For each encryption block, the last 4 bytes of + * the counter is increased by 1. After 2^32 blocks, the counter will be wrapped around causing + * counter collision and hence, leaking plaintext and authentication key as explained below. The + * library must make a check to make sure that the plaintext's length never exceeds 2^32 - 2 + * blocks. Note that this is different from usual IV collisions because it happens even if users + * use different IVs. <br> + * We have: <br> + * J0 = IV || 0^31 || 1 <br> + * Plaintext: P[0], P[1], P[2], .... <br> + * Ciphertext: <br> + * C[0] = Enc(K, (J0 + 1) % 2^32) XOR P[0] <br> + * C[1] = Enc(K, (J0 + 2) % 2^32) XOR P[1] <br> + * C[2] = Enc(K, (J0 + 3) % 2^32) XOR P[2] <br> + * ... <br> + * C[2^32 - 1] = Enc(K, J0) XOR P[2^32 - 1] <br> + * C[2^32] = Enc(K, (J0 + 1)% 2^32) XOR P[2^32] <br> + * It means that after 2^32 blocks, the counter is wrapped around causing counter collisions. In + * counter mode, once the counter is collided then it's reasonable to assume that the plaintext is + * leaked. As the ciphertext is already known to attacker, Enc(K, J0) is leaked. <br> + * Now, as the authentication tag T is computed as GHASH(H, {}, C) XOR E(K, J0), the attacker can + * learn GHASH(H, {}, C}. It essentially means that the attacker finds a polynomial where H is the + * root (see Joux attack http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/Joux_comments.pdf). + * Solving polynomial equation in GF(2^128) is enough to extract the authentication key. + * + * <p>BouncyCastle used to have this bug (CVE-2015-6644). + * + * <p>OpenJDK8 used to have this bug (http://hg.openjdk.java.net/jdk8u/jdk8u/jdk/rev/0c3ed12cdaf5) + * + * <p>The test is slow as we have to encrypt 2^32 blocks. + */ + // TODO(quannguyen): Is there a faster way to test it? + @ExcludedTest( + providers = {ProviderType.CONSCRYPT}, + comment = "Conscrypt doesn't support streaming, would crash") + @SlowTest( + providers = {ProviderType.BOUNCY_CASTLE, ProviderType.SPONGY_CASTLE, ProviderType.OPENJDK}) + public void testWrappedAroundCounter() throws Exception { + try { + byte[] iv = new byte[12]; + byte[] input = new byte[16]; + byte[] key = new byte[16]; + (new SecureRandom()).nextBytes(key); + Cipher cipher = Cipher.getInstance("AES/GCM/NoPadding"); + cipher.init( + Cipher.ENCRYPT_MODE, new SecretKeySpec(key, "AES"), new GCMParameterSpec(16 * 8, iv)); + byte[] output = cipher.update(input); + for (long i = 0; i < 4294967296L + 2; i++) { + byte[] output1 = cipher.update(input); + assertFalse("GCM Wrapped Around Counter" + i, Arrays.equals(output, output1)); + } + fail("Expected Exception"); + } catch (Exception expected) { + System.out.println("testWrappedAroundcounter:" + expected.toString()); + } + } } diff --git a/java/com/google/security/wycheproof/testcases/BigIntegerTest.java b/java/com/google/security/wycheproof/testcases/BigIntegerTest.java index cd5a992..8173a89 100644 --- a/java/com/google/security/wycheproof/testcases/BigIntegerTest.java +++ b/java/com/google/security/wycheproof/testcases/BigIntegerTest.java @@ -50,17 +50,12 @@ public class BigIntegerTest extends TestCase { new BigInteger("164280218643672633986221"), new BigInteger("318665857834031151167461"), new BigInteger("7395010240794120709381"), - new BigInteger("164280218643672633986221"), - new BigInteger("318665857834031151167461"), new BigInteger("2995741773170734841812261"), new BigInteger("667636712015520329618581"), new BigInteger("3317044064679887385961981"), new BigInteger("3110269097300703345712981"), new BigInteger("552727880697763694556181"), - new BigInteger("360681321802296925566181"), - new BigInteger("7395010240794120709381"), new BigInteger("3404730287403079539471001"), - new BigInteger("164280218643672633986221"), // Richarg G.E. Pinch, "Some primality testing algorithms" // Some composites that passed Maple V's primality test. new BigInteger("10710604680091"), diff --git a/java/com/google/security/wycheproof/testcases/DhTest.java b/java/com/google/security/wycheproof/testcases/DhTest.java index 3e9c9e7..84be8f2 100644 --- a/java/com/google/security/wycheproof/testcases/DhTest.java +++ b/java/com/google/security/wycheproof/testcases/DhTest.java @@ -358,6 +358,8 @@ public class DhTest extends TestCase { * itself cannot prevent all small-subgroup attacks because of the missing parameter q in the * Diffie-Hellman parameters. Implementations must add additional countermeasures such as the ones * proposed in RFC 2785. + * + * <p> CVE-2016-1000346: BouncyCastle before v.1.56 did not validate the other parties public key. */ public void testSubgroupConfinement() throws Exception { KeyPairGenerator keyGen = KeyPairGenerator.getInstance("DH"); diff --git a/java/com/google/security/wycheproof/testcases/DhiesTest.java b/java/com/google/security/wycheproof/testcases/DhiesTest.java index 17ab513..fbf8054 100644 --- a/java/com/google/security/wycheproof/testcases/DhiesTest.java +++ b/java/com/google/security/wycheproof/testcases/DhiesTest.java @@ -35,15 +35,18 @@ import junit.framework.TestCase; * * @author bleichen@google.com (Daniel Bleichenbacher) */ -// Tested providers: -// BC (not recommended) -// // TODO(bleichen): // - maybe again CipherInputStream, CipherOutputStream, // - byteBuffer. // - Exception handling // - Is DHIES using the key derivation function for the key stream? // - BouncyCastle knows an algorithm IES. Is this the same as DHIES? +// - Bouncy fixed a padding oracle bug in version 1.56 (CVE-2016-1000345) +// So far we have no test for this bug mainly because this cannot be tested +// through the JCA interface. BC does not register and algorithm such as +// Cipher.DHIESWITHAES-CBC. +// - So far only BouncyCastles is tesed because this is the only provider +// we use that implements DHIES. public class DhiesTest extends TestCase { // TODO(bleichen): This is the same as DhTest.java diff --git a/java/com/google/security/wycheproof/testcases/DsaTest.java b/java/com/google/security/wycheproof/testcases/DsaTest.java index e466900..4d546bb 100644 --- a/java/com/google/security/wycheproof/testcases/DsaTest.java +++ b/java/com/google/security/wycheproof/testcases/DsaTest.java @@ -15,7 +15,6 @@ */ // TODO(bleichen): -// - add tests for signature malleability and ASN parsing. // - add tests for SHA1WithDSA with wrong key // - add tests for "alternative" algorithm names // - convert tests for deterministic DSA variants. @@ -29,6 +28,8 @@ package com.google.security.wycheproof; import com.google.security.wycheproof.WycheproofRunner.ProviderType; import com.google.security.wycheproof.WycheproofRunner.SlowTest; +import java.lang.management.ManagementFactory; +import java.lang.management.ThreadMXBean; import java.math.BigInteger; import java.security.GeneralSecurityException; import java.security.KeyFactory; @@ -111,7 +112,338 @@ public class DsaTest extends TestCase { + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", }; + /** + * The following test vectos are derived from a valid signature by + * using alternative BER encoding as well as legacy formats. + * Accepting such signatures is in many cases benign. Hence the tests + * below will pass if such signatures are accepted as valid. + * The test vectors could be used to check for signature malleability. + * An example where this kind of signature malleability was a problem is + * https://en.bitcoin.it/wiki/Transaction_Malleability + */ + static final String[] MODIFIED_SIGNATURES = { + // BER:long form encoding of length + "30813d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" + + "cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303e02811c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" + + "cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303e021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "02811d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + // BER:length contains leading 0 + "3082003d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" + + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "36", + "303f0282001c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" + + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "36", + "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "0282001d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "36", + // BER:prepending 0's to integer + "303f021e00001e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" + + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "36", + "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021f000000ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "36", + // The Sun provider accepts DSA signatures where a leading 00 has + // been omitted in the ASN encoding. + "303c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021cade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + }; + + /** + * The following test vectors are invalid DSA signatures. + * According to {@link java.security.Signature#verify(byte[])} verifying an invalid + * signature may either return false or throw a SignatureException. + * We expect that a correct implementation of DSA signatures satisfies this contract. + * Throwing a RuntimeException instead of a SignatureException could for example + * result in a denial of service attack. + * + * <p>A list of problems that are caught by these signatures: + * <li> CVE-2016-5546: OpenJDK8 throwed java.lang.ArrayIndexOutOfBoundsException for + * some invalid DSA signatures. + * </ul> + */ static final String[] INVALID_SIGNATURES = { + // wrong length + "303e021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d021d1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d021b1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021e00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021c00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + // uint32 overflow in length + "3085010000003d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916" + + "173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" + + "e8786236", + "30420285010000001c1e41b479ad576905b960fe14eadb91b0ccf34843dab916" + + "173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" + + "e8786236", + "3042021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "0285010000001d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" + + "e8786236", + // uint64 overflow in length + "308901000000000000003d021c1e41b479ad576905b960fe14eadb91b0ccf348" + + "43dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf" + + "3365813fe8786236", + "3046028901000000000000001c1e41b479ad576905b960fe14eadb91b0ccf348" + + "43dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf" + + "3365813fe8786236", + "3046021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "028901000000000000001d00ade65988d237d30f9ef41dd424a4e1c8f16967cf" + + "3365813fe8786236", + // length = 2**31 - 1 + "30847fffffff021c1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" + + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + "304102847fffffff1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" + + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + "3041021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "02847fffffff00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + // length = 2**32 - 1 + "3084ffffffff021c1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" + + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + "30410284ffffffff1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" + + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + "3041021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "0284ffffffff00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + // length = 2**64 - 1 + "3088ffffffffffffffff021c1e41b479ad576905b960fe14eadb91b0ccf34843" + + "dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" + + "65813fe8786236", + "30450288ffffffffffffffff1e41b479ad576905b960fe14eadb91b0ccf34843" + + "dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" + + "65813fe8786236", + "3045021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "0288ffffffffffffffff00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" + + "65813fe8786236", + // removing sequence + "", + // appending 0's to sequence + "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623600" + + "00", + // prepending 0's to sequence + "303f0000021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" + + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "36", + // appending unused 0's + "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "0000021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "36", + // appending null value + "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623605" + + "00", + "303f021e1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "0500021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "36", + "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021f00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623605" + + "00", + // including garbage + "3042498177303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916" + + "173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" + + "e8786236", + "30412500303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" + + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + "303f303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" + + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "360004deadbeef", + "30422221498177021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916" + + "173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" + + "e8786236", + "304122202500021c1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" + + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + "3045221e021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" + + "c9cd0004deadbeef021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" + + "65813fe8786236", + "3042021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "2222498177021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813f" + + "e8786236", + "3041021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "22212500021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + "3045021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "221f021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "360004deadbeef", + // including undefined tags + "3045aa00bb00cd00303d021c1e41b479ad576905b960fe14eadb91b0ccf34843" + + "dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" + + "65813fe8786236", + "3043aa02aabb303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab9" + + "16173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf336581" + + "3fe8786236", + "30452224aa00bb00cd00021c1e41b479ad576905b960fe14eadb91b0ccf34843" + + "dab916173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" + + "65813fe8786236", + "30432222aa02aabb021c1e41b479ad576905b960fe14eadb91b0ccf34843dab9" + + "16173bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf336581" + + "3fe8786236", + "3045021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "2225aa00bb00cd00021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf33" + + "65813fe8786236", + "3043021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "2223aa02aabb021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf336581" + + "3fe8786236", + // changing tag value + "2e3d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "323d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "ff3d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d001c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d041c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303dff1c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "001d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "041d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "ff1d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + // dropping value of sequence + "3000", + // using composition + "3041300102303c1c1e41b479ad576905b960fe14eadb91b0ccf34843dab91617" + + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + "3041222002011e021b41b479ad576905b960fe14eadb91b0ccf34843dab91617" + + "3bb8c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + "3041021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "2221020100021cade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8" + + "786236", + // truncate sequence + "303c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862", + "303c1c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd02" + + "1d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + // indefinite length with no delimiter + "3080021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + // prepend empty sequence + "303f3000021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" + + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "36", + // append empty sequence + "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623630" + + "00", + // sequence of sequence + "303f303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8" + + "c9cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "36", + // truncated sequence + "301e021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd", + // repeat element in sequence + "305c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623602" + + "1d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + // removing integer + "301f021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + // appending 0's to integer + "303f021e1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "0000021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862" + + "36", + "303f021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021f00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe878623600" + + "00", + // dropping value of integer + "30210200021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "3020021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd0200", + // modify first byte of integer + "303d021c1f41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + // modify last byte of integer + "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cc" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786237", + // truncate integer + "303c021b1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c902" + + "1d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303c021b41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd02" + + "1d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021c00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe87862", + // leading ff in integer + "303e021dff1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" + + "cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303e021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021eff00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + // infinity + "3022090180021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "3021021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd090180", + // Vectors where r or s have been modified e.g. by adding or subtracting the order of the + // group and hence violate the range check for r and s required by