Java tutorial
package org.bouncycastle.crypto.generators; import java.math.BigInteger; import java.security.SecureRandom; import org.bouncycastle.crypto.Digest; import org.bouncycastle.crypto.digests.SHA1Digest; import org.bouncycastle.crypto.params.DSAParameterGenerationParameters; import org.bouncycastle.crypto.params.DSAParameters; import org.bouncycastle.crypto.params.DSAValidationParameters; import org.bouncycastle.crypto.util.DigestFactory; import org.bouncycastle.util.Arrays; import org.bouncycastle.util.BigIntegers; import org.bouncycastle.util.encoders.Hex; /** * Generate suitable parameters for DSA, in line with FIPS 186-2, or FIPS 186-3. */ public class DSAParametersGenerator { private static final BigInteger ZERO = BigInteger.valueOf(0); private static final BigInteger ONE = BigInteger.valueOf(1); private static final BigInteger TWO = BigInteger.valueOf(2); private Digest digest; private int L, N; private int certainty; private int iterations; private SecureRandom random; private boolean use186_3; private int usageIndex; public DSAParametersGenerator() { this(DigestFactory.createSHA1()); } public DSAParametersGenerator(Digest digest) { this.digest = digest; } /** * initialise the key generator. * * @param size size of the key (range 2^512 -> 2^1024 - 64 bit increments) * @param certainty measure of robustness of prime (for FIPS 186-2 compliance this should be at least 80). * @param random random byte source. */ public void init(int size, int certainty, SecureRandom random) { this.L = size; this.N = getDefaultN(size); this.certainty = certainty; this.iterations = Math.max(getMinimumIterations(L), (certainty + 1) / 2); this.random = random; this.use186_3 = false; this.usageIndex = -1; } /** * Initialise the key generator for DSA 2. * <p> * Use this init method if you need to generate parameters for DSA 2 keys. * </p> * * @param params DSA 2 key generation parameters. */ public void init(DSAParameterGenerationParameters params) { int L = params.getL(), N = params.getN(); if ((L < 1024 || L > 3072) || L % 1024 != 0) { throw new IllegalArgumentException("L values must be between 1024 and 3072 and a multiple of 1024"); } else if (L == 1024 && N != 160) { throw new IllegalArgumentException("N must be 160 for L = 1024"); } else if (L == 2048 && (N != 224 && N != 256)) { throw new IllegalArgumentException("N must be 224 or 256 for L = 2048"); } else if (L == 3072 && N != 256) { throw new IllegalArgumentException("N must be 256 for L = 3072"); } if (digest.getDigestSize() * 8 < N) { throw new IllegalStateException("Digest output size too small for value of N"); } this.L = L; this.N = N; this.certainty = params.getCertainty(); this.iterations = Math.max(getMinimumIterations(L), (certainty + 1) / 2); this.random = params.getRandom(); this.use186_3 = true; this.usageIndex = params.getUsageIndex(); } /** * which generates the p and g values from the given parameters, * returning the DSAParameters object. * <p> * Note: can take a while... * @return a generated DSA parameters object. */ public DSAParameters generateParameters() { return (use186_3) ? generateParameters_FIPS186_3() : generateParameters_FIPS186_2(); } private DSAParameters generateParameters_FIPS186_2() { byte[] seed = new byte[20]; byte[] part1 = new byte[20]; byte[] part2 = new byte[20]; byte[] u = new byte[20]; int n = (L - 1) / 160; byte[] w = new byte[L / 8]; if (!