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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.nio.ByteBuffer;
import java.security.GeneralSecurityException;
import java.util.Random;
/**
* A collection of utilities for testing random number generators. So far this util simply checks
* that random numbers are not generated by java.util.Random. Eventually we plan to add detection
* for other random number generators too.
*
* @author bleichen@google.com (Daniel Bleichenbacher)
*/
public class RandomUtil {
// Constants for java.util.Random;
static final long A = 0x5DEECE66DL;
static final long A_INVERSE = 246154705703781L;
static final long C = 0xBL;
/** Given a state of a java.util.Random object compute the next state. */
protected static long nextState(long seed) {
return (seed * A + C) & ((1L << 48) - 1);
}
/** Give the state after stepping java.util.Random n times. */
protected static long step(long seed, long n) {
long a = A;
long c = C;
n = n & 0xffffffffffffL;
while (n != 0) {
if ((n & 1) == 1) {
seed = seed * a + c;
}
c = c * (a + 1);
a = a * a;
n = n >> 1;
}
return seed & 0xffffffffffffL;
}
/** Given a state of a java.util.Random object compute the previous state. */
protected static long previousState(long seed) {
return ((seed - C) * A_INVERSE) & ((1L << 48) - 1);
}
/** Computes a seed that would initialize a java.util.Random object with a given state. */
protected static long getSeedForState(long seed) {
return seed ^ A;
}
protected static long getStateForSeed(long seed) {
return (seed ^ A) & 0xffffffffffffL;
}
/**
* Given two subsequent outputs x0 and x1 from java.util.Random this function computes the
* internal state of java.util.Random after returning x0 or returns -1 if no such state exists.
*/
protected static long getState(int x0, int x1) {
long mask = (1L << 48) - 1;
long multiplier = A;
// The state of the random number generator after returning x0 is
// l0 + eps for some 0 <= eps < 2**16.
long l0 = ((long) x0 << 16) & mask;
// The state of the random number generator after returning x1 is
// l1 + delta for some 0 <= delta < 2**16.
long l1 = ((long) x1 << 16) & mask;
// We have l1 + delta = (l0 + eps)*multiplier + 0xBL (mod 2**48).
// This allows to find an upper bound w for eps * multiplier mod 2**48
// by assuming delta = 2**16-1.
long w = (l1 - l0 * multiplier + 65535L - 0xBL) & mask;
// The reduction eps * multiplier mod 2**48 only cuts off at most 3 bits.
// Hence a simple search is sufficient. The maximal number of loops is 6.
for (long em = w; em < (multiplier << 16); em += 1L << 48) {
// If the high order bits of em are guessed correctly then
// em == eps * multiplier + 65535 - delta.
long eps = em / multiplier;
long state0 = l0 + eps;
long state1 = nextState(state0);
if ((state1 & 0xffffffff0000L) == l1) {
return state0;
}
}
return -1;
}
/**
* Find a seed such that this integer is the result of
*
* <pre>{@code
* Random rand = new Random();
* rand.setSeed(seed);
* return new BigInteger(k, rand);
* }</pre>
*
* where k is max(64, x.BitLength());
*
* <p>Returns -1 if no such seed exists.
*/
// TODO(bleichen): We want to detect cases where some of the bits
// (i.e. most significant bits or least significant bits have
// been modified. Often this happens during the generation
// of primes or other things.
// TODO(bleichen): This method is incomplete.
protected static long getSeedFor(java.math.BigInteger x) {
byte[] bytes = x.toByteArray();
if (bytes.length == 0) {
return -1;
}
ByteBuffer buffer = ByteBuffer.allocate(8);
int offset = bytes[0] == 0 ? 1 : 0;
if (bytes.length - offset < 8) {
int size = bytes.length - offset;
buffer.position(8 - size);
buffer.put(bytes, offset, size);
} else {
buffer.put(bytes, offset, 8);
}
buffer.flip();
buffer.order(java.nio.ByteOrder.LITTLE_ENDIAN);
int x0 = buffer.getInt();
int x1 = buffer.getInt();
long state = getState(x0, x1);
if (state == -1) {
return -1;
}
return getSeedForState(previousState(state));
}
/** Attempts to find a seed such that it generates the prime p. Returns -1 if no seed is found. */
static long getSeedForPrime(BigInteger p) {
int confidence = 64;
Random rand = new Random();
int size = p.bitLength();
// Prime generation often sets the most significant bit.
// Hence, clearing the most significant bit can help to find
// the seed used for the prime generation.
for (BigInteger x : new BigInteger[] {p, p.clearBit(size - 1)}) {
long seed = getSeedFor(x);
if (seed != -1) {
rand.setSeed(seed);
BigInteger q = new BigInteger(size, confidence, rand);
if (q.equals(p)) {
return seed;
}
}
}
return -1;
}
/**
* Checks whether p is a random prime. A prime generated with a secure random number generator
* passes with probability > 1-2^{-32}. No checks are performed for primes smaller than 96 bits.
*
* @throws GeneralSecurityException if the prime was generated using java.util.Random
*/
static void checkPrime(BigInteger p) throws GeneralSecurityException {
// We can't reliably detect java.util.Random for small primes.
if (p.bitLength() < 96) {
return;
}
long seed = getSeedForPrime(p);
if (seed != -1) {
throw new GeneralSecurityException(
"java.util.Random with seed " + seed + " was likely used to generate prime");
}
}
}
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