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+/**
+ * @license
+ * Copyright 2016 Google Inc. All rights reserved.
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.google.security.wycheproof;
+
+import java.math.BigInteger;
+import java.security.AlgorithmParameters;
+import java.security.GeneralSecurityException;
+import java.security.KeyPair;
+import java.security.KeyPairGenerator;
+import java.security.NoSuchAlgorithmException;
+import java.security.interfaces.ECPublicKey;
+import java.security.spec.ECField;
+import java.security.spec.ECFieldFp;
+import java.security.spec.ECGenParameterSpec;
+import java.security.spec.ECParameterSpec;
+import java.security.spec.ECPoint;
+import java.security.spec.ECPublicKeySpec;
+import java.security.spec.EllipticCurve;
+import java.security.spec.InvalidParameterSpecException;
+import java.util.Arrays;
+
+/**
+ * Some utilities for testing Elliptic curve crypto. This code is for testing only and hasn't been
+ * reviewed for production.
+ */
+public class EcUtil {
+ /**
+ * Returns the ECParameterSpec for a named curve. Not every provider implements the
+ * AlgorithmParameters. Therefore, most test use alternative functions.
+ */
+ public static ECParameterSpec getCurveSpec(String name)
+ throws NoSuchAlgorithmException, InvalidParameterSpecException {
+ AlgorithmParameters parameters = AlgorithmParameters.getInstance("EC");
+ parameters.init(new ECGenParameterSpec(name));
+ return parameters.getParameterSpec(ECParameterSpec.class);
+ }
+
+ /**
+ * Returns the ECParameterSpec for a named curve. Only a handful curves that are used in the tests
+ * are implemented.
+ */
+ public static ECParameterSpec getCurveSpecRef(String name) throws NoSuchAlgorithmException {
+ if (name.equals("secp224r1")) {
+ return getNistP224Params();
+ } else if (name.equals("secp256r1")) {
+ return getNistP256Params();
+ } else if (name.equals("secp384r1")) {
+ return getNistP384Params();
+ } else if (name.equals("secp521r1")) {
+ return getNistP521Params();
+ } else if (name.equals("brainpoolp256r1")) {
+ return getBrainpoolP256r1Params();
+ } else {
+ throw new NoSuchAlgorithmException("Curve not implemented:" + name);
+ }
+ }
+
+ public static ECParameterSpec getNistCurveSpec(
+ String decimalP, String decimalN, String hexB, String hexGX, String hexGY) {
+ final BigInteger p = new BigInteger(decimalP);
+ final BigInteger n = new BigInteger(decimalN);
+ final BigInteger three = new BigInteger("3");
+ final BigInteger a = p.subtract(three);
+ final BigInteger b = new BigInteger(hexB, 16);
+ final BigInteger gx = new BigInteger(hexGX, 16);
+ final BigInteger gy = new BigInteger(hexGY, 16);
+ final int h = 1;
+ ECFieldFp fp = new ECFieldFp(p);
+ java.security.spec.EllipticCurve curveSpec = new java.security.spec.EllipticCurve(fp, a, b);
+ ECPoint g = new ECPoint(gx, gy);
+ ECParameterSpec ecSpec = new ECParameterSpec(curveSpec, g, n, h);
+ return ecSpec;
+ }
+
+ public static ECParameterSpec getNistP224Params() {
+ return getNistCurveSpec(
+ "26959946667150639794667015087019630673557916260026308143510066298881",
+ "26959946667150639794667015087019625940457807714424391721682722368061",
+ "b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4",
+ "b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
+ "bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34");
+ }
+
+ public static ECParameterSpec getNistP256Params() {
+ return getNistCurveSpec(
+ "115792089210356248762697446949407573530086143415290314195533631308867097853951",
+ "115792089210356248762697446949407573529996955224135760342422259061068512044369",
+ "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
+ "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
+ "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5");
+ }
+
+ public static ECParameterSpec getNistP384Params() {
+ return getNistCurveSpec(
+ "3940200619639447921227904010014361380507973927046544666794829340"
+ + "4245721771496870329047266088258938001861606973112319",