DSA. + "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d0168dcf02f57b0caef7ddc183bee1ca94ee09c1a02ee4b0200a54dcb93", + "303c021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021cf2efc2e24cbedb2fc00c236c5b2d1a430236b59b7880007f2ba2f8d9", + "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021dff5219a6772dc82cf0610be22bdb5b1e370e969830cc9a7ec017879dca", + "303d021c1e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9cd" + + "021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303e021d00d9384b2032d060e59848f87cb4535936bc25fa77959e96d7f88e33" + + "2a021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303e021d00d9384b2032d060e59848f87cb4535936bc25fa77959e96d7f88e33" + + "2a021d0168dcf02f57b0caef7ddc183bee1ca94ee09c1a02ee4b0200a54dcb93", + "303d021d00d9384b2032d060e59848f87cb4535936bc25fa77959e96d7f88e33" + + "2a021cf2efc2e24cbedb2fc00c236c5b2d1a430236b59b7880007f2ba2f8d9", + "303e021d00d9384b2032d060e59848f87cb4535936bc25fa77959e96d7f88e33" + + "2a021dff5219a6772dc82cf0610be22bdb5b1e370e969830cc9a7ec017879dca", + "303e021d00d9384b2032d060e59848f87cb4535936bc25fa77959e96d7f88e33" + + "2a021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303e021dff634b1dd327de7125da7903ad2163ca2addc096101fd395567ee360" + + "70021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303e021dff634b1dd327de7125da7903ad2163ca2addc096101fd395567ee360" + + "70021d0168dcf02f57b0caef7ddc183bee1ca94ee09c1a02ee4b0200a54dcb93", + "303d021dff634b1dd327de7125da7903ad2163ca2addc096101fd395567ee360" + + "70021cf2efc2e24cbedb2fc00c236c5b2d1a430236b59b7880007f2ba2f8d9", + "303e021dff634b1dd327de7125da7903ad2163ca2addc096101fd395567ee360" + + "70021dff5219a6772dc82cf0610be22bdb5b1e370e969830cc9a7ec017879dca", + "303e021dff634b1dd327de7125da7903ad2163ca2addc096101fd395567ee360" + + "70021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d021ce1be4b8652a896fa469f01eb15246e4f330cb7bc2546e9e8c4473633" + + "021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303d021ce1be4b8652a896fa469f01eb15246e4f330cb7bc2546e9e8c4473633" + + "021d0168dcf02f57b0caef7ddc183bee1ca94ee09c1a02ee4b0200a54dcb93", + "303c021ce1be4b8652a896fa469f01eb15246e4f330cb7bc2546e9e8c4473633" + + "021cf2efc2e24cbedb2fc00c236c5b2d1a430236b59b7880007f2ba2f8d9", + "303d021ce1be4b8652a896fa469f01eb15246e4f330cb7bc2546e9e8c4473633" + + "021dff5219a6772dc82cf0610be22bdb5b1e370e969830cc9a7ec017879dca", + "303d021ce1be4b8652a896fa469f01eb15246e4f330cb7bc2546e9e8c4473633" + + "021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303e021d011e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" + + "cd021d00ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", + "303e021d011e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" + + "cd021d0168dcf02f57b0caef7ddc183bee1ca94ee09c1a02ee4b0200a54dcb93", + "303d021d011e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" + + "cd021cf2efc2e24cbedb2fc00c236c5b2d1a430236b59b7880007f2ba2f8d9", + "303e021d011e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" + + "cd021dff5219a6772dc82cf0610be22bdb5b1e370e969830cc9a7ec017879dca", + "303e021d011e41b479ad576905b960fe14eadb91b0ccf34843dab916173bb8c9" + + "cd021d01ade65988d237d30f9ef41dd424a4e1c8f16967cf3365813fe8786236", // Signatures with special case values for r and s. E.g. r=1, s=0 are values that can lead to // forgeries if the DSA implementation does not check boundaries and computes s^(-1) == 0. "3022020100021dff450969597a870820211805983688387a10cd4dcc451a7f3f432a96a3", @@ -346,9 +678,10 @@ public class DsaTest extends TestCase { String message, String algorithm, String signatureType, - boolean isValid) + boolean isValidDER, + boolean isValidBER) throws Exception { - byte[] messageBytes = "Hello".getBytes("UTF-8"); + byte[] messageBytes = message.getBytes("UTF-8"); Signature verifier = Signature.getInstance(algorithm); KeyFactory kf = KeyFactory.getInstance("DSA"); PublicKey pub = kf.generatePublic(key); @@ -371,10 +704,10 @@ public class DsaTest extends TestCase { errors++; continue; } - if (isValid && !verified) { + if (isValidDER && !verified) { System.out.println(signatureType + " was not verified:" + signature); errors++; - } else if (!isValid && verified) { + } else if (!isValidBER && verified) { System.out.println(signatureType + " was verified:" + signature); errors++; } @@ -384,12 +717,19 @@ public class DsaTest extends TestCase { public void testValidSignatures() throws Exception { testVectors( - VALID_SIGNATURES, publicKey1, "Hello", "SHA224WithDSA", "Valid DSA signature", true); + VALID_SIGNATURES, publicKey1, "Hello", "SHA224WithDSA", "Valid DSA signature", true, true); + } + + public void testModifiedSignatures() throws Exception { + testVectors( + MODIFIED_SIGNATURES, publicKey1, "Hello", "SHA224WithDSA", "Modified DSA signature", + false, true); } public void testInvalidSignatures() throws Exception { testVectors( - INVALID_SIGNATURES, publicKey1, "Hello", "SHA224WithDSA", "Invalid DSA signature", false); + INVALID_SIGNATURES, publicKey1, "Hello", "SHA224WithDSA", "Invalid DSA signature", + false, false); } // Extract the integer r from a DSA signature. @@ -493,6 +833,55 @@ public class DsaTest extends TestCase { System.out.println("s:" + extractS(signature).toString()); } + public void testKeyGeneration(int keysize) throws Exception { + KeyPairGenerator generator = KeyPairGenerator.getInstance("DSA"); + generator.initialize(keysize); + KeyPair keyPair = generator.generateKeyPair(); + DSAPrivateKey priv = (DSAPrivateKey) keyPair.getPrivate(); + DSAParams params = priv.getParams(); + assertEquals(keysize, params.getP().bitLength()); + // The NIST standard does not fully specify the size of q that + // must be used for a given key size. Hence there are differences. + // For example if keysize = 2048, then OpenSSL uses 256 bit q's by default, + // but the SUN provider uses 224 bits. Both are acceptable sizes. + // The tests below simply asserts that the size of q does not decrease the + // overall security of the DSA. + int qsize = params.getQ().bitLength(); + switch (keysize) { + case 1024: + assertTrue("Invalid qsize for 1024 bit key:" + qsize, qsize >= 160); + break; + case 2048: + assertTrue("Invalid qsize for 2048 bit key:" + qsize, qsize >= 224); + break; + case 3072: + assertTrue("Invalid qsize for 3072 bit key:" + qsize, qsize >= 256); + break; + default: + fail("Invalid key size:" + keysize); + } + // Check the length of the private key. + // For example GPG4Browsers or the KJUR library derived from it use + // q.bitCount() instead of q.bitLength() to determine the size of the private key + // and hence would generate keys that are much too small. + assertTrue(priv.getX().bitLength() >= qsize - 32); + } + + /** + * Tests the key generation for DSA. + * + * <p>Problems found: + * <ul> + * <li> CVE-2016-1000343 BouncyCastle before v.1.56 always generated DSA keys with + * a 160-bit q. + * </ul> + */ + @SlowTest(providers = {ProviderType.BOUNCY_CASTLE, ProviderType.SPONGY_CASTLE}) + public void testKeyGenerationAll() throws Exception { + testKeyGeneration(1024); + testKeyGeneration(2048); + } + /** * Checks whether the one time key k in DSA is biased. For example the SUN provider fell for this * test until April 2016. @@ -611,6 +1000,129 @@ public class DsaTest extends TestCase { } /** + * This test checks for potential of a timing attack. The test generates a number of signatures, + * selects a fraction of them with a small timing and then compares the values k for the selected + * signatures with a normal distribution. The test fails if these ks are much smaller than + * expected. An implementation flaw that can lead to a test failure is to compute the signature + * with a modular exponentiation with a runtime that depend on the length of the exponent. + * + * <p>A failing test simply means that the timing can be used to get information about k. Further + * analysis is necessary to determine if the bias is exploitable and how many timings are + * necessary for an attack. A passing test does not mean that the implementation is secure against + * timing attacks. The test only catches relatively big timing differences. It requires high + * confidence to fail. Noise on the test machine can prevent that a relation between timing and k + * can be detected. + * + * <p>Claims of what is exploitable: http://www.hpl.hp.com/techreports/1999/HPL-1999-90.pdf 30 + * signatures are sufficient to find the private key if the attacker knows 8 bits of each k. + * http://eprint.iacr.org/2004/277.pdf 27 signatures are sufficient if 8 bits of each k is known. + * Our own old experiments (using 1GB memory on a Pentium-4? CPU): 2^11 signatures are sufficient + * with a 3 bit leakage. 2^15 signatures are sufficient with a 2 bit leakage. 2^24 signatures are + * sufficient with a 1 bit leakage. Estimate for biased generation in the NIST standard: e.g. 2^22 + * signatures, 2^40 memory, 2^64 time + * + * <p><b>Sample output for the SUN provider:</b> <code> + * count:50000 cutoff:4629300 relative average:0.9992225872624547 sigmas:0.3010906585642381 + * count:25000 cutoff:733961 relative average:0.976146066585879 sigmas:6.532668708070148 + * count:12500 cutoff:688305 relative average:0.9070352192339134 sigmas:18.00255238454385 + * count:6251 cutoff:673971 relative average:0.7747148791368986 sigmas:30.850903417893825 + * count:3125 cutoff:667045 relative average:0.5901994097874541 sigmas:39.67877152897901 + * count:1563 cutoff:662088 relative average:0.4060286694971057 sigmas:40.67294313795137 + * count:782 cutoff:657921 relative average:0.2577955312387898 sigmas:35.94906247333319 + * count:391 cutoff:653608 relative average:0.1453438859272699 sigmas:29.271192100879457 + * count:196 cutoff:649280 relative average:0.08035497211567771 sigmas:22.300206785132406 + * count:98 cutoff:645122 relative average:0.05063589092661368 sigmas:16.27820353139225 + * count:49 cutoff:641582 relative average:0.018255560447883384 sigmas:11.903018745467488 + * count:25 cutoff:638235 relative average:0.009082660721102722 sigmas:8.581595888660086 + * count:13 cutoff:633975 relative average:0.0067892346039088326 sigmas:6.20259924188633 + * </code> + * + * <p><b>What this shows:</b> The first line uses all 50'000 signatures. The average k of these + * signatures is close to the expected value q/2. Being more selective gives us signatures with a + * more biased k. For example, the 196 signatures with the fastest timing have about a 3-bit bias. + * From this we expect that 2^19 signatures and timings are sufficient to find the private key. + * + * <p>A list of problems caught by this test: + * <ul> + * <li> CVE-2016-5548 OpenJDK8's DSA is vulnerable to timing attacks. + * <li> CVE-2016-1000341 BouncyCastle before v 1.56 is vulnernerable to timing attacks. + * </ul> + */ + @SlowTest(providers = {ProviderType.BOUNCY_CASTLE, ProviderType.OPENJDK, + ProviderType.SPONGY_CASTLE}) + public void testTiming() throws Exception { + ThreadMXBean bean = ManagementFactory.getThreadMXBean(); + if (!bean.isCurrentThreadCpuTimeSupported()) { + System.out.println("getCurrentThreadCpuTime is not supported. Skipping"); + return; + } + String hashAlgorithm = "SHA-1"; + String message = "Hello"; + byte[] messageBytes = message.getBytes("UTF-8"); + byte[] digest = MessageDigest.getInstance(hashAlgorithm).digest(messageBytes); + BigInteger h = new BigInteger(1, digest); + KeyPairGenerator generator = java.security.KeyPairGenerator.getInstance("DSA"); + generator.initialize(1024); + KeyPair keyPair = generator.generateKeyPair(); + DSAPrivateKey priv = (DSAPrivateKey) keyPair.getPrivate(); + Signature signer = Signature.getInstance("SHA1WITHDSA"); + signer.initSign(priv); + // The timings below are quite noisy. Thus we need a large number of samples. + int samples = 50000; + long[] timing = new long[samples]; + BigInteger[] k = new BigInteger[samples]; + for (int i = 0; i < samples; i++) { + long start = bean.getCurrentThreadCpuTime(); + signer.update(messageBytes); + byte[] signature = signer.sign(); + timing[i] = bean.getCurrentThreadCpuTime() - start; + k[i] = extractK(signature, h, priv, false); + } + long[] sorted = Arrays.copyOf(timing, timing.length); + Arrays.sort(sorted); + // Here we are only interested in roughly the 8 most significant bits of the ks. + // Hence, using double is sufficiently precise. + double q = priv.getParams().getQ().doubleValue(); + double expectedAverage = q / 2; + double maxSigmas = 0; + System.out.println("testTiming: SHA1WITHDSA"); + for (int idx = samples - 1; idx > 10; idx /= 2) { + long cutoff = sorted[idx]; + int count = 0; + double total = 0; + for (int i = 0; i < samples; i++) { + if (timing[i] <= cutoff) { + total += k[i].doubleValue(); + count += 1; + } + } + double expectedStdDev = q / Math.sqrt(12 * count); + double average = total / count; + // Number of standard deviations that the average is away from + // the expected value: + double sigmas = (expectedAverage - average) / expectedStdDev; + if (sigmas > maxSigmas) { + maxSigmas = sigmas; + } + System.out.println( + "count:" + + count + + " cutoff:" + + cutoff + + " relative average:" + + (average / expectedAverage) + + " sigmas:" + + sigmas); + } + // Checks if the signatures with a small timing have a biased k. + // We use 7 standard deviations, so that the probability of a false positive is smaller + // than 10^{-10}. + if (maxSigmas >= 7) { + fail("Signatures with short timing have a biased k"); + } + } + + /** * DSA does not allow encryption. This test verifies that a provider does not implement an ad hoc * scheme that attempts to turn DSA into a public key encryption scheme. */ diff --git a/java/com/google/security/wycheproof/testcases/EcdhTest.java b/java/com/google/security/wycheproof/testcases/EcdhTest.java index 4094f41..8bfe03f 100644 --- a/java/com/google/security/wycheproof/testcases/EcdhTest.java +++ b/java/com/google/security/wycheproof/testcases/EcdhTest.java @@ -508,301 +508,322 @@ public class EcdhTest extends TestCase { new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)); public static final EcPublicKeyTestVector[] EC_MODIFIED_PUBLIC_KEYS = { - // Modified keys - new EcPublicKeyTestVector( - "public point not on curve", - "3059301306072a8648ce3d020106082a8648ce3d03010703420004cdeb39edd0" - + "3e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b84" - + "29598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebaca", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), - new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), - 1, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebaca", 16)), - new EcPublicKeyTestVector( - "public point = (0,0)", - "3059301306072a8648ce3d020106082a8648ce3d030107034200040000000000" - + "0000000000000000000000000000000000000000000000000000000000000000" - + "000000000000000000000000000000000000000000000000000000", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), - new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), - 1, - new BigInteger("0"), - new BigInteger("0")), - new EcPublicKeyTestVector( - "order = 1", - "308201133081cc06072a8648ce3d02013081c0020101302c06072a8648ce3d01" - + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" - + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" - + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" - + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" - + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" - + "576b315ececbb6406837bf51f502010102010103420004cdeb39edd03e2b1a11" - + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" - + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("01", 16), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), - new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), - 1, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), - new EcPublicKeyTestVector( - "order = 26959946660873538060741835960514744168612397095220107664" + "918121663170", - "3082012f3081e806072a8648ce3d02013081dc020101302c06072a8648ce3d01" - + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" - + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" - + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" - + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" - + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" - + "576b315ececbb6406837bf51f5021d00ffffffff00000000ffffffffffffffff" - + "bce6faada7179e84f3b9cac202010103420004cdeb39edd03e2b1a11a5e134ec" - + "99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b49bbb85c" - + "3303ddb1553c3b761c2caacca71606ba9ebac8", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2", 16), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), - new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), - 1, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), - new EcPublicKeyTestVector( - "generator = (0,0)", - "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" - + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" - + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" - + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" - + "b0f63bce3c3e27d2604b04410400000000000000000000000000000000000000" - + "0000000000000000000000000000000000000000000000000000000000000000" - + "00000000000000000000000000022100ffffffff00000000ffffffffffffffff" - + "bce6faada7179e84f3b9cac2fc63255102010103420004cdeb39edd03e2b1a11" - + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" - + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("0"), - new BigInteger("0"), - 1, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), - new EcPublicKeyTestVector( - "generator not on curve", - "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" - + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" - + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" - + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" - + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" - + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" - + "576b315ececbb6406837bf51f7022100ffffffff00000000ffffffffffffffff" - + "bce6faada7179e84f3b9cac2fc63255102010103420004cdeb39edd03e2b1a11" - + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" - + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), - new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f7", 16), - 1, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), - new EcPublicKeyTestVector( - "cofactor = 2", - "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" - + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" - + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" - + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" - + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" - + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" - + "576b315ececbb6406837bf51f5022100ffffffff00000000ffffffffffffffff" - + "bce6faada7179e84f3b9cac2fc63255102010203420004cdeb39edd03e2b1a11" - + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" - + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), - new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), - 2, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), - new EcPublicKeyTestVector( - "cofactor = None", - "308201303081e906072a8648ce3d02013081dd020101302c06072a8648ce3d01" - + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" - + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" - + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" - + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" - + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" - + "576b315ececbb6406837bf51f5022100ffffffff00000000ffffffffffffffff" - + "bce6faada7179e84f3b9cac2fc63255103420004cdeb39edd03e2b1a11a5e134" - + "ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b49bbb8" - + "5c3303ddb1553c3b761c2caacca71606ba9ebac8", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), - new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), - null, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), - new