(digest instanceof SHA1Digest)) { throw new IllegalStateException("can only use SHA-1 for generating FIPS 186-2 parameters"); } for (;;) { random.nextBytes(seed); hash(digest, seed, part1, 0); System.arraycopy(seed, 0, part2, 0, seed.length); inc(part2); hash(digest, part2, part2, 0); for (int i = 0; i != u.length; i++) { u[i] = (byte) (part1[i] ^ part2[i]); } u[0] |= (byte) 0x80; u[19] |= (byte) 0x01; BigInteger q = new BigInteger(1, u); if (!isProbablePrime(q)) { continue; } byte[] offset = Arrays.clone(seed); inc(offset); for (int counter = 0; counter < 4096; ++counter) { { for (int k = 1; k <= n; k++) { inc(offset); hash(digest, offset, w, w.length - k * part1.length); } int remaining = w.length - (n * part1.length); inc(offset); hash(digest, offset, part1, 0); System.arraycopy(part1, part1.length - remaining, w, 0, remaining); w[0] |= (byte) 0x80; } BigInteger x = new BigInteger(1, w); BigInteger c = x.mod(q.shiftLeft(1)); BigInteger p = x.subtract(c.subtract(ONE)); if (p.bitLength() != L) { continue; } if (isProbablePrime(p)) { BigInteger g = calculateGenerator_FIPS186_2(p, q, random); return new DSAParameters(p, q, g, new DSAValidationParameters(seed, counter)); } } } } private static BigInteger calculateGenerator_FIPS186_2(BigInteger p, BigInteger q, SecureRandom r) { BigInteger e = p.subtract(ONE).divide(q); BigInteger pSub2 = p.subtract(TWO); for (;;) { BigInteger h = BigIntegers.createRandomInRange(TWO, pSub2, r); BigInteger g = h.modPow(e, p); if (g.bitLength() > 1) { return g; } } } /** * generate suitable parameters for DSA, in line with * <i>FIPS 186-3 A.1 Generation of the FFC Primes p and q</i>. */ private DSAParameters generateParameters_FIPS186_3() { // A.1.1.2 Generation of the Probable Primes p and q Using an Approved Hash Function // FIXME This should be configurable (digest size in bits must be >= N) Digest d = digest; int outlen = d.getDigestSize() * 8; // 1. Check that the (L, N) pair is in the list of acceptable (L, N pairs) (see Section 4.2). If // the pair is not in the list, then return INVALID. // Note: checked at initialisation // 2. If (seedlen < N), then return INVALID. // FIXME This should be configurable (must be >= N) int seedlen = N; byte[] seed = new byte[seedlen / 8]; // 3. n = ceiling(L / outlen) - 1. int n = (L - 1) / outlen; // 4. b = L - 1 - (n * outlen). int b = (L - 1) % outlen; byte[] w = new byte[L / 8]; byte[] output = new byte[d.getDigestSize()]; for (;;) { // 5. Get an arbitrary sequence of seedlen bits as the domain_parameter_seed. random.nextBytes(seed); // 6. U = Hash (domain_parameter_seed) mod 2^(N1). hash(d, seed, output, 0); BigInteger U = new BigInteger(1, output).mod(ONE.shiftLeft(N - 1)); // 7. q = 2^(N1) + U + 1 ( U mod 2). BigInteger q = U.setBit(0).setBit(N - 1); // 8. Test whether or not q is prime as specified in Appendix C.3. if (!isProbablePrime(q)) { // 9. If q is not a prime, then go to step 5. continue; } // 10. offset = 1. // Note: 'offset' value managed incrementally byte[] offset = Arrays.clone(seed); // 11. For counter = 0 to (4L 1) do int counterLimit = 4 * L; for (int counter = 0; counter < counterLimit; ++counter) { // 11.1 For j = 0 to n do // Vj = Hash ((domain_parameter_seed + offset + j) mod 2^seedlen). // 11.2 W = V0 + (V1 2^outlen) + ... + (V^(n1) 2^((n1) outlen)) + ((Vn mod 2^b) 2^(n outlen)). { for (int j = 1; j <= n; ++j) { inc(offset); hash(d, offset, w, w.length - j * output.length); } int remaining = w.length - (n * output.length); inc(offset); hash(d, offset, output, 0); System.arraycopy(output, output.length - remaining, w, 0, remaining); // 11.3 X = W + 2^(L1). Comment: 0 W < 2^(L1); hence, 2