+ "3940200619639447921227904010014361380507973927046544666794690527"
+ + "9627659399113263569398956308152294913554433653942643",
+ "b3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875a"
+ + "c656398d8a2ed19d2a85c8edd3ec2aef",
+ "aa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a38"
+ + "5502f25dbf55296c3a545e3872760ab7",
+ "3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c0"
+ + "0a60b1ce1d7e819d7a431d7c90ea0e5f");
+ }
+
+ public static ECParameterSpec getNistP521Params() {
+ return getNistCurveSpec(
+ "6864797660130609714981900799081393217269435300143305409394463459"
+ + "18554318339765605212255964066145455497729631139148085803712198"
+ + "7999716643812574028291115057151",
+ "6864797660130609714981900799081393217269435300143305409394463459"
+ + "18554318339765539424505774633321719753296399637136332111386476"
+ + "8612440380340372808892707005449",
+ "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef10"
+ + "9e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00",
+ "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3d"
+ + "baa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66",
+ "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e6"
+ + "62c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650");
+ }
+
+ public static ECParameterSpec getBrainpoolP256r1Params() {
+ BigInteger p =
+ new BigInteger("A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377", 16);
+ BigInteger a =
+ new BigInteger("7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9", 16);
+ BigInteger b =
+ new BigInteger("26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6", 16);
+ BigInteger x =
+ new BigInteger("8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262", 16);
+ BigInteger y =
+ new BigInteger("547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997", 16);
+ BigInteger n =
+ new BigInteger("A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7", 16);
+ final int h = 1;
+ ECFieldFp fp = new ECFieldFp(p);
+ EllipticCurve curve = new EllipticCurve(fp, a, b);
+ ECPoint g = new ECPoint(x, y);
+ return new ECParameterSpec(curve, g, n, h);
+ }
+
+ /**
+ * Compute the Legendre symbol of x mod p. This implementation is slow. Faster would be the
+ * computation for the Jacobi symbol.
+ *
+ * @param x an integer
+ * @param p a prime modulus
+ * @returns 1 if x is a quadratic residue, -1 if x is a non-quadratic residue and 0 if x and p are
+ * not coprime.
+ * @throws GeneralSecurityException when the computation shows that p is not prime.
+ */
+ public static int legendre(BigInteger x, BigInteger p) throws GeneralSecurityException {
+ BigInteger q = p.subtract(BigInteger.ONE).shiftRight(1);
+ BigInteger t = x.modPow(q, p);
+ if (t.equals(BigInteger.ONE)) {
+ return 1;
+ } else if (t.equals(BigInteger.ZERO)) {
+ return 0;
+ } else if (t.add(BigInteger.ONE).equals(p)) {
+ return -1;
+ } else {
+ throw new GeneralSecurityException("p is not prime");
+ }
+ }
+
+ /**
+ * Computes a modular square root. Timing and exceptions can leak information about the inputs.
+ * Therefore this method must only be used in tests.
+ *
+ * @param x the square
+ * @param p the prime modulus
+ * @returns a value s such that s^2 mod p == x mod p
+ * @throws GeneralSecurityException if the square root could not be found.
+ */
+ public static BigInteger modSqrt(BigInteger x, BigInteger p) throws GeneralSecurityException {
+ if (p.signum() != 1) {
+ throw new GeneralSecurityException("p must be positive");
+ }
+ x = x.mod(p);
+ BigInteger squareRoot = null;
+ // Special case for x == 0.
+ // This check is necessary for Cipolla's algorithm.
+ if (x.equals(BigInteger.ZERO)) {
+ return x;
+ }
+ if (p.testBit(0) && p.testBit(1)) {
+ // Case p % 4 == 3
+ // q = (p + 1) / 4
+ BigInteger q = p.add(BigInteger.ONE).shiftRight(2);
+ squareRoot = x.modPow(q, p);
+ } else if (p.testBit(0) && !p.testBit(1)) {
+ // Case p % 4 == 1
+ // For this case we use Cipolla's algorithm.