EcPublicKeyTestVector( - "modified prime", - "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" - + "01022100fd091059a6893635f900e9449d63f572b2aebc4cff7b4e5e33f1b200" - + "e8bbc1453044042002f6efa55976c9cb06ff16bb629c0a8d4d5143b40084b1a1" - + "cc0e4dff17443eb704205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" - + "b0f63bce3c3e27d2604b0441040000000000000000000006597fa94b1fd90000" - + "000000000000000000000000021b8c7dd77f9a95627922eceefea73f028f1ec9" - + "5ba9b8fa95a3ad24bdf9fff414022100ffffffff00000000ffffffffffffffff" - + "bce6faada7179e84f3b9cac2fc63255102010103420004000000000000000000" - + "0006597fa94b1fd90000000000000000000000000000021b8c7dd77f9a956279" - + "22eceefea73f028f1ec95ba9b8fa95a3ad24bdf9fff414", - new BigInteger("fd091059a6893635f900e9449d63f572b2aebc4cff7b4e5e33f1b200e8bbc145", 16), - new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("06597fa94b1fd9000000000000000000000000000002", 16), - new BigInteger("1b8c7dd77f9a95627922eceefea73f028f1ec95ba9b8fa95a3ad24bdf9fff414", 16), - 1, - new BigInteger("06597fa94b1fd9000000000000000000000000000002", 16), - new BigInteger("1b8c7dd77f9a95627922eceefea73f028f1ec95ba9b8fa95a3ad24bdf9fff414", 16)), - new EcPublicKeyTestVector( - "using secp224r1", - "304e301006072a8648ce3d020106052b81040021033a0004074f56dc2ea648ef" - + "89c3b72e23bbd2da36f60243e4d2067b70604af1c2165cec2f86603d60c8a611" - + "d5b84ba3d91dfe1a480825bcc4af3bcf", - new BigInteger("ffffffffffffffffffffffffffffffff000000000000000000000001", 16), - new BigInteger("ffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d", 16), - new BigInteger("fffffffffffffffffffffffffffffffefffffffffffffffffffffffe", 16), - new BigInteger("b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4", 16), - new BigInteger("b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21", 16), - new BigInteger("bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34", 16), - 1, - new BigInteger("074f56dc2ea648ef89c3b72e23bbd2da36f60243e4d2067b70604af1", 16), - new BigInteger("c2165cec2f86603d60c8a611d5b84ba3d91dfe1a480825bcc4af3bcf", 16)), - new EcPublicKeyTestVector( - "a = 0", - "308201143081cd06072a8648ce3d02013081c1020101302c06072a8648ce3d01" - + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" - + "ffffffff30250401000420f104880c3980129c7efa19b6b0cb04e547b8d0fc0b" - + "95f4946496dd4ac4a7c440044104cdeb39edd03e2b1a11a5e134ec99d5f25f21" - + "673d403f3ecb47bd1fa676638958ea58493b8429598c0b49bbb85c3303ddb155" - + "3c3b761c2caacca71606ba9ebac8022100ffffffff00000000ffffffffffffff" - + "ffbce6faada7179e84f3b9cac2fc63255102010103420004cdeb39edd03e2b1a" - + "11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c" - + "0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), - new BigInteger("0"), - new BigInteger("f104880c3980129c7efa19b6b0cb04e547b8d0fc0b95f4946496dd4ac4a7c440", 16), - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16), - 1, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), - // Invalid keys - new EcPublicKeyTestVector( - "order = -1157920892103562487626974469494075735299969552241357603" - + "42422259061068512044369", - "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" - + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" - + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" - + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" - + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" - + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" - + "576b315ececbb6406837bf51f50221ff00000000ffffffff0000000000000000" - + "4319055258e8617b0c46353d039cdaaf02010103420004cdeb39edd03e2b1a11" - + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" - + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger( - "-115792089210356248762697446949407573529996955224135760342422259" + "061068512044369"), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), - new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), - 1, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), - new EcPublicKeyTestVector( - "order = 0", - "308201123081cb06072a8648ce3d02013081bf020101302c06072a8648ce3d01" - + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" - + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" - + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" - + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" - + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" - + "576b315ececbb6406837bf51f5020002010103420004cdeb39edd03e2b1a11a5" - + "e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b49" - + "bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("0"), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), - new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), - 1, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), - new EcPublicKeyTestVector( - "cofactor = -1", - "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" - + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" - + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" - + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" - + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" - + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" - + "576b315ececbb6406837bf51f5022100ffffffff00000000ffffffffffffffff" - + "bce6faada7179e84f3b9cac2fc6325510201ff03420004cdeb39edd03e2b1a11" - + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" - + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), - new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), - -1, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), - new EcPublicKeyTestVector( - "cofactor = 0", - "308201323081eb06072a8648ce3d02013081df020101302c06072a8648ce3d01" - + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" - + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" - + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" - + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" - + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" - + "576b315ececbb6406837bf51f5022100ffffffff00000000ffffffffffffffff" - + "bce6faada7179e84f3b9cac2fc632551020003420004cdeb39edd03e2b1a11a5" - + "e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b49" - + "bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", - new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), - new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), - new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), - new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), - new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), - new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), - 0, - new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), - new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), + // Modified keys + new EcPublicKeyTestVector( + "public point not on curve", + "3059301306072a8648ce3d020106082a8648ce3d03010703420004cdeb39edd0" + + "3e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b84" + + "29598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebaca", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), + new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), + 1, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebaca", 16)), + new EcPublicKeyTestVector( + "public point = (0,0)", + "3059301306072a8648ce3d020106082a8648ce3d030107034200040000000000" + + "0000000000000000000000000000000000000000000000000000000000000000" + + "000000000000000000000000000000000000000000000000000000", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), + new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), + 1, + new BigInteger("0"), + new BigInteger("0")), + new EcPublicKeyTestVector( + "order = 1", + "308201133081cc06072a8648ce3d02013081c0020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" + + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" + + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" + + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" + + "576b315ececbb6406837bf51f502010102010103420004cdeb39edd03e2b1a11" + + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" + + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("01", 16), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), + new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), + 1, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), + new EcPublicKeyTestVector( + "order = 26959946660873538060741835960514744168612397095220107664918121663170", + "3082012f3081e806072a8648ce3d02013081dc020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" + + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" + + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" + + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" + + "576b315ececbb6406837bf51f5021d00ffffffff00000000ffffffffffffffff" + + "bce6faada7179e84f3b9cac202010103420004cdeb39edd03e2b1a11a5e134ec" + + "99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b49bbb85c" + + "3303ddb1553c3b761c2caacca71606ba9ebac8", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2", 16), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), + new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), + 1, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), + new EcPublicKeyTestVector( + "generator = (0,0)", + "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" + + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" + + "b0f63bce3c3e27d2604b04410400000000000000000000000000000000000000" + + "0000000000000000000000000000000000000000000000000000000000000000" + + "00000000000000000000000000022100ffffffff00000000ffffffffffffffff" + + "bce6faada7179e84f3b9cac2fc63255102010103420004cdeb39edd03e2b1a11" + + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" + + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("0"), + new BigInteger("0"), + 1, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), + new EcPublicKeyTestVector( + "generator not on curve", + "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" + + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" + + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" + + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" + + "576b315ececbb6406837bf51f7022100ffffffff00000000ffffffffffffffff" + + "bce6faada7179e84f3b9cac2fc63255102010103420004cdeb39edd03e2b1a11" + + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" + + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), + new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f7", 16), + 1, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), + new EcPublicKeyTestVector( + "cofactor = 2", + "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" + + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" + + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" + + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" + + "576b315ececbb6406837bf51f5022100ffffffff00000000ffffffffffffffff" + + "bce6faada7179e84f3b9cac2fc63255102010203420004cdeb39edd03e2b1a11" + + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" + + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), + new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), + 2, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), + new EcPublicKeyTestVector( + "cofactor = None", + "308201303081e906072a8648ce3d02013081dd020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" + + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" + + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" + + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" + + "576b315ececbb6406837bf51f5022100ffffffff00000000ffffffffffffffff" + + "bce6faada7179e84f3b9cac2fc63255103420004cdeb39edd03e2b1a11a5e134" + + "ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b49bbb8" + + "5c3303ddb1553c3b761c2caacca71606ba9ebac8", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), + new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), + null, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), + new EcPublicKeyTestVector( + "modified prime", + "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" + + "01022100fd091059a6893635f900e9449d63f572b2aebc4cff7b4e5e33f1b200" + + "e8bbc1453044042002f6efa55976c9cb06ff16bb629c0a8d4d5143b40084b1a1" + + "cc0e4dff17443eb704205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" + + "b0f63bce3c3e27d2604b0441040000000000000000000006597fa94b1fd90000" + + "000000000000000000000000021b8c7dd77f9a95627922eceefea73f028f1ec9" + + "5ba9b8fa95a3ad24bdf9fff414022100ffffffff00000000ffffffffffffffff" + + "bce6faada7179e84f3b9cac2fc63255102010103420004000000000000000000" + + "0006597fa94b1fd90000000000000000000000000000021b8c7dd77f9a956279" + + "22eceefea73f028f1ec95ba9b8fa95a3ad24bdf9fff414", + new BigInteger("fd091059a6893635f900e9449d63f572b2aebc4cff7b4e5e33f1b200e8bbc145", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("06597fa94b1fd9000000000000000000000000000002", 16), + new BigInteger("1b8c7dd77f9a95627922eceefea73f028f1ec95ba9b8fa95a3ad24bdf9fff414", 16), + 1, + new BigInteger("06597fa94b1fd9000000000000000000000000000002", 16), + new BigInteger("1b8c7dd77f9a95627922eceefea73f028f1ec95ba9b8fa95a3ad24bdf9fff414", 16)), + new EcPublicKeyTestVector( + "using secp224r1", + "304e301006072a8648ce3d020106052b81040021033a0004074f56dc2ea648ef" + + "89c3b72e23bbd2da36f60243e4d2067b70604af1c2165cec2f86603d60c8a611" + + "d5b84ba3d91dfe1a480825bcc4af3bcf", + new BigInteger("ffffffffffffffffffffffffffffffff000000000000000000000001", 16), + new BigInteger("ffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d", 16), + new BigInteger("fffffffffffffffffffffffffffffffefffffffffffffffffffffffe", 16), + new BigInteger("b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4", 16), + new BigInteger("b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21", 16), + new BigInteger("bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34", 16), + 1, + new BigInteger("074f56dc2ea648ef89c3b72e23bbd2da36f60243e4d2067b70604af1", 16), + new BigInteger("c2165cec2f86603d60c8a611d5b84ba3d91dfe1a480825bcc4af3bcf", 16)), + new EcPublicKeyTestVector( + "a = 0", + "308201143081cd06072a8648ce3d02013081c1020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff30250401000420f104880c3980129c7efa19b6b0cb04e547b8d0fc0b" + + "95f4946496dd4ac4a7c440044104cdeb39edd03e2b1a11a5e134ec99d5f25f21" + + "673d403f3ecb47bd1fa676638958ea58493b8429598c0b49bbb85c3303ddb155" + + "3c3b761c2caacca71606ba9ebac8022100ffffffff00000000ffffffffffffff" + + "ffbce6faada7179e84f3b9cac2fc63255102010103420004cdeb39edd03e2b1a" + + "11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c" + + "0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), + new BigInteger("0"), + new BigInteger("f104880c3980129c7efa19b6b0cb04e547b8d0fc0b95f4946496dd4ac4a7c440", 16), + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16), + 1, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), + new EcPublicKeyTestVector( + "new curve with generator of order 3 that is also on secp256r1", + "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff3044042046dc879a5c2995d0e6f682468ea95791b7bbd0225cfdb251" + + "3fb10a737afece170420bea6c109251bfe4acf2eeda7c24c4ab70a1473335dec" + + "28b244d4d823d15935e2044104701c05255026aa4630b78fc6b769e388059ab1" + + "443cbdd1f8348bedc3be589dc34cfdab998ad27738ae382aa013986ade0f4859" + + "2a9a1ae37ca61d25ec5356f1bd022100ffffffff00000000ffffffffffffffff" + + "bce6faada7179e84f3b9cac2fc63255102010103420004701c05255026aa4630" + + "b78fc6b769e388059ab1443cbdd1f8348bedc3be589dc3b3025465752d88c851" + + "c7d55fec679521f0b7a6d665e51c8359e2da13aca90e42", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), + new BigInteger("46dc879a5c2995d0e6f682468ea95791b7bbd0225cfdb2513fb10a737afece17", 16), + new BigInteger("bea6c109251bfe4acf2eeda7c24c4ab70a1473335dec28b244d4d823d15935e2", 16), + new BigInteger("701c05255026aa4630b78fc6b769e388059ab1443cbdd1f8348bedc3be589dc3", 16), + new BigInteger("4cfdab998ad27738ae382aa013986ade0f48592a9a1ae37ca61d25ec5356f1bd", 16), + 1, + new BigInteger("701c05255026aa4630b78fc6b769e388059ab1443cbdd1f8348bedc3be589dc3", 16), + new BigInteger("b3025465752d88c851c7d55fec679521f0b7a6d665e51c8359e2da13aca90e42", 16)), + // Invalid keys + new EcPublicKeyTestVector( + "order = -1157920892103562487626974469494075735299969552241357603" + + "42422259061068512044369", + "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" + + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" + + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" + + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" + + "576b315ececbb6406837bf51f50221ff00000000ffffffff0000000000000000" + + "4319055258e8617b0c46353d039cdaaf02010103420004cdeb39edd03e2b1a11" + + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" + + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger( + "-115792089210356248762697446949407573529996955224135760342422259061068512044369"), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), + new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), + 1, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), + new EcPublicKeyTestVector( + "order = 0", + "308201133081cc06072a8648ce3d02013081c0020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" + + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" + + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" + + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" + + "576b315ececbb6406837bf51f502010002010103420004cdeb39edd03e2b1a11" + + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" + + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("0"), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), + new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), + 1, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), + new EcPublicKeyTestVector( + "cofactor = -1", + "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" + + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" + + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" + + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" + + "576b315ececbb6406837bf51f5022100ffffffff00000000ffffffffffffffff" + + "bce6faada7179e84f3b9cac2fc6325510201ff03420004cdeb39edd03e2b1a11" + + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" + + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), + new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), + -1, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), + new EcPublicKeyTestVector( + "cofactor = 0", + "308201333081ec06072a8648ce3d02013081e0020101302c06072a8648ce3d01" + + "01022100ffffffff00000001000000000000000000000000ffffffffffffffff" + + "ffffffff30440420ffffffff00000001000000000000000000000000ffffffff" + + "fffffffffffffffc04205ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53" + + "b0f63bce3c3e27d2604b0441046b17d1f2e12c4247f8bce6e563a440f277037d" + + "812deb33a0f4a13945d898c2964fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33" + + "576b315ececbb6406837bf51f5022100ffffffff00000000ffffffffffffffff" + + "bce6faada7179e84f3b9cac2fc63255102010003420004cdeb39edd03e2b1a11" + + "a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958ea58493b8429598c0b" + + "49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", + new BigInteger("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", 