+ // This alogorithm is preferrable to Tonelli-Shanks for primes p where p-1 is divisible by
+ // a large power of 2, which is a frequent choice since it simplifies modular reduction.
+ BigInteger a = BigInteger.ONE;
+ BigInteger d = null;
+ while (true) {
+ d = a.multiply(a).subtract(x).mod(p);
+ // Computes the Legendre symbol. Using the Jacobi symbol would be a faster. Using Legendre
+ // has the advantage, that it detects a non prime p with high probability.
+ // On the other hand if p = q^2 then the Jacobi (d/p)==1 for almost all d's and thus
+ // using the Jacobi symbol here can result in an endless loop with invalid inputs.
+ int t = legendre(d, p);
+ if (t == -1) {
+ break;
+ } else {
+ a = a.add(BigInteger.ONE);
+ }
+ }
+ // Since d = a^2 - n is a non-residue modulo p, we have
+ // a - sqrt(d) == (a+sqrt(d))^p (mod p),
+ // and hence
+ // n == (a + sqrt(d))(a - sqrt(d) == (a+sqrt(d))^(p+1) (mod p).
+ // Thus if n is square then (a+sqrt(d))^((p+1)/2) (mod p) is a square root of n.
+ BigInteger q = p.add(BigInteger.ONE).shiftRight(1);
+ BigInteger u = a;
+ BigInteger v = BigInteger.ONE;
+ for (int bit = q.bitLength() - 2; bit >= 0; bit--) {
+ // Compute (u + v sqrt(d))^2
+ BigInteger tmp = u.multiply(v);
+ u = u.multiply(u).add(v.multiply(v).mod(p).multiply(d)).mod(p);
+ v = tmp.add(tmp).mod(p);
+ if (q.testBit(bit)) {
+ tmp = u.multiply(a).add(v.multiply(d)).mod(p);
+ v = a.multiply(v).add(u).mod(p);
+ u = tmp;
+ }
+ }
+ squareRoot = u;
+ }
+ // The methods used to compute the square root only guarantee a correct result if the
+ // preconditions (i.e. p prime and x is a square) are satisfied. Otherwise the value is
+ // undefined. Hence, it is important to verify that squareRoot is indeed a square root.
+ if (squareRoot != null && squareRoot.multiply(squareRoot).mod(p).compareTo(x) != 0) {
+ throw new GeneralSecurityException("Could not find square root");
+ }
+ return squareRoot;
+ }
+
+ /**
+ * Returns the modulus of the field used by the curve specified in ecParams.
+ *
+ * @param curve must be a prime order elliptic curve
+ * @return the order of the finite field over which curve is defined.
+ */
+ public static BigInteger getModulus(EllipticCurve curve) throws GeneralSecurityException {
+ java.security.spec.ECField field = curve.getField();
+ if (field instanceof java.security.spec.ECFieldFp) {
+ return ((java.security.spec.ECFieldFp) field).getP();
+ } else {
+ throw new GeneralSecurityException("Only curves over prime order fields are supported");
+ }
+ }
+
+ /**
+ * Returns the size of an element of the field over which the curve is defined.
+ *
+ * @param curve must be a prime order elliptic curve
+ * @return the size of an element in bits
+ */
+ public static int fieldSizeInBits(EllipticCurve curve) throws GeneralSecurityException {
+ return getModulus(curve).subtract(BigInteger.ONE).bitLength();
+ }
+
+ /**
+ * Returns the size of an element of the field over which the curve is defined.
+ *
+ * @param curve must be a prime order elliptic curve
+ * @return the size of an element in bytes.
+ */
+ public static int fieldSizeInBytes(EllipticCurve curve) throws GeneralSecurityException {
+ return (fieldSizeInBits(curve) + 7) / 8;
+ }
+
+ /**
+ * Checks that a point is on a given elliptic curve. This method implements the partial public key
+ * validation routine from Section 5.6.2.6 of NIST SP 800-56A
+ * http://csrc.nist.gov/publications/nistpubs/800-56A/SP800-56A_Revision1_Mar08-2007.pdf A partial
+ * public key validation is sufficient for curves with cofactor 1. See Section B.3 of
+ * http://www.nsa.gov/ia/_files/SuiteB_Implementer_G-113808.pdf The point validations above are
+ * taken from recommendations for ECDH, because parameter checks in ECDH are much more important
+ * than for the case of ECDSA. Performing this test for ECDSA keys is mainly a sanity check.
+ *
+ * @param point the point that needs verification
+ * @param ec the elliptic curve. This must be a curve over a prime order field.
+ * @throws GeneralSecurityException if the field is binary or if the point is not on the curve.
+ */
+ public static void checkPointOnCurve(ECPoint point, EllipticCurve ec)
+ throws GeneralSecurityException {
+ BigInteger p = getModulus(ec);
+ BigInteger x = point.getAffineX();
+ BigInteger y = point.getAffineY();
+ if (x == null || y == null) {
+ throw new GeneralSecurityException("point is at infinity");
+ }
+ // Check 0 <= x < p and 0 <= y < p.
+ if (x.signum() == -1 || x.compareTo(p) != -1) {
+ throw new GeneralSecurityException("x is out of range");
+ }
+ if (y.signum() == -1 || y.compareTo(p) != -1) {
+ throw new GeneralSecurityException("y is out of range");
+ }
+ // Check y^2 == x^3 + a x + b (mod p)
+ BigInteger lhs = y.multiply(y).mod(p);
+ BigInteger rhs = x.multiply(x).add(ec.getA()).multiply(x).add(ec.getB()).mod(p);
+ if (!lhs.equals(rhs)) {
+ throw new GeneralSecurityException("Point is not on curve");
+ }
+ }
+
+ /**
+ * Checks a public key. I.e. this checks that the point defining the public key is on the curve.
+ *
+ * @param key must be a key defined over a curve using a prime order field.
+ * @throws GeneralSecurityException if the key is not valid.
+ */
+ public static void checkPublicKey(ECPublicKey key) throws GeneralSecurityException {
+ checkPointOnCurve(key.getW(), key.getParams().getCurve());
+ }
+
+ /**
+ * Decompress a point
+ *
+ * @param x The x-coordinate of the point
+ * @param bit0 true if the least significant bit of y is set.
+ * @param ecParams contains the curve of the point. This must be over a prime order field.
+ */
+ public static ECPoint getPoint(BigInteger x, boolean bit0, ECParameterSpec ecParams)
+ throws GeneralSecurityException {
+ EllipticCurve ec = ecParams.getCurve();
+ ECField field = ec.getField();
+ if (!(field instanceof ECFieldFp)) {
+ throw new GeneralSecurityException("Only curves over prime order fields are supported");
+ }
+ BigInteger p = ((java.security.spec.ECFieldFp) field).getP();
+ if (x.compareTo(BigInteger.ZERO) == -1 || x.compareTo(p) != -1) {
+ throw new GeneralSecurityException("x is out of range");
+ }
+ // Compute rhs == x^3 + a x + b (mod p)
+ BigInteger rhs = x.multiply(x).add(ec.getA()).multiply(x).add(ec.getB()).mod(p);
+ BigInteger y = modSqrt(rhs, p);
+ if (bit0 != y.testBit(0)) {
+ y = p.subtract(y).mod(p);
+ }
+ return new ECPoint(x, y);
+ }
+
+ /**
+ * Decompress a point on an elliptic curve.
+ *
+ * @param bytes The compressed point. Its representation is z || x where z is 2+lsb(y) and x is
+ * using a unsigned fixed length big-endian representation.
+ * @param ecParams the specification of the curve. Only Weierstrass curves over prime order fields
+ * are implemented.