16), + new BigInteger("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", 16), + new BigInteger("ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", 16), + new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16), + new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16), + new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16), + 0, + new BigInteger("cdeb39edd03e2b1a11a5e134ec99d5f25f21673d403f3ecb47bd1fa676638958", 16), + new BigInteger("ea58493b8429598c0b49bbb85c3303ddb1553c3b761c2caacca71606ba9ebac8", 16)), }; /** Checks that key agreement using ECDH works. */ @@ -946,6 +967,16 @@ public class EcdhTest extends TestCase { } } + public void testModifiedPublic() throws Exception { + testModifiedPublic("ECDH"); + testModifiedPublic("ECDHC"); + } + + public void testModifiedPublicSpec() throws Exception { + testModifiedPublicSpec("ECDH"); + testModifiedPublicSpec("ECDHC"); + } + public void testDistinctCurves(String algorithm, ECPrivateKey priv, ECPublicKey pub) throws Exception { KeyAgreement kaA; @@ -1002,41 +1033,6 @@ public class EcdhTest extends TestCase { } /** - * This test tries to catch implementations that verify that the point of the public key is on the - * curve defined by the private key, but fails to verify that public key and private key use the - * same curve. - * - * <p>Bouncycastle v.1.53 fails this test. I.e. this version only checks that the shared secret is - * on the curve, but does not check whether the two curves are the same. Currently the test fails - * with a NullPointerException (possibly because of unexpected points at infinity) and it is - * unclear if the bug is exploitable. - */ - // TODO(bleichen): This can be merged with testModifiedPublic once this is fixed. - public void testDistinctCurvesSmallSubGroup() throws Exception { - KeyPairGenerator keyGen = KeyPairGenerator.getInstance("EC"); - ECGenParameterSpec ecSpec256 = new ECGenParameterSpec("secp256r1"); - keyGen.initialize(ecSpec256); - ECPrivateKey priv = (ECPrivateKey) keyGen.generateKeyPair().getPrivate(); - // Get public key for a group of order 3. I.e., (W, -W, infinity) where W is the public key - // point. Since W ,-W and infinity are points on secp256r1, implementations fail if they only - // check whether points are on the curve but fail to compare the parameters of the curve. - ECPublicKeySpec weak = EcUtil.getWeakPublicKey(EcUtil.getNistP256Params()); - KeyFactory kf = KeyFactory.getInstance("EC"); - ECPublicKey weakPub; - try { - weakPub = (ECPublicKey) kf.generatePublic(weak); - } catch (GeneralSecurityException ex) { - // The provider does not support non-standard curves or did a validity check. - // Both would be correct. - System.out.println("Skipping testDistinctCurvesSmallSubGroup: can't forge weak public key."); - return; - } - for (String algorithm : ECDH_VARIANTS) { - testDistinctCurves(algorithm, priv, weakPub); - } - } - - /** * This test modifies the order of group in the public key. A severe bug would be an * implementation that leaks information whether the private key is larger than the order given in * the public key. Also a severe bug would be to reduce the private key modulo the order given in diff --git a/java/com/google/security/wycheproof/testcases/EcdsaTest.java b/java/com/google/security/wycheproof/testcases/EcdsaTest.java index 37cfa82..92058a7 100644 --- a/java/com/google/security/wycheproof/testcases/EcdsaTest.java +++ b/java/com/google/security/wycheproof/testcases/EcdsaTest.java @@ -18,6 +18,8 @@ package com.google.security.wycheproof; import com.google.security.wycheproof.WycheproofRunner.ProviderType; import com.google.security.wycheproof.WycheproofRunner.SlowTest; +import java.lang.management.ManagementFactory; +import java.lang.management.ThreadMXBean; import java.math.BigInteger; import java.security.InvalidAlgorithmParameterException; import java.security.KeyFactory; @@ -54,10 +56,10 @@ public class EcdsaTest extends TestCase { static final String CURVE = "secp256r1"; static final BigInteger PubX = new BigInteger( - "3390396496586153202365024500890309020181905168626402195853036609" + "0984128098564"); + "33903964965861532023650245008903090201819051686264021958530366090984128098564"); static final BigInteger PubY = new BigInteger( - "1135421298983937257390683162600855221890652900790509030911087400" + "65052129055287"); + "113542129898393725739068316260085522189065290079050903091108740065052129055287"); // Valid signatures for MESSAGE static final String[] VALID_SIGNATURES = { @@ -67,82 +69,387 @@ public class EcdsaTest extends TestCase { }; /** - * Test vectors with invalid signatures. The motivation for these test vectors are previously - * broken implementations. - The implementation of DSA in gpg4browsers accepted signatures with - * r=1 and s=q as valid. Similar bugs in ECDSA are thinkable, hence the test vectors contain a - * number of tests with edge case integers. - CVE-2013-2944: strongSwan 5.0.4 accepts invalid - * ECDSA signatures when openssl is used. (Not sure if the following interpretation is correct, - * because of missing details). OpenSSLs error codes are easy to misinterpret. For many functions - * the result can be 0 (verification failed), 1 (verification succeded) or -1 (invalid format). A - * simple if (result) { ... } will be incorrect in such situations. The test vectors below contain - * incorrectly encoded signatures. - careless ASN parsing. For example SunEC throws various run - * time exceptions when the ASN encoding is broken. NOTE(bleichen): The following test vectors - * were generated with some python code. New test vectors should best be done by extending this - * code. + * The following test vectors contain a valid signature that use alternative BER encoding. + * Whether such signatures are accepted as valid or rejected depends on the implementation. + * Allowing alternative BER encodings is in many cases benign. However, there are cases where this + * kind of signature malleability was a problem. See for example + * https://en.bitcoin.it/wiki/Transaction_Malleability */ + // NOTE(bleichen): The following test vectors were generated with some python code. + // New test vectors should best be done by extending this code. Some of the signatures + // can be moved to INVALID_SIGNATURES, when b/31572415 is fixed. + static final String[] MODIFIED_SIGNATURES = { + // BER:long form encoding of length + "308145022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d" + + "491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e762" + + "85cd59f43260ecce", + "304602812100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d" + + "491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e762" + + "85cd59f43260ecce", + "3046022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f028120747291dd2f3f44af7ace68ea33431d6f94e418c106a6e762" + + "85cd59f43260ecce", + // BER:length contains leading 0 + "30820045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a" + + "3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + "30470282002100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a" + + "3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + "3047022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f02820020747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + // BER:prepending 0's to integer + "30470223000000b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a" + + "3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + "3047022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f02220000747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + // NOTE (bleichen): belongs into INVALID_SIGNATURES. We only keep these + // sigantures here because of b/31572415. + // length = 2**31 - 1 + "30847fffffff022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7" + + "db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "304902847fffffff00b7babae9332b54b8a3a05b7004579821a887a1b21465f7" + + "db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "3049022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f02847fffffff747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + }; + + /** + * Test vectors with invalid signatures. + * The motivation for these test vectors are previously broken implementations. E.g. + * <ul> + * <li> The implementation of DSA in gpg4browsers accepted signatures with r=1 and s=q as valid. + * Similar bugs in ECDSA are thinkable, hence the test vectors contain a number of tests with + * edge case integers. + * <li> CVE-2013-2944: strongSwan 5.0.4 accepts invalid ECDSA signatures when openssl is used. + * (Not sure if the following interpretation is correct, because of missing details). + * OpenSSLs error codes are easy to misinterpret. For many functions + * the result can be 0 (verification failed), 1 (verification succeded) + * or -1 (invalid format). A simple <code>if (result) { ... }</code> will be incorrect in + * such situations. The test vectors below contain incorrectly encoded signatures. + * </ul> + * <p> {@link java.security.Signature#verify(byte[])} should either return false or throw a + * SignatureException. Other behaviour such as throwing a RuntimeException might allow a denial + * of service attack: + * <ul> + * <li> CVE-2016-5546: OpenJDK8 throwed an OutOfmemoryError on some signatures. + * </ul> + * Some of the test vectors were derived from a valid signature by corrupting the DER encoding. + * If providers accepts such modified signatures for legacy purpose, then these signatures + * should be moved to MODIFIED_SIGNATURES. + */ + // NOTE(bleichen): The following test vectors were generated with some python code. New test + // vectors should best be done by extending the python code. static final String[] INVALID_SIGNATURES = { - // missing argument - "30220220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285cd59f4" + "3260ecce", - "3023022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + "1b39fd2c3f", - "", - // empty - "302402000220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285cd" + "59f43260ecce", - "3025022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + "1b39fd2c3f0200", - "3000", - // integer overflows + // wrong length + "3046022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3044022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045022200b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045022000b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0221747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f021f747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + // uint32 overflow in length + "30850100000045022100b7babae9332b54b8a3a05b7004579821a887a1b21465" + + "f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c1" + + "06a6e76285cd59f43260ecce", "304a0285010000002100b7babae9332b54b8a3a05b7004579821a887a1b21465" + "f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c1" + "06a6e76285cd59f43260ecce", - "304e028901000000000000002100b7babae9332b54b8a3a05b7004579821a887" - + "a1b21465f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f" - + "94e418c106a6e76285cd59f43260ecce", "304a022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + "1b39fd2c3f02850100000020747291dd2f3f44af7ace68ea33431d6f94e418c1" + "06a6e76285cd59f43260ecce", - "304e022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" - + "1b39fd2c3f0289010000000000000020747291dd2f3f44af7ace68ea33431d6f" - + "94e418c106a6e76285cd59f43260ecce", - "30850100000045022100b7babae9332b54b8a3a05b7004579821a887a1b21465" - + "f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c1" - + "06a6e76285cd59f43260ecce", + // uint64 overflow in length "3089010000000000000045022100b7babae9332b54b8a3a05b7004579821a887" + "a1b21465f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f" + "94e418c106a6e76285cd59f43260ecce", + "304e028901000000000000002100b7babae9332b54b8a3a05b7004579821a887" + + "a1b21465f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f" + + "94e418c106a6e76285cd59f43260ecce", + "304e022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0289010000000000000020747291dd2f3f44af7ace68ea33431d6f" + + "94e418c106a6e76285cd59f43260ecce", + // length = 2**32 - 1 + "3084ffffffff022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7" + + "db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "30490284ffffffff00b7babae9332b54b8a3a05b7004579821a887a1b21465f7" + + "db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "3049022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0284ffffffff747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + // length = 2**64 - 1 + "3088ffffffffffffffff022100b7babae9332b54b8a3a05b7004579821a887a1" + + "b21465f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94" + + "e418c106a6e76285cd59f43260ecce", + "304d0288ffffffffffffffff00b7babae9332b54b8a3a05b7004579821a887a1" + + "b21465f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94" + + "e418c106a6e76285cd59f43260ecce", + "304d022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0288ffffffffffffffff747291dd2f3f44af7ace68ea33431d6f94" + + "e418c106a6e76285cd59f43260ecce", + // removing sequence + "", + // appending 0's to sequence + "3047022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce0000", + // prepending 0's to sequence + "30470000022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a" + + "3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + // appending unused 0's + "3045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce0000", + "3047022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f00000220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + // appending null value + "3047022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce0500", + "3047022300b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f05000220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + "3047022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0222747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce0500", + // including garbage + "304949803045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7" + + "db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "304925003045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7" + + "db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "30473045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a" + + "3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce0004deadbeef", + "304922254980022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7" + + "db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "304922252500022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7" + + "db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "304d2223022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a" + + "3d491b39fd2c3f0004deadbeef0220747291dd2f3f44af7ace68ea33431d6f94" + + "e418c106a6e76285cd59f43260ecce", + "3049022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f222449800220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "3049022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f222425000220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "304d022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f22220220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce0004deadbeef", + // including undefined tags + "304daa00bb00cd003045022100b7babae9332b54b8a3a05b7004579821a887a1" + + "b21465f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94" + + "e418c106a6e76285cd59f43260ecce", + "304baa02aabb3045022100b7babae9332b54b8a3a05b7004579821a887a1b214" + + "65f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418" + + "c106a6e76285cd59f43260ecce", + "304d2229aa00bb00cd00022100b7babae9332b54b8a3a05b7004579821a887a1" + + "b21465f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94" + + "e418c106a6e76285cd59f43260ecce", + "304b2227aa02aabb022100b7babae9332b54b8a3a05b7004579821a887a1b214" + + "65f7db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418" + + "c106a6e76285cd59f43260ecce", + "304d022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f2228aa00bb00cd000220747291dd2f3f44af7ace68ea33431d6f94" + + "e418c106a6e76285cd59f43260ecce", + "304b022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f2226aa02aabb0220747291dd2f3f44af7ace68ea33431d6f94e418" + + "c106a6e76285cd59f43260ecce", + // changing tag value + "2e45022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3245022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "ff45022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045002100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045042100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045ff2100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0020747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0420747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3fff20747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + // dropping value of sequence + "3000", + // using composition + "304930010230442100b7babae9332b54b8a3a05b7004579821a887a1b21465f7" + + "db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "304922250201000220b7babae9332b54b8a3a05b7004579821a887a1b21465f7" + + "db8a3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + "3049022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f2224020174021f7291dd2f3f44af7ace68ea33431d6f94e418c106" + + "a6e76285cd59f43260ecce", + // truncate sequence + "3044022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ec", + "30442100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d491b" + + "39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285cd" + + "59f43260ecce", + // prepend empty sequence + "30473000022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a" + + "3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + // append empty sequence + "3047022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce3000", + // sequence of sequence + "30473045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a" + + "3d491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + // truncated sequence + "3023022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d491b39fd2c3f", + // repeat element in sequence + "3067022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + // removing integer + "30220220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285cd59f43260ecce", + // appending 0's to integer + "3047022300b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f00000220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e7" + + "6285cd59f43260ecce", + "3047022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0222747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce0000", + // dropping value of integer + "302402000220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285cd59f43260ecce", + "3025022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d491b39fd2c3f0200", + // modify first byte of integer + "3045022101b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220757291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + // modify last byte of integer + "3045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3e0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260eccf", + // truncate integer + "3044022000b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285cd" + + "59f43260ecce", + "30440220b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d491b" + + "39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285cd" + + "59f43260ecce", + "3044022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f021f747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ec", + "3044022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f021f7291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285cd" + + "59f43260ecce", + // leading ff in integer + "30460222ff00b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d" + + "491b39fd2c3f0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e762" + + "85cd59f43260ecce", + "3046022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f0221ff747291dd2f3f44af7ace68ea33431d6f94e418c106a6e762" + + "85cd59f43260ecce", // infinity - "30250901800220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + "cd59f43260ecce", - "3026022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + "1b39fd2c3f090180", - // Signatures with special case values for r and s (such as 0 and 1). - // Such values often uncover implementation errors. - "300402000200", - "30050200020101", - "300502000201ff", - "30250200022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3" + "b9cac2fc632551", - "30250200022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3" + "b9cac2fc632550", - "30250200022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3" + "b9cac2fc632552", - "30250200022100ffffffff00000001000000000000000000000000ffffffffff" + "ffffffffffffff", - "30250200022100ffffffff000000010000000000000000000000010000000000" + "00000000000000", - "30070200090380fe01", - "30050201010200", + "30250901800220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285cd59f43260ecce", + "3026022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d491b39fd2c3f090180", + // Vectors where r or s have been modified e.g. by adding or subtracting the order of the + // group or field and hence violate the range check for r and s required by ECDSA. + "30450221ff48454516ccd4ab475c5fa48ffba867de57785e4deb9a082475c2b6" + + "e4c602d3c10220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045022101b7babae8332b54b9a3a05b7004579821656e9c5fbb7d96607df713" + + "de366051900220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3044022048454515ccd4ab485c5fa48ffba867de145f58fb92b1a6a9697c81a7" + + "c265f9120220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285cd" + + "59f43260ecce", + "3045022101b7babae8332b54b9a3a05b7004579821a887a1b31465f7db8a3d49" + + "1b39fd2c3e0220747291dd2f3f44af7ace68ea33431d6f94e418c106a6e76285" + + "cd59f43260ecce", + "3045022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f02208b8d6e22d0c0bb5085319715ccbce2906b1be73ef959189d7a" + + "32a60bcd9f1332", + "3046022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f022101747291dc2f3f44b07ace68ea33431d6f51cb136eadbe85e7" + + "798724b72ec4121f", + "3046022100b7babae9332b54b8a3a05b7004579821a887a1b21465f7db8a3d49" + + "1b39fd2c3f022101747291dc2f3f44b07ace68ea33431d6f94e418c206a6e762" + + "85cd59f43260eccd", + // Signatures with special case values for r and s (such as 0 and 1). Such values often + // uncover implementation errors. + "3006020100020100", + "3006020100020101", + "30060201000201ff", + "3026020100022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", + "3026020100022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632550", + "3026020100022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632552", + "3026020100022100ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", + "3026020100022100ffffffff00000001000000000000000000000001000000000000000000000000", + "3008020100090380fe01", + "3006020101020100", "3006020101020101", "30060201010201ff", - "3026020101022100ffffffff00000000ffffffffffffffffbce6faada7179e84" + "f3b9cac2fc632551", - "3026020101022100ffffffff00000000ffffffffffffffffbce6faada7179e84" + "f3b9cac2fc632550", - "3026020101022100ffffffff00000000ffffffffffffffffbce6faada7179e84" + "f3b9cac2fc632552", - "3026020101022100ffffffff00000001000000000000000000000000ffffffff" + "ffffffffffffffff", - "3026020101022100ffffffff0000000100000000000000000000000100000000" + "0000000000000000", + "3026020101022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", + "3026020101022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632550", + "3026020101022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632552", + "3026020101022100ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", + "3026020101022100ffffffff00000001000000000000000000000001000000000000000000000000", "3008020101090380fe01", - "30050201ff0200", + "30060201ff020100", "30060201ff020101", "30060201ff0201ff", - "30260201ff022100ffffffff00000000ffffffffffffffffbce6faada7179e84" + "f3b9cac2fc632551", - "30260201ff022100ffffffff00000000ffffffffffffffffbce6faada7179e84" + "f3b9cac2fc632550", - "30260201ff022100ffffffff00000000ffffffffffffffffbce6faada7179e84" + "f3b9cac2fc632552", - "30260201ff022100ffffffff00000001000000000000000000000000ffffffff" + "ffffffffffffffff", - "30260201ff022100ffffffff0000000100000000000000000000000100000000" + "0000000000000000", + "30260201ff022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", + "30260201ff022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632550", + "30260201ff022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632552", + "30260201ff022100ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", + "30260201ff022100ffffffff00000001000000000000000000000001000000000000000000000000", "30080201ff090380fe01", - "3025022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc6325510200", - "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632551020101", - "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc6325510201ff", + "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551020100", + "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551020101", + "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc6325510201ff", "3046022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632551022100ffffffff00000000ffffffffffffffffbce6faada7179e84" + "f3b9cac2fc632551", @@ -158,10 +465,11 @@ public class EcdsaTest extends TestCase { "3046022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632551022100ffffffff0000000100000000000000000000000100000000" + "0000000000000000", - "3028022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632551090380fe01", - "3025022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc6325500200", - "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632550020101", - "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc6325500201ff", + "3028022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + + "c2fc632551090380fe01", + "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632550020100", + "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632550020101", + "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc6325500201ff", "3046022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632550022100ffffffff00000000ffffffffffffffffbce6faada7179e84" + "f3b9cac2fc632551", @@ -177,10 +485,11 @@ public class EcdsaTest extends TestCase { "3046022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632550022100ffffffff0000000100000000000000000000000100000000" + "0000000000000000", - "3028022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632550090380fe01", - "3025022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc6325520200", - "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632552020101", - "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc6325520201ff", + "3028022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + + "c2fc632550090380fe01", + "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632552020100", + "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632552020101", + "3026022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc6325520201ff", "3046022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632552022100ffffffff00000000ffffffffffffffffbce6faada7179e84" + "f3b9cac2fc632551", @@ -196,10 +505,11 @@ public class EcdsaTest extends TestCase { "3046022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632552022100ffffffff0000000100000000000000000000000100000000" + "0000000000000000", - "3028022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + "c2fc632552090380fe01", - "3025022100ffffffff00000001000000000000000000000000ffffffffffffff" + "ffffffffff0200", - "3026022100ffffffff00000001000000000000000000000000ffffffffffffff" + "ffffffffff020101", - "3026022100ffffffff00000001000000000000000000000000ffffffffffffff" + "ffffffffff0201ff", + "3028022100ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9ca" + + "c2fc632552090380fe01", + "3026022100ffffffff00000001000000000000000000000000ffffffffffffffffffffffff020100", + "3026022100ffffffff00000001000000000000000000000000ffffffffffffffffffffffff020101", + "3026022100ffffffff00000001000000000000000000000000ffffffffffffffffffffffff0201ff", "3046022100ffffffff00000001000000000000000000000000ffffffffffffff" + "ffffffffff022100ffffffff00000000ffffffffffffffffbce6faada7179e84" + "f3b9cac2fc632551", @@ -215,10 +525,11 @@ public class EcdsaTest extends TestCase { "3046022100ffffffff00000001000000000000000000000000ffffffffffffff" + "ffffffffff022100ffffffff0000000100000000000000000000000100000000" + "0000000000000000", - "3028022100ffffffff00000001000000000000000000000000ffffffffffffff" + "ffffffffff090380fe01", - "3025022100ffffffff0000000100000000000000000000000100000000000000" + "00000000000200", - "3026022100ffffffff0000000100000000000000000000000100000000000000" + "0000000000020101", - "3026022100ffffffff0000000100000000000000000000000100000000000000" + "00000000000201ff", + "3028022100ffffffff00000001000000000000000000000000ffffffffffffff" + + "ffffffffff090380fe01", + "3026022100ffffffff00000001000000000000000000000001000000000000000000000000020100", + "3026022100ffffffff00000001000000000000000000000001000000000000000000000000020101", + "3026022100ffffffff000000010000000000000000000000010000000000000000000000000201ff", "3046022100ffffffff0000000100000000000000000000000100000000000000" + "0000000000022100ffffffff00000000ffffffffffffffffbce6faada7179e84" + "f3b9cac2fc632551", @@ -234,7 +545,8 @@ public class EcdsaTest extends TestCase { "3046022100ffffffff0000000100000000000000000000000100000000000000" + "0000000000022100ffffffff0000000100000000000000000000000100000000" + "0000000000000000", - "3028022100ffffffff0000000100000000000000000000000100000000000000" + "0000000000090380fe01", + "3028022100ffffffff0000000100000000000000000000000100000000000000" + + "0000000000090380fe01", }; /** @@ -295,7 +607,8 @@ public class EcdsaTest extends TestCase { String message, String algorithm, String signatureType, - boolean isValid) + boolean isValidDER, + boolean isValidBER) throws Exception { byte[] messageBytes = message.getBytes("UTF-8"); Signature verifier = Signature.getInstance(algorithm); @@ -314,11 +627,11 @@ public class EcdsaTest extends TestCase { // We don't flag these cases and simply consider the signature as invalid. verified = false; } - // - if (isValid && !verified) { + if (!verified && isValidDER) { System.out.println(signatureType + " was not verified:" + signature); errors++; - } else if (!isValid && verified) { + } + if (verified && !isValidBER) { System.out.println(signatureType + " was verified:" + signature); errors++; } @@ -328,7 +641,19 @@ public class EcdsaTest extends TestCase { public void testValidSignatures() throws Exception { testVectors( - VALID_SIGNATURES, publicKey1(), "Hello", "SHA256WithECDSA", "Valid ECDSA signature", true); + VALID_SIGNATURES, publicKey1(), "Hello", "SHA256WithECDSA", "Valid ECDSA signature", + true, true); + } + + public void testModifiedSignatures() throws Exception { + testVectors( + MODIFIED_SIGNATURES, + publicKey1(), + "Hello", + "SHA256WithECDSA", + "Modified ECDSA signature", + false, + true); } public void testInvalidSignatures() throws Exception { @@ -338,6 +663,7 @@ public class EcdsaTest extends TestCase { "Hello", "SHA256WithECDSA", "Invalid ECDSA signature", + false, false); } @@ -459,4 +785,118 @@ public class EcdsaTest extends TestCase { testBias("SHA512WithECDSA", "secp521r1", EcUtil.getNistP521Params()); testBias("SHA256WithECDSA", "brainpoolP256r1", EcUtil.getBrainpoolP256r1Params()); } + + /** + * Tests for a potential timing attack. This test checks if there is a correlation between the + * timing of signature generation and the size of the one-time key k. This is for example the case + * if a double and add method is used for the point multiplication. The test fails if such a + * correlation can be shown with high confidence. Further analysis will be necessary to determine + * how easy it is to exploit the bias in a timing attack. + */ + // TODO(bleichen): Determine if there are exploitable providers. + // + // SunEC currently fails this test. Since ECDSA typically is used with EC groups whose order + // is 224 bits or larger, it is unclear whether the same attacks that apply to DSA are practical. + // + // The ECDSA implementation in BouncyCastle leaks information about k through timing too. + // The test has not been optimized to detect this bias. It would require about 5'000'000 samples, + // which is too much for a simple unit test. + // + // BouncyCastle uses FixedPointCombMultiplier for ECDSA. This is a method using + // precomputation. The implementation is not constant time, since the precomputation table + // contains the point at infinity and adding this point is faster than ordinary point additions. + // The timing leak only has a small correlation to the size of k and at the moment it is is very + // unclear if the can be exploited. (Randomizing the precomputation table by adding the same + // random point to each element in the table and precomputing the necessary offset to undo the + // precomputation seems much easier than analyzing this.) + public void testTiming(String algorithm, String curve, ECParameterSpec ecParams) + throws Exception { + ThreadMXBean bean = ManagementFactory.getThreadMXBean(); + if (!bean.isCurrentThreadCpuTimeSupported()) { + System.out.println("getCurrentThreadCpuTime is not supported. Skipping"); + return; + } + KeyPairGenerator keyGen = KeyPairGenerator.getInstance("EC"); + try { + keyGen.initialize(ecParams); + } catch (InvalidAlgorithmParameterException ex) { + System.out.println("This provider does not support curve:" + curve); + return; + } + KeyPair keyPair = keyGen.generateKeyPair(); + ECPrivateKey priv = (ECPrivateKey) keyPair.getPrivate(); + + String message = "Hello"; + String hashAlgorithm = getHashAlgorithm(algorithm); + byte[] messageBytes = message.getBytes("UTF-8"); + byte[] digest = MessageDigest.getInstance(hashAlgorithm).digest(messageBytes); + BigInteger h = new BigInteger(1, digest); + Signature signer = Signature.getInstance(algorithm); + signer.initSign(priv); + // The number of samples used for the test. This number is a bit low. + // I.e. it just barely detects that SunEC leaks information about the size of k. + int samples = 50000; + long[] timing = new long[samples]; + BigInteger[] k = new BigInteger[samples]; + for (int i = 0; i < samples; i++) { + long start = bean.getCurrentThreadCpuTime(); + signer.update(messageBytes); + byte[] signature = signer.sign(); + timing[i] = bean.getCurrentThreadCpuTime() - start; + k[i] = extractK(signature, h, priv); + } + long[] sorted = Arrays.copyOf(timing, timing.length); + Arrays.sort(sorted); + double n = priv.getParams().getOrder().doubleValue(); + double expectedAverage = n / 2; + double maxSigma = 0; + System.out.println("testTiming algorithm:" + algorithm); + for (int idx = samples - 1; idx > 10; idx /= 2) { + long cutoff = sorted[idx]; + int count = 0; + BigInteger total = BigInteger.ZERO; + for (int i = 0; i < samples; i++) { + if (timing[i] <= cutoff) { + total = total.add(k[i]); + count += 1; + } + } + double expectedStdDev = n / Math.sqrt(12 * count); + double average = total.doubleValue() / count; + // Number of standard deviations that the average is away from + // the expected value: + double sigmas = (expectedAverage - average) / expectedStdDev; + if (sigmas > maxSigma) { + maxSigma = sigmas; + } + System.out.println( + "count:" + + count + + " cutoff:" + + cutoff + + " relative average:" + + (average / expectedAverage) + + " sigmas:" + + sigmas); + } + // Checks if the signatures with a small timing have a biased k. + // We use 7 standard deviations, so that the probability of a false positive is smaller + // than 10^{-10}. + if (maxSigma >= 7) { + fail("Signatures with short timing have a biased k"); + } + } + + @SlowTest(providers = {ProviderType.BOUNCY_CASTLE, ProviderType.CONSCRYPT, ProviderType.OPENJDK, + ProviderType.SPONGY_CASTLE}) + public void testTimingAll() throws Exception { + testTiming("SHA256WithECDSA", "secp256r1", EcUtil.getNistP256Params()); + // TODO(bleichen): crypto libraries sometimes use optimized code for curves that are frequently + // used. Hence it would make sense to test distinct curves. But at the moment testing many + // curves is not practical since one test alone is already quite time consuming. + // testTiming("SHA224WithECDSA", "secp224r1", EcUtil.getNistP224Params()); + // testTiming("SHA384WithECDSA", "secp384r1", EcUtil.getNistP384Params()); + // testTiming("SHA512WithECDSA", "secp521r1", EcUtil.getNistP521Params()); + // testTiming("SHA256WithECDSA", "brainpoolP256r1", EcUtil.getBrainpoolP256r1Params()); + } } diff --git a/java/com/google/security/wycheproof/testcases/EciesTest.java b/java/com/google/security/wycheproof/testcases/EciesTest.java index 534a224..791d6ea 100644 --- a/java/com/google/security/wycheproof/testcases/EciesTest.java +++ b/java/com/google/security/wycheproof/testcases/EciesTest.java @@ -142,31 +142,16 @@ public class EciesTest extends TestCase { } /** - * Check the length of the ciphertext. TODO(bleichen): This is more an explanation what is going - * on than a test. Maybe remove this later. + * Tries to decrypt ciphertexts where the symmetric part has been randomized. + * If this randomization leads to distinguishable exceptions then this may indicate that the + * implementation is vulnerable to a padding attack. + * + * Problems detected: + * <ul> + * <li> CVE-2016-1000345 BouncyCastle before v.1.56 is vulnerable to a padding oracle attack. + * </ul> */ @SuppressWarnings("InsecureCipherMode") - public void testCiphertextLength() throws Exception { - String algorithm = "ECIESwithAES-CBC"; - final int messageLength = 40; - final int coordinateSize = 32; - byte[] message = new byte[messageLength]; - ECGenParameterSpec ecSpec = new ECGenParameterSpec("secp256r1"); - KeyPairGenerator kf = KeyPairGenerator.getInstance("EC"); - kf.initialize(ecSpec); - KeyPair keyPair = kf.generateKeyPair(); - PublicKey pub = keyPair.getPublic(); - Cipher ecies = Cipher.getInstance(algorithm); - ecies.init(Cipher.ENCRYPT_MODE, pub); - byte[] ciphertext = ecies.doFinal(message); - assertEquals( - expectedCiphertextLength(algorithm, coordinateSize, messageLength), ciphertext.length); - } - - // Tries to decrypt ciphertexts where the symmetric part has been - // randomized. Distinguishable exceptions mean that a padding attack - // may be possible. - @SuppressWarnings("InsecureCipherMode") public void testExceptions(String algorithm) throws Exception { Cipher ecies; try { @@ -317,8 +302,7 @@ public class EciesTest extends TestCase { * * <p>This test tries to verify this. */ - /* TODO(bleichen): There's no point to