+ */
+ public static ECPoint decompressPoint(byte[] bytes, ECParameterSpec ecParams)
+ throws GeneralSecurityException {
+ EllipticCurve ec = ecParams.getCurve();
+ ECField field = ec.getField();
+ if (!(field instanceof ECFieldFp)) {
+ throw new GeneralSecurityException("Only curves over prime order fields are supported");
+ }
+ BigInteger p = ((java.security.spec.ECFieldFp) field).getP();
+ int expectedLength = 1 + (p.bitLength() + 7) / 8;
+ if (bytes.length != expectedLength) {
+ throw new GeneralSecurityException("compressed point has wrong length");
+ }
+ boolean lsb;
+ switch (bytes[0]) {
+ case 2:
+ lsb = false;
+ break;
+ case 3:
+ lsb = true;
+ break;
+ default:
+ throw new GeneralSecurityException("Invalid format");
+ }
+ BigInteger x = new BigInteger(1, Arrays.copyOfRange(bytes, 1, bytes.length));
+ if (x.compareTo(BigInteger.ZERO) == -1 || x.compareTo(p) != -1) {
+ throw new GeneralSecurityException("x is out of range");
+ }
+ // Compute rhs == x^3 + a x + b (mod p)
+ BigInteger rhs = x.multiply(x).add(ec.getA()).multiply(x).add(ec.getB()).mod(p);
+ BigInteger y = modSqrt(rhs, p);
+ if (lsb != y.testBit(0)) {
+ y = p.subtract(y).mod(p);
+ }
+ return new ECPoint(x, y);
+ }
+
+ /**
+ * Returns a weak public key of order 3 such that the public key point is on the curve specified
+ * in ecParams. This method is used to check ECC implementations for missing step in the
+ * verification of the public key. E.g. implementations of ECDH must verify that the public key
+ * contains a point on the curve as well as public and secret key are using the same curve.
+ *
+ * @param ecParams the parameters of the key to attack. This must be a curve in Weierstrass form
+ * over a prime order field.
+ * @return a weak EC group with a genrator of order 3.
+ */
+ public static ECPublicKeySpec getWeakPublicKey(ECParameterSpec ecParams)
+ throws GeneralSecurityException {
+ EllipticCurve curve = ecParams.getCurve();
+ KeyPairGenerator keyGen = KeyPairGenerator.getInstance("EC");
+ keyGen.initialize(ecParams);
+ BigInteger p = getModulus(curve);
+ BigInteger three = new BigInteger("3");
+ while (true) {
+ // Generate a point on the original curve
+ KeyPair keyPair = keyGen.generateKeyPair();
+ ECPublicKey pub = (ECPublicKey) keyPair.getPublic();
+ ECPoint w = pub.getW();
+ BigInteger x = w.getAffineX();
+ BigInteger y = w.getAffineY();
+ // Find the curve parameters a,b such that 3*w = infinity.
+ // This is the case if the following equations are satisfied:
+ // 3x == l^2 (mod p)
+ // l == (3x^2 + a) / 2*y (mod p)
+ // y^2 == x^3 + ax + b (mod p)
+ BigInteger l;
+ try {
+ l = modSqrt(x.multiply(three), p);
+ } catch (GeneralSecurityException ex) {
+ continue;
+ }
+ BigInteger xSqr = x.multiply(x).mod(p);
+ BigInteger a = l.multiply(y.add(y)).subtract(xSqr.multiply(three)).mod(p);
+ BigInteger b = y.multiply(y).subtract(x.multiply(xSqr.add(a))).mod(p);
+ EllipticCurve newCurve = new EllipticCurve(curve.getField(), a, b);
+ // Just a sanity check.
+ checkPointOnCurve(w, newCurve);
+ // Cofactor and order are of course wrong.
+ ECParameterSpec spec = new ECParameterSpec(newCurve, w, p, 1);
+ return new ECPublicKeySpec(w, spec);
+ }
+ }
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-04 13:35:32 +0000