run this test as long as not even the previous basic - test fails. + /* TODO(bleichen): There's no point to run this test as long as the previous basic test fails. public void testByteBufferAlias() throws Exception { byte[] message = "Hello".getBytes("UTF-8"); String algorithm = "ECIESWithAES-CBC"; diff --git a/java/com/google/security/wycheproof/testcases/RsaKeyTest.java b/java/com/google/security/wycheproof/testcases/RsaKeyTest.java index 26480b6..b761dae 100644 --- a/java/com/google/security/wycheproof/testcases/RsaKeyTest.java +++ b/java/com/google/security/wycheproof/testcases/RsaKeyTest.java @@ -23,6 +23,7 @@ import java.security.KeyPairGenerator; import java.security.interfaces.RSAPrivateCrtKey; import java.security.interfaces.RSAPrivateKey; import java.security.interfaces.RSAPublicKey; +import java.security.spec.InvalidKeySpecException; import java.security.spec.X509EncodedKeySpec; import junit.framework.TestCase; @@ -53,6 +54,1344 @@ public class RsaKeyTest extends TestCase { + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + "0001"; + /** + * Encodings of the public key from ENCODED_PUBLIC_KEY with modifications. + * This list so far has just a simple purpose: it is used to check whether parsing the key + * leads to some unexpected exceptions. I.e. it should not be possible to crash an + * application with an modified public key. + */ + public static final String[] MODIFIED_PUBLIC_KEY = { + // length contains leading 0 + "3082009f300d06092a864886f70d010101050003818d0030818902818100ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "010001", + "3081a13082000d06092a864886f70d010101050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a1300f068200092a864886f70d010101050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a1300f06092a864886f70d0101010582000003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a0300d06092a864886f70d01010105000382008d0030818902818100ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "010001", + "30819f300d06092a864886f70d010101050003818d3082008902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d06092a864886f70d010101050003818d30818a0282008100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "3081a0300d06092a864886f70d010101050003818e30818b02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02820003" + + "010001", + // wrong length + "30a0300d06092a864886f70d010101050003818d0030818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "309e300d06092a864886f70d010101050003818d0030818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819f300e06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300c06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d060a2a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d06082a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d06092a864886f70d010101050103818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819e300d06092a864886f70d0101010500038e0030818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819e300d06092a864886f70d0101010500038c0030818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819d300d06092a864886f70d010101050003818b308a02818100ab9014dc47" + + "d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d05" + + "02c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8823236" + + "ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295db" + + "c3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203010001", + "30819d300d06092a864886f70d010101050003818b308802818100ab9014dc47" + + "d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d05" + + "02c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8823236" + + "ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295db" + + "c3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203010001", + "30819d300d06092a864886f70d010101050003818b308188028200ab9014dc47" + + "d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d05" + + "02c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8823236" + + "ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295db" + + "c3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203010001", + "30819d300d06092a864886f70d010101050003818b308188028000ab9014dc47" + + "d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d05" + + "02c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8823236" + + "ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295db" + + "c3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203010001", + "30819e300d06092a864886f70d010101050003818c30818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02040100" + + "01", + "30819e300d06092a864886f70d010101050003818c30818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02020100" + + "01", + // uint32 overflow in length + "3085010000009f300d06092a864886f70d010101050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a43085010000000d06092a864886f70d010101050003818d003081890281" + + "8100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4" + + "edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb" + + "5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e" + + "6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351" + + "a23f0203010001", + "3081a43012068501000000092a864886f70d010101050003818d003081890281" + + "8100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4" + + "edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb" + + "5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e" + + "6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351" + + "a23f0203010001", + "3081a4301206092a864886f70d0101010585010000000003818d003081890281" + + "8100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4" + + "edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb" + + "5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e" + + "6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351" + + "a23f0203010001", + "3081a3300d06092a864886f70d01010105000385010000008d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a2300d06092a864886f70d01010105000381903085010000008902818100" + + "ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9" + + "8590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26" + + "c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6feb" + + "e1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f" + + "0203010001", + "3081a2300d06092a864886f70d010101050003819030818d0285010000008100" + + "ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9" + + "8590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26" + + "c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6feb" + + "e1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f" + + "0203010001", + "3081a3300d06092a864886f70d010101050003819130818e02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02850100" + + "000003010001", + // uint64 overflow in length + "308901000000000000009f300d06092a864886f70d010101050003818d003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a8308901000000000000000d06092a864886f70d010101050003818d0030" + + "818902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c5410" + + "0cb6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4" + + "d0f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984" + + "b562517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315ac" + + "f9a0b351a23f0203010001", + "3081a8301606890100000000000000092a864886f70d010101050003818d0030" + + "818902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c5410" + + "0cb6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4" + + "d0f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984" + + "b562517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315ac" + + "f9a0b351a23f0203010001", + "3081a8301606092a864886f70d010101058901000000000000000003818d0030" + + "818902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c5410" + + "0cb6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4" + + "d0f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984" + + "b562517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315ac" + + "f9a0b351a23f0203010001", + "3081a7300d06092a864886f70d0101010500038901000000000000008d003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a6300d06092a864886f70d01010105000381943089010000000000000089" + + "02818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6" + + "e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f1" + + "09fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562" + + "517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0" + + "b351a23f0203010001", + "3081a6300d06092a864886f70d01010105000381943081910289010000000000" + + "00008100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6" + + "e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f1" + + "09fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562" + + "517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0" + + "b351a23f0203010001", + "3081a7300d06092a864886f70d010101050003819530819202818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02890100" + + "00000000000003010001", + // length = 2**32 - 1 + "3084ffffffff300d06092a864886f70d010101050003818d0030818902818100" + + "ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9" + + "8590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26" + + "c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6feb" + + "e1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f" + + "0203010001", + "3081a33084ffffffff06092a864886f70d010101050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a330110684ffffffff2a864886f70d010101050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a3301106092a864886f70d0101010584ffffffff03818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a2300d06092a864886f70d01010105000384ffffffff0030818902818100" + + "ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9" + + "8590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26" + + "c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6feb" + + "e1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f" + + "0203010001", + "3081a1300d06092a864886f70d010101050003818f3084ffffffff02818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a1300d06092a864886f70d010101050003818f30818c0284ffffffff00ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a2300d06092a864886f70d010101050003819030818d02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0284ffff" + + "ffff010001", + // length = 2**64 - 1 + "3088ffffffffffffffff300d06092a864886f70d010101050003818d00308189" + + "02818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6" + + "e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f1" + + "09fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562" + + "517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0" + + "b351a23f0203010001", + "3081a73088ffffffffffffffff06092a864886f70d010101050003818d003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a730150688ffffffffffffffff2a864886f70d010101050003818d003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a7301506092a864886f70d0101010588ffffffffffffffff03818d003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a6300d06092a864886f70d01010105000388ffffffffffffffff00308189" + + "02818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6" + + "e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f1" + + "09fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562" + + "517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0" + + "b351a23f0203010001", + "3081a5300d06092a864886f70d01010105000381933088ffffffffffffffff02" + + "818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1" + + "d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109" + + "fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b56251" + + "7e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b3" + + "51a23f0203010001", + "3081a5300d06092a864886f70d01010105000381933081900288ffffffffffff" + + "ffff00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1" + + "d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109" + + "fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b56251" + + "7e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b3" + + "51a23f0203010001", + "3081a6300d06092a864886f70d010101050003819430819102818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0288ffff" + + "ffffffffffff010001", + // removing sequence + "", + "30819003818d0030818902818100ab9014dc47d44b6d260fc1fef9ab022042fd" + + "9566e9d7b60c54100cb6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb1" + + "67d8a44ab93d73c4d0f109fb5a26c2f8823236ff517cf84412e173679cfae42e" + + "043b6fec81f9d984b562517e6febe1f72295dbc3fdfc19d3240aa75515563f31" + + "dad83563f3a315acf9a0b351a23f0203010001", + // appending 0's to sequence + "3081a1300d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "00010000", + "3081a1300f06092a864886f70d0101010500000003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a0300d06092a864886f70d010101050003818e30818b02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "010000", + // prepending 0's to sequence + "3081a10000300d06092a864886f70d010101050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a1300f000006092a864886f70d010101050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a0300d06092a864886f70d010101050003818e30818b000002818100ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "010001", + // appending unused 0's + "30819f300d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "00010000", + "3081a1300d06092a864886f70d0101010500000003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a1300f06092a864886f70d0101010000050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a0300d06092a864886f70d010101050003818e30818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "010000", + "3081a0300d06092a864886f70d010101050003818e30818b02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f00000203" + + "010001", + // appending null value + "3081a1300d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "00010500", + "3081a1300f06092a864886f70d0101010500050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a1300f060b2a864886f70d0101010500050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a1300f06092a864886f70d0101010502050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a1300d06092a864886f70d010101050003818f0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "00010500", + "3081a0300d06092a864886f70d010101050003818e30818b02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "010500", + "3081a0300d06092a864886f70d010101050003818e30818b02818300ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f05000203" + + "010001", + "3081a0300d06092a864886f70d010101050003818e30818b02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02050100" + + "010500", + // including garbage + "3081a4498030819f300d06092a864886f70d010101050003818d003081890281" + + "8100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4" + + "edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb" + + "5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e" + + "6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351" + + "a23f0203010001", + "3081a4250030819f300d06092a864886f70d010101050003818d003081890281" + + "8100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4" + + "edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb" + + "5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e" + + "6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351" + + "a23f0203010001", + "3081a230819f300d06092a864886f70d010101050003818d0030818902818100" + + "ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9" + + "8590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26" + + "c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6feb" + + "e1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f" + + "02030100010004deadbeef", + "3081a330114980300d06092a864886f70d010101050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a330112500300d06092a864886f70d010101050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a7300f300d06092a864886f70d01010105000004deadbeef03818d003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a33011260d498006092a864886f70d010101050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a33011260d250006092a864886f70d010101050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a73015260b06092a864886f70d0101010004deadbeef050003818d003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a3301106092a864886f70d01010125044980050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a3301106092a864886f70d01010125042500050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a7301506092a864886f70d010101250205000004deadbeef03818d003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a4300d06092a864886f70d0101010500238192498003818d003081890281" + + "8100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4" + + "edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb" + + "5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e" + + "6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351" + + "a23f0203010001", + "3081a4300d06092a864886f70d0101010500238192250003818d003081890281" + + "8100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4" + + "edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb" + + "5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e" + + "6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351" + + "a23f0203010001", + "3081a8300d06092a864886f70d010101050023819003818d0030818902818100" + + "ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9" + + "8590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26" + + "c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6feb" + + "e1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f" + + "02030100010004deadbeef", + "3081a3300d06092a864886f70d010101050003819130818e4980308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a3300d06092a864886f70d010101050003819130818e2500308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a7300d06092a864886f70d010101050003819530818c30818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "030100010004deadbeef", + "3081a3300d06092a864886f70d010101050003819130818e2281864980028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a3300d06092a864886f70d010101050003819130818e2281862500028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a7300d06092a864886f70d010101050003819530819222818402818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f00" + + "04deadbeef0203010001", + "3081a2300d06092a864886f70d010101050003819030818d02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f22074980" + + "0203010001", + "3081a2300d06092a864886f70d010101050003819030818d02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f22072500" + + "0203010001", + "3081a6300d06092a864886f70d010101050003819430819102818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f22050203" + + "0100010004deadbeef", + // including undefined tags + "3081a8aa00bb00cd0030819f300d06092a864886f70d010101050003818d0030" + + "818902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c5410" + + "0cb6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4" + + "d0f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984" + + "b562517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315ac" + + "f9a0b351a23f0203010001", + "3081a6aa02aabb30819f300d06092a864886f70d010101050003818d00308189" + + "02818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6" + + "e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f1" + + "09fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562" + + "517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0" + + "b351a23f0203010001", + "3081a73015aa00bb00cd00300d06092a864886f70d010101050003818d003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a53013aa02aabb300d06092a864886f70d010101050003818d0030818902" + + "818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1" + + "d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109" + + "fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b56251" + + "7e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b3" + + "51a23f0203010001", + "3081a730152611aa00bb00cd0006092a864886f70d010101050003818d003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a53013260faa02aabb06092a864886f70d010101050003818d0030818902" + + "818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1" + + "d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109" + + "fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b56251" + + "7e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b3" + + "51a23f0203010001", + "3081a7301506092a864886f70d0101012508aa00bb00cd00050003818d003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a5301306092a864886f70d0101012506aa02aabb050003818d0030818902" + + "818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1" + + "d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109" + + "fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b56251" + + "7e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b3" + + "51a23f0203010001", + "3081a8300d06092a864886f70d0101010500238196aa00bb00cd0003818d0030" + + "818902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c5410" + + "0cb6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4" + + "d0f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984" + + "b562517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315ac" + + "f9a0b351a23f0203010001", + "3081a6300d06092a864886f70d0101010500238194aa02aabb03818d00308189" + + "02818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6" + + "e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f1" + + "09fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562" + + "517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0" + + "b351a23f0203010001", + "3081a7300d06092a864886f70d0101010500038195308192aa00bb00cd003081" + + "8902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a5300d06092a864886f70d0101010500038193308190aa02aabb30818902" + + "818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1" + + "d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109" + + "fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b56251" + + "7e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b3" + + "51a23f0203010001", + "3081a7300d06092a864886f70d010101050003819530819222818aaa00bb00cd" + + "0002818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100c" + + "b6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0" + + "f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b5" + + "62517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9" + + "a0b351a23f0203010001", + "3081a5300d06092a864886f70d0101010500038193308190228188aa02aabb02" + + "818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1" + + "d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109" + + "fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b56251" + + "7e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b3" + + "51a23f0203010001", + "3081a6300d06092a864886f70d010101050003819430819102818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f220baa00" + + "bb00cd000203010001", + "3081a4300d06092a864886f70d010101050003819230818f02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f2209aa02" + + "aabb0203010001", + // changing tag value + "2e819f300d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "32819f300d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "ff819f300d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f2e0d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f320d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819fff0d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d04092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d08092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300dff092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d06092a864886f70d010101030003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d06092a864886f70d010101070003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d06092a864886f70d010101ff0003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d06092a864886f70d010101050001818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d06092a864886f70d010101050005818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d06092a864886f70d0101010500ff818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819e300d06092a864886f70d010101050003818c2e818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819e300d06092a864886f70d010101050003818c32818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819e300d06092a864886f70d010101050003818cff818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819e300d06092a864886f70d010101050003818c30818900818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819e300d06092a864886f70d010101050003818c30818904818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819e300d06092a864886f70d010101050003818c308189ff818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819e300d06092a864886f70d010101050003818c30818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f00030100" + + "01", + "30819e300d06092a864886f70d010101050003818c30818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f04030100" + + "01", + "30819e300d06092a864886f70d010101050003818c30818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23fff030100" + + "01", + // dropping value of sequence + "3000", + "308192300003818d0030818902818100ab9014dc47d44b6d260fc1fef9ab0220" + + "42fd9566e9d7b60c54100cb6e1d4edc98590467d0502c17fce69d00ac5efb40b" + + "2cb167d8a44ab93d73c4d0f109fb5a26c2f8823236ff517cf84412e173679cfa" + + "e42e043b6fec81f9d984b562517e6febe1f72295dbc3fdfc19d3240aa7551556" + + "3f31dad83563f3a315acf9a0b351a23f0203010001", + // using composition + "3081a430013030819e0d06092a864886f70d010101050003818d003081890281" + + "8100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4" + + "edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb" + + "5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e" + + "6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351" + + "a23f0203010001", + "3081a33011300106300c092a864886f70d010101050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a33011260d06012a0608864886f70d010101050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a4300d06092a864886f70d010101050023819203010003818c3081890281" + + "8100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4" + + "edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb" + + "5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e" + + "6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351" + + "a23f0203010001", + "3081a3300d06092a864886f70d010101050003819130818e3001023081888181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a3300d06092a864886f70d010101050003819130818e2281860201000281" + + "80ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + "3081a2300d06092a864886f70d010101050003819030818d02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f22070201" + + "0102020001", + // truncate sequence + "30819e300d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "00", + "30819e0d06092a864886f70d010101050003818d0030818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819e300c06092a864886f70d0101010503818d0030818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819e300c092a864886f70d010101050003818d0030818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819d300d06092a864886f70d010101050003818b30818802818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100", + "30819d300d06092a864886f70d010101050003818b308188818100ab9014dc47" + + "d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d05" + + "02c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8823236" + + "ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295db" + + "c3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203010001", + // prepend empty sequence + "3081a13000300d06092a864886f70d010101050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a1300f300006092a864886f70d010101050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a0300d06092a864886f70d010101050003818e30818b300002818100ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "010001", + // append empty sequence + "3081a1300d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "00013000", + "3081a1300f06092a864886f70d0101010500300003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a0300d06092a864886f70d010101050003818e30818b02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "013000", + // sequence of sequence + "3081a230819f300d06092a864886f70d010101050003818d0030818902818100" + + "ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9" + + "8590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26" + + "c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6feb" + + "e1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f" + + "0203010001", + "3081a1300f300d06092a864886f70d010101050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + "3081a1300d06092a864886f70d010101050003818f30818c30818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + // truncated sequence + "300f300d06092a864886f70d0101010500", + "30819d300b06092a864886f70d01010103818d0030818902818100ab9014dc47" + + "d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d05" + + "02c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8823236" + + "ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295db" + + "c3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203010001", + "308199300d06092a864886f70d010101050003818730818402818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f", + // repeat element in sequence + "3082012f300d06092a864886f70d010101050003818d0030818902818100ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "01000103818d0030818902818100ab9014dc47d44b6d260fc1fef9ab022042fd" + + "9566e9d7b60c54100cb6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb1" + + "67d8a44ab93d73c4d0f109fb5a26c2f8823236ff517cf84412e173679cfae42e" + + "043b6fec81f9d984b562517e6febe1f72295dbc3fdfc19d3240aa75515563f31" + + "dad83563f3a315acf9a0b351a23f0203010001", + "3081a3300d06092a864886f70d010101050003819130818e02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "010203010001", + // long form encoding of length + "3081a030810d06092a864886f70d010101050003818d0030818902818100ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "010001", + "3081a0300e0681092a864886f70d010101050003818d0030818902818100ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "010001", + "3081a0300e06092a864886f70d01010105810003818d0030818902818100ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "010001", + "30819f300d06092a864886f70d010101050003818d30818a02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02810301" + + "0001", + // removing oid + "3081943002050003818d0030818902818100ab9014dc47d44b6d260fc1fef9ab" + + "022042fd9566e9d7b60c54100cb6e1d4edc98590467d0502c17fce69d00ac5ef" + + "b40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8823236ff517cf84412e17367" + + "9cfae42e043b6fec81f9d984b562517e6febe1f72295dbc3fdfc19d3240aa755" + + "15563f31dad83563f3a315acf9a0b351a23f0203010001", + // appending 0's to oid + "3081a1300f060b2a864886f70d0101010000050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + // prepending 0's to oid + "3081a1300f060b00002a864886f70d010101050003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + // dropping value of oid + "30819630040600050003818d0030818902818100ab9014dc47d44b6d260fc1fe" + + "f9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d0502c17fce69d00a" + + "c5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8823236ff517cf84412e1" + + "73679cfae42e043b6fec81f9d984b562517e6febe1f72295dbc3fdfc19d3240a" + + "a75515563f31dad83563f3a315acf9a0b351a23f0203010001", + // modify first byte of oid + "30819f300d06092b864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + // modify last byte of oid + "30819f300d06092a864886f70d010100050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + // truncate oid + "30819e300c06082a864886f70d0101050003818d0030818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819e300c0608864886f70d010101050003818d0030818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + // wrong oid + "30819b300906052b0e03021a050003818d0030818902818100ab9014dc47d44b" + + "6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d0502c1" + + "7fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8823236ff51" + + "7cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295dbc3fd" + + "fc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203010001", + "30819f300d0609608648016503040201050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + // longer oid + "3081a0300e060a2a864886f70d01010101050003818d0030818902818100ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "010001", + // oid with modified node + "30819f300d06092a864886f70d010111050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "3081a33011060d2a864886f70d01018880808001050003818d00308189028181" + + "00ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4ed" + + "c98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a" + + "26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6f" + + "ebe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a2" + + "3f0203010001", + // large integer in oid + "3081a8301606122a864886f70d010182808080808080808001050003818d0030" + + "818902818100ab9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c5410" + + "0cb6e1d4edc98590467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4" + + "d0f109fb5a26c2f8823236ff517cf84412e173679cfae42e043b6fec81f9d984" + + "b562517e6febe1f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315ac" + + "f9a0b351a23f0203010001", + // oid with invalid node + "3081a0300e060a2a864886f70d010101e0050003818d0030818902818100ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "010001", + "3081a0300e060a2a80864886f70d010101050003818d0030818902818100ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "010001", + // appending 0's to null + "3081a1300f06092a864886f70d0101010502000003818d0030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + // appending 0's to bit string + "3081a1300d06092a864886f70d010101050003818f0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "00010000", + // prepending 0's to bit string + "3081a1300d06092a864886f70d010101050003818f00000030818902818100ab" + + "9014dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc985" + + "90467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2" + + "f8823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1" + + "f72295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02" + + "03010001", + // modify first byte of bit string + "30819f300d06092a864886f70d010101050003818d0130818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + // modify last byte of bit string + "30819f300d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0000", + // truncate bit string + "30819e300d06092a864886f70d010101050003818c0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "00", + "30819e300d06092a864886f70d010101050003818c30818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + // removing integer + "3018300d06092a864886f70d0101010500030730050203010001", + // appending 0's to integer + "3081a0300d06092a864886f70d010101050003818e30818b02818300ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f00000203" + + "010001", + "3081a0300d06092a864886f70d010101050003818e30818b02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02050100" + + "010000", + // prepending 0's to integer + "3081a0300d06092a864886f70d010101050003818e30818b028183000000ab90" + + "14dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590" + + "467d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8" + + "823236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f7" + + "2295dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203" + + "010001", + "3081a0300d06092a864886f70d010101050003818e30818b02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02050000" + + "010001", + // dropping value of integer + "301a300d06092a864886f70d01010105000309300702000203010001", + "30819b300d06092a864886f70d010101050003818930818602818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0200", + // modify first byte of integer + "30819e300d06092a864886f70d010101050003818c30818902818101ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "01", + "30819e300d06092a864886f70d010101050003818c30818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030000" + + "01", + // modify last byte of integer + "30819e300d06092a864886f70d010101050003818c30818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23e02030100" + + "01", + "30819e300d06092a864886f70d010101050003818c30818902818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02030100" + + "00", + // truncate integer + "30819d300d06092a864886f70d010101050003818b30818802818000ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a20203010001", + "30819d300d06092a864886f70d010101050003818b308188028180ab9014dc47" + + "d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d05" + + "02c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f8823236" + + "ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295db" + + "c3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203010001", + "30819d300d06092a864886f70d010101050003818b30818802818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02020100", + "30819d300d06092a864886f70d010101050003818b30818802818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f02020001", + // leading ff in integer + "30819f300d06092a864886f70d010101050003818d30818a028182ff00ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020301" + + "0001", + "30819f300d06092a864886f70d010101050003818d30818a02818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0204ff01" + + "0001", + // infinity + "301b300d06092a864886f70d0101010500030a30080901800203010001", + "30819c300d06092a864886f70d010101050003818a30818702818100ab9014dc" + + "47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc98590467d" + + "0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f88232" + + "36ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f72295" + + "dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f090180", + // n=0 + "301c300d06092a864886f70d0101010500030b0030080201000203010001", + // negative n + "30819f300d06092a864886f70d010101050003818d00308189028181ff546feb" + + "23b82bb492d9f03e010654fddfbd026a99162849f3abeff3491e2b12367a6fb9" + + "82fafd3e8031962ff53a104bf4d34e98275bb546c28c3b2f0ef604a5d93d077d" + + "cdc900ae8307bbed1e8c9863051bd1fbc490137e06267b4a9dae8190141e08dd" + + "6a243c0203e62cdbf558aaeaa9c0ce2527ca9c0c5cea53065f4cae5dc1020301" + + "0001", + // e=0 + "30819d300d06092a864886f70d010101050003818b0030818702818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020100", + // e=1 + "30819d300d06092a864886f70d010101050003818b0030818702818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020101", + // e=2 + "30819d300d06092a864886f70d010101050003818b0030818702818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f020102", + // negative e + "30819f300d06092a864886f70d010101050003818d0030818902818100ab9014" + + "dc47d44b6d260fc1fef9ab022042fd9566e9d7b60c54100cb6e1d4edc9859046" + + "7d0502c17fce69d00ac5efb40b2cb167d8a44ab93d73c4d0f109fb5a26c2f882" + + "3236ff517cf84412e173679cfae42e043b6fec81f9d984b562517e6febe1f722" + + "95dbc3fdfc19d3240aa75515563f31dad83563f3a315acf9a0b351a23f0203fe" + + "ffff", + }; + private void checkPrivateCrtKey(RSAPrivateCrtKey key, int expectedKeySize) throws Exception { BigInteger p = key.getPrimeP(); BigInteger q = key.getPrimeQ(); @@ -136,4 +1475,39 @@ public class RsaKeyTest extends TestCase { "X.509", pub.getFormat()); assertEquals(ENCODED_PUBLIC_KEY, TestUtil.bytesToHex(pub.getEncoded())); } + + /** + * Parses a list of modified encodings of an RSA public key. + * Expects that any modification either results in an InvalidKeySpecException + * or an altered PublicKey. + * This test has mostly "defense in depth" characteristic, since applications should + * never accept unauthenticated public keys. + */ + public void testModifiedPublicKeyDecoding() throws Exception { + KeyFactory kf = KeyFactory.getInstance("RSA"); + int cnt = 0; + for (String encoded : MODIFIED_PUBLIC_KEY) { + X509EncodedKeySpec spec = new X509EncodedKeySpec(TestUtil.hexToBytes(encoded)); + try { + RSAPublicKey unusedKey = (RSAPublicKey) kf.generatePublic(spec); + // TODO(bleichen): check the keys that are accepted. + // To decide whether a key should have been rejected or not the test vectors must be + // divided into several categories: + // - keys that use BER encoding: these are OK + // - keys that include additional fields or garbage: might be OK + // - keys where the modification does not change the values: are probably OK + // - keys with missing parameters: should be rejected + // - keys with impossible values (negative n, negative e): should be rejected. + } catch (InvalidKeySpecException ex) { + // expected + } catch (Exception ex) { + System.out.println("generatePublic throws:" + ex.getMessage() + " for " + encoded); + cnt++; + } + } + assertEquals(0, cnt); + } + + // TODO(bleichen): This test is only needed as long as there are open issues. + } diff --git a/java/com/google/security/wycheproof/testcases/RsaSignatureTest.java b/java/com/google/security/wycheproof/testcases/RsaSignatureTest.java index 2759a84..3d214fe 100644 --- a/java/com/google/security/wycheproof/testcases/RsaSignatureTest.java +++ b/java/com/google/security/wycheproof/testcases/RsaSignatureTest.java @@ -65,6 +65,8 @@ public class RsaSignatureTest extends TestCase { * around 2012. * <li> Berserk: http://www.intelsecurity.com/advanced-threat-research/berserk.html * <li> Truncated comparison of hashes e.g.: http://wiibrew.org/wiki/Signing_bug + * <li> CVE-2016-5547: OpenJDK8 RSA signature's throws an OutOfMemoryError for some invalid + * signatures * </ul> */ static final String[] SIGNATURES_KEY1 = { @@ -264,6 +266,38 @@ public class RsaSignatureTest extends TestCase { + "3a3d5b1cb1e7dded3352c3c92ded891839263a501afaa78fedfd04546c43d16f" + "7a52b800abc9ab1ef827ae0eb19d9b52def2435f1477a48dff61800b4db830e4", + // length = 2**31 - 1 + // padding:30847fffffff300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 + // ec113d682299550d7a6e0f345e25 + "9dcc651cc0a1b4d406112c0d1ebd7a9fb5a2c9d9f9cffbeab2d2821e5ed01efa" + + "9d191665794649bd1f588b729e8fba1eaa37a5a736a5863973c338a92b2665d6" + + "ead13b72a19d2da778febb94b150e8d750340a3b856fca8b3b6e3cbfecb9c397" + + "c23f46912ba546ab0f64ed88404ce317f8fb2278b68950e9712d6b11f5cdfcaa", + // padding:303530847fffffff060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 + // ec113d682299550d7a6e0f345e25 + "0397d14205c2f52423ef69c874294dc2b37d5be5d5647f7e83f1dd6783cb41cc" + + "e52e6de1dc8c9e93ca1ef887d4c0ea79cd8b26391d638bbd8080bce830bf1bd7" + + "fb1de31346f28d609874fafd4a34fb7bee900441f55589ec3c5e190106d8816c" + + "adfcfb445834739cafaaa3903ed93cedc41a76aa0ce18fb49a3a73b7b5928735", + // padding:3035301106847fffffff60864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 + // ec113d682299550d7a6e0f345e25 + "2c3ffd881c1c0ce2e4c98282d6011179a89b1e84b17072bcbbb64164e5e05410" + + "d0414a1fdbbc04564f3d80f3891f28c3f02e92bf97b4339b5bd4699614e236d4" + + "223cef0688c44b297eb9c0e22246b4cb28983b102a446dc76671206c3b77af68" + + "97f2f445512abda37bc9c37257dd4f1c6f0e6ec40929eb6b0058682b9d2f6c66", + // padding:30353011060960864801650304020105847fffffff0420532eaabd9574880dbf76b9b8cc00832c20a6 + // ec113d682299550d7a6e0f345e25 + "668bd06eafe953fca6a17b0da0f9006ceadb09ad904786b7530148df7eedc146" + + "d20a5472c39677d65e59934c00227fb662b3474596e6072f56d2c00c3d31e66f" + + "0da85f4670e75c3f2c910c0fec8c98bc31fb2eceff80350b78aec0d316e9bbb3" + + "31544d8a3d0b1649291396c717e350bebba3d3c3a0b1d55f010879b8c7b7d4f9", + // padding:3035300d0609608648016503040201050004847fffffff532eaabd9574880dbf76b9b8cc00832c20a6 + // ec113d682299550d7a6e0f345e25 + "87482257ae1d18d0357428b756ae35a48549536a3439ca3c148eee64f4c096d8" + + "96219097d55c14a25eb1490779f6b1471aed238cc0d6aaf265c12ac086d04de9" + + "b79a37518056dfacc12cb4916c17505fc7e2e6c1e0db720a286ea65bde4d3da1" + + "d2dcb8d0276e8ce73f3f923209149955285c602572cfd24c82e8d96d45f569e6", + // length = 2**32 - 1 // padding:3084ffffffff300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 // ec113d682299550d7a6e0f345e25 @@ -421,42 +455,42 @@ public class RsaSignatureTest extends TestCase { + "ad8393d281eca07ebd287364a19045029fa7ed0e62a21e5e42a88a52ea4abc8b", // including garbage - // padding:503549803031300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 + // padding:303549803031300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 // ec113d682299550d7a6e0f345e25 - "654b1ba6cd1b13e112c5bbcbae8ea2094a1c6f8c6bb73c9225688aa93fc0e8d3" - + "26e411bdf2bb8de3951b2f55ccb19d4880a93ed1519021ee8bef1b04997a31e5" - + "3586c56587e3554bec3c606125ce719b96223fca2b55bed5560ff51ad4ef8018" - + "d648cd1f4c6354e0fb920fcda79ef68d51d7ef16ec93e74aee9ae4ba1f9f00e7", - // padding:503525003031300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 + "236a815c2441d111d254172149ab2429cc4e6caf3335579bf438f22723de0a4a" + + "5e532ed71f24c0fc6032c60aebb2b7e76cd0d14f262d1d9bba80a53dbdb12c9b" + + "89902fc5f5511125d21b7df32e9b303c4b393fd6add6ac7536901ea8ae5785dc" + + "fe90e85ad0c16146b1f15036c31d7758a364fb54cc1d183b8566bda592ba446c", + // padding:303525003031300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 // ec113d682299550d7a6e0f345e25 - "04aa2d0bb7edcbad611d49a58b687bf4d0e7e81ce8c05def3f61fb7f5041706b" - + "61fcffb3fcdc839b3957a64999a3c800449df841c5a6d5af4ab03b6271a0d573" - + "cea8d8c23ba9db1f5d81ad3b58998c56193ea2445a2f0dad9cc0b91d853ab984" - + "436b698d31d1caf62c59009750d2395d875811d3919bb8ebac3eb65e0c19e34c", - // padding:50333031300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6ec11 + "762d30b302cd76b021e237f28017e48488ff3bb30ff9e92db5b1e76eec2ee91c" + + "9af03e1c5038afc22591b1cd8cfae648a33ab77901f9f3736e50eea83f7c7a45" + + "46dc55c0265fb17dfdd30250fa3881e34e51b4f2e54554ad098eee952ec888e9" + + "11a0ea5df42c0560bcb4bdd718c88d834b534917e555c38fd1ec3593b2f25b39", + // padding:30333031300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6ec11 // 3d682299550d7a6e0f345e250004deadbeef - "4bd7c5fde38919661cf5784ed09aa3abebf7c16b8a70c3ebbff8f8727cefb3d2" - + "532229adefbb7432e38b1cc13fdd2c05202e8f3d1b669256ef34e4c2f091d724" - + "e06e019104c0656bf3bea6bc604e4343ff6fd7eabd29a33ff8391ab4b761bbf8" - + "3141fc12c6ffece32d3623a01d0dfba0dbcc0eedcb042cf33d915cbc41ddb1d8", - // padding:303550114980300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 + "8cbf9d425abef67ff0a7fb648e70b82b1556ac80e46dcff37145b9041bee2bbb" + + "fa56817e04994c9cf1123c6df2aeeb1637595eb1e20adef51d657943fd67826a" + + "c5d5dfba106ae9cd243f12746917a446ce955034b46ceb0f4d542b7bcd06ad3e" + + "6e10899d5338e6d8caf3d4de3cbf45d45a58d946a64d0bc13e97a4ab4e6b6016", + // padding:303530114980300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 // ec113d682299550d7a6e0f345e25 - "441c9007aeac4adb44dfeca1e583e31e3bf948eaabb7864882a6f178f8f6d5ab" - + "fe4faed96df55f71652761512223eea64b571735500379e2f8b5d92c1c9a95a0" - + "276edda1f9902b8a3dc6941e2a09ce5a382c29fd4d4688efe0d532b6430bf0a2" - + "bd86d28832da4f6e4c2013e31267406b44f60d39d4e21049e25ff7beada5c2e5", - // padding:303550112500300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 + "6477bd3337d601fe92e19e7f6b216f73eaca68aa408c5a570876ad8db6113505" + + "43d1dd458b511e3095e57996ca589c00f2beb6b6fe4564f4373571d904958acd" + + "1bcd33f57959a231bb126bb2b37bf1403d52836752198b6954567f07b31ed110" + + "5dcc50004e4cd7e897516c536c205b339ff0d35463ca6871ea5dce7a8daed8d7", + // padding:303530112500300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 // ec113d682299550d7a6e0f345e25 - "3a95f36a85061148ac22700478bcbe609b6148abadac9f4e53e24ab9aa2c712a" - + "3fa6a869cce665de06b0049959529c888145f9468d245c1098b2cfa74ca99e3b" - + "2de839e8a1cd3b3ca5a56e9b9d047ba758301ec42f39af26e3c514a9436115f9" - + "a446f8f6ec11351ed5234eb63dbc0ea434119042fd0c929d0f54591e1899c0e0", - // padding:3039500f300d060960864801650304020105000004deadbeef0420532eaabd9574880dbf76b9b8cc00 + "975d07b7295268a8662aedbd2b65b5eb10bb496077f41b90d12d34ebc7e492f0" + + "c7f3a41d4164a279f06ea616f91968628be4ceecd4a554477bc76cc6b2e6bda4" + + "042dc253327c4b8fc40e9242cbc8b835114a7379a3081bae4b2803a99deb4a54" + + "0f8c149ca5db3a61c7bc9f61cd7e55521660a06603849896c791a18d1c7360e1", + // padding:3039300f300d060960864801650304020105000004deadbeef0420532eaabd9574880dbf76b9b8cc00 // 832c20a6ec113d682299550d7a6e0f345e25 - "4531b3c930bce54375573269f91d5c2decaf35ff71b27938abc4ded9c1eb77c1" - + "244af6d660ad21d1cb224f2f8b791e331597b0a8591844e5c292024cc4994dda" - + "105e693b0b29642090b502aaa44e3adab3308a66167e2313b8c6dc5a63777959" - + "be1730d69bef6c0e8116898f4fcc05611af94d5e37ed4ae6e7275c40ab4a47d9", + "37352cd11eb5ff7380bfb7c0d3e8d9979ae7cb489a71c31a077d59496547b0c9" + + "5a760387ed50eefde0b762222f05a6033740f6e010693edf3ef8ab5f9c57f4eb" + + "1f6ccd83287dcc2e90857defe5ba4109bf79ad84ab069c85a25758d22536c688" + + "2919245fa2d7e7921b3635d984deeb6555cabdfc46a42c75875d55924c8bac62", // padding:30353011260d4980060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 // ec113d682299550d7a6e0f345e25 "0c783603c7af53df27538b983fb7368e9f62d4552f008f2920a21cff3186d2ac" @@ -513,30 +547,30 @@ public class RsaSignatureTest extends TestCase { + "0fd7bc325b1cf75e1079f8d6df53fe495722cc1ce707cca49bc6f4ed2ca6c4f9", // including undefined tags - // padding:5039aa00bb00cd003031300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00 + // padding:3039aa00bb00cd003031300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00 // 832c20a6ec113d682299550d7a6e0f345e25 - "3507fbbb0ae37992789b22c27dc2b5ecc6c3a2cd555ca9049388e1b0c84c14c4" - + "f3a98d14d7f80ab79d68d2ea140ceb7967171cd153039e98c703b4ce434a37aa" - + "6ec7e13f06a76ae3a49057394393e20dff96b5157fddbb39faa094b4598c41fd" - + "a2410510490c54e5184264e74ed7a734cee0d5c536ce68f76509447ebccacea7", - // padding:5037aa02aabb3031300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c + "9f2234b108a45abaed850e19d2f9576f59bb83dbc6165da61c4798638f9c9858" + + "7c7eb92a8c901dc4430e4a47dc05681ae811ffcad6f7a604c43551cd0f5d1235" + + "49435d622f7efec578301efd49dc6b139abbc3c7d6a26858f6d18f09b863a145" + + "d6483c9efc6c322fec1341b6362dc1d752c714efcdfb09097a0ce6df7dbe88a9", + // padding:3037aa02aabb3031300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c // 20a6ec113d682299550d7a6e0f345e25 - "5edc1fd6fd901165dce272e6c5d4ed3fae7917d28aafa278c5bc5eb71a5b4671" - + "00b9f3afe956e1d61ba2a3936bde573f92096c4500e62d49479f51b0350a3586" - + "fbf216f56b23cd598118f6ee26cbaea2ba3dc373a0cb789a8a2da057075f063c" - + "703b12e772e35db546ce0ea3a803d61d2623bea3f1d31e80f8f5b4b410d70677", - // padding:30395015aa00bb00cd00300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00 + "24ba137a293599ab7e50a0a4f8c7a5cd02dda6a4568c93f84d00ff4729656456" + + "3c9051b334db2fd2c081b23d322d4870a61b2435d651d7efb4e1b0920e759f7f" + + "d81a937bbc85ff43dbe2b702dec3acf4db68d5fd7b8a2f6d32cc49a7300dd659" + + "623b391927a2442d69c6c3c29e59eb80b1d0a95bec6d18a6223cf4357eb7cc96", + // padding:30393015aa00bb00cd00300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00 // 832c20a6ec113d682299550d7a6e0f345e25 - "493eb9e477f0a6e8e92c8c8b10e2817c3f6061248c3ce16347eb21c35dd41906" - + "add2d69f5cf6023725e9dd5183bba8d2bbf7be5899c84ec089472477ac016d18" - + "bdbc04ef27d05c6c21867bae6adba66f1336b5c8944b06a64558982fd07d51ed" - + "cc4efc4d1f01542094e6dce82a063da4a68aa92afed00d3ace9a9bedea086c61", - // padding:30375013aa02aabb300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c + "04023dd35fa479f8156794d02935f8669c023c774b95c5a0e02837e32ccaf7a4" + + "ba5195835a15de6a21796eb96bdaed868f9e8b7f0a5a21c1a3058f53aadb62d6" + + "ee74cd70b2c38f17e42a1f7ffd88955731b4e15368211ad53f617aacbb54a7e7" + + "078740ba6daaca81c1b321b748ea1d13f7aece490226636ecac41bdc275175d6", + // padding:30373013aa02aabb300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c // 20a6ec113d682299550d7a6e0f345e25 - "a173341d877e70d384521f1832878599bb93e457cf78b0984f130b9af16ad90d" - + "0ed8c58f8651d05aed66f359bd20022fd71139880ec7b3896206e662bd96ba49" - + "f9976e0170884a5726dc097ba3c66227b058a9189b7868259f71b507253761b5" - + "d634abc8dd27c6bdde54e1062252bd0a1e4aa829886ca778a3f914174094a81b", + "253bed76e4b8465ebfffd1b7214ce586294d3bea290517ca2bfc417ba9d8e72d" + + "286570c348dc6084fd379c2bf4dae424189964639533e17c409ae18e445210ed" + + "4dc98de4ad7336554740d1532d5010a1bd7ebbc33ba48a3365d50669e4f4522d" + + "0e5ff7a3bdb1c42c42dee647a8a3ce16633eb33bbc0a869e12cf99f9481dcf85", // padding:303930152611aa00bb00cd00060960864801650304020105000420532eaabd9574880dbf76b9b8cc00 // 832c20a6ec113d682299550d7a6e0f345e25 "0775598491297eb9004eed66234ded82e047ea2f06837425e6bd27f33b137366" @@ -679,18 +713,18 @@ public class RsaSignatureTest extends TestCase { + "9056ba13b77d35239eea164ddbc8808f8e7e1beb070f551b6e95f90d5bdbd925", // using composition - // padding:503530013030300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 + // padding:303530013030300d060960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 // ec113d682299550d7a6e0f345e25 - "24fa27f7c532f1d58d98309957a42eb0be15acc0038c3a012b3d5a7ff7e0d13b" - + "696f16fb8eac88ddead2a40a9686ca361fd72afbe4dbe4b3ae6d9ba390564723" - + "dff0f45fde7db6ebb83bc16573ef2d21f51689a7ad4b8edfbaea1f0674e43868" - + "0c6ab19cb5a1fe2e90a7082a6217f0f453ba25933b25a7cc65e8562bc78e4fc3", - // padding:30355011300106300c0960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 + "09342a8fb8402b5e50fbf8c5d1cae415ce02c0a803adfed88188982129e84809" + + "18dc21616bb5f8381e8dfe13f63234090c32e542a005df70df5e8e00dd2a478d" + + "10fff1b61efbdcf0e410236f7c031c9a5f7cd0db9098f8a32a6a49f408e72c4a" + + "29b7d27e8041ba605bf089bbdb9777e19b31ecca0d49b90d54701721af79cf3a", + // padding:30353011300106300c0960864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 // ec113d682299550d7a6e0f345e25 - "1a9fe9f10dcf04f35187f5298448adf2f48ce7f0e556d699a42f721289f04390" - + "48527c3fe0751bc871fd7afb3d70771c048f5b319a40154451e3a3336cc6169b" - + "73ec5dac98b8f57710b12bf81cdf07228483e66a38f543ea03f9480875eb9b0d" - + "27d5fb7d53c43106935de0e416dde4cdd33667d730b71e30a63cfa86d3f9de11", + "3ef90c414a64601c538c286f2c35f32445039799b8c266eed605027578edda79" + + "6a409d905a751bf5c1cdea97840437fa82733d8f27efbbc05da732887078a8f5" + + "47bbfb54607a54f893df7dde0c35c45f9c2402bed0405c72e98175e5b9d6f902" + + "24e07d12e8c1bbad2fc8b1a14c42dd5fb7e554db5edae89d335705c672cd7b55", // padding:30353011260d0601600608864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6 // ec113d682299550d7a6e0f345e25 "3ad3e4ec3636b5eb8aac2161c04d228491ca0d9da2abd69d8904054373940b39" @@ -848,14 +882,6 @@ public class RsaSignatureTest extends TestCase { + "9dbbb126b314312539931a0163c911f0234f5c3f683c9376f2ecaa3294d71a12" + "74f6c63b84ea8faf826eacb05e4fa5459b787ff384b2cfe0f1f4c755f32b5c50", - // prefix in oid - // padding:3032300e060a0860864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6ec113d - // 682299550d7a6e0f345e25 - "7b4b34bc61b0576e3f940e1d5a281bde047ece50316cc111f08b7278bef71e90" - + "029db2d63b64268edbfbed464d3c3dd2b9341c8a51fdbb5bb1ea44d86366c0ac" - + "bfd17515300a50195a9caf34b2b84ee641a405864a7b2b91ed452052f114459a" - + "316d6afa8e93134e655c0d8befffe5fcf4d48c9e43cfa593893157d6ade8d04d", - // wrong oid // padding:302d300906052b0e03021a05000420532eaabd9574880dbf76b9b8cc00832c20a6ec113d682299550d // 7a6e0f345e25 @@ -864,6 +890,50 @@ public class RsaSignatureTest extends TestCase { + "6e73ecd8ced0adb52db2c374297119f5fe571bd5396529d13b7225e87db5b5b0" + "df38e4c56f2349071b09ff5c1ded919b398d4aff38c6ae29af6f6ff99d3e8836", + // longer oid + // padding:3032300e060a6086480165030402010105000420532eaabd9574880dbf76b9b8cc00832c20a6ec113d + // 682299550d7a6e0f345e25 + "2054d402bf6a148b52972b830c8c8a16a6aeddbcd5c2ae3fd83de67c666e712f" + + "a98650308658837a67ab87b2c444bedc7cf995c19af433da9343f260049b1bcb" + + "436ebe27d8a502728dfb0daac5d2710e2c39fa000b909aede07ad7a0d27629e0" + + "ac27ed9fcd41a39e09f7acdec4c2df77f38c535f46e3b96f2772a81e65e74bb8", + + // oid with modified node + // padding:3031300d060960864801650304021105000420532eaabd9574880dbf76b9b8cc00832c20a6ec113d68 + // 2299550d7a6e0f345e25 + "3a94d241563a2ad97574ec82baefccd9dd114e21fa9169d0f54c4d0f57826224" + + "804ddc9b29c1905c59f39bd6aa3366705a85f5e6e18c0eb0f67986b5265e7371" + + "865b618e90e5c5313f0b6fce2343aa12d4ed44d6770fa08d4f1342608a4fb627" + + "a273f3a1f1340d1f5c55957ce51048e3690a845851009cbfe38d3c96e96d4172", + // padding:30353011060d6086480165030402888080800105000420532eaabd9574880dbf76b9b8cc00832c20a6 + // ec113d682299550d7a6e0f345e25 + "079cb62831dbeb40a638402865cc92cb49913dae214babc3f4f8d69d64cf1436" + + "2c23c8dd6ebcee9c44633dd54a62bb2f0042c20033728fc2f8ff482cf0be3ee1" + + "03bacf757b50319495d9a838844ea1064f4bd1f1ebdc1b71a318c3c8f7d76ebd" + + "79ef2f3991d4d87e110d60e5fc655adfa4a8e792e46c1c7aa96156b884e2f7a9", + + // large integer in oid + // padding:303a3016061260864801650304028280808080808080800105000420532eaabd9574880dbf76b9b8cc + // 00832c20a6ec113d682299550d7a6e0f345e25 + "2c9083459ba6504dc10e0e63edf8ede8bdb4a9728673306908ad4e8f25656d48" + + "65f0748b9fd2cf7b51db0a2c659e0ce021fef3d2d3d0cf7c45343729c2001a19" + + "d37e29398a9a7e92d7f62693252261f1f7406b54af5447db6e846f981722059b" + + "7bb09ba95268c321c156ff659e0ce8e709d2819d5ce15f5dcfa54c55114a611a", + + // oid with invalid node + // padding:3032300e060a608648016503040201e005000420532eaabd9574880dbf76b9b8cc00832c20a6ec113d + // 682299550d7a6e0f345e25 + "9a76669c75f0f11399699f76e7bfbefc0d29feb5a8d86de1f751eedbb5c9e7b8" + + "1ecbc224534db67cfe1b611951a6ff499d86e11cac4a1725e2ff707085a81a76" + + "c73d5b53d1b0b2c4fab2d2eebe57eca83242a261cfca768abcd8e1f42e3841d6" + + "98bef3d4f16ac2dfab0fd42ef0abb0463474367dff7ec99d665a9838f2cfc24c", + // padding:3032300e060a6080864801650304020105000420532eaabd9574880dbf76b9b8cc00832c20a6ec113d + // 682299550d7a6e0f345e25 + "6674ec2352f0d3e90f4b72086f39815db11b056babc57644c8a703014f439baa" + + "46e8ed961714d5c7b5f0ec97ba3fe5ab867c16b7e1de089868dcb195fc20cc42" + + "fa1b3d3060f50cca77281bb6be18d65a1ee8e5a381e21e7f02e819752b71327a" + + "28719c7284f6425bc9241abb08d000faf58d48848d7f4b8d68b28266e663f36b", + // appending 0's to null // padding:3033300f0609608648016503040201050200000420532eaabd9574880dbf76b9b8cc00832c20a6ec11 // 3d682299550d7a6e0f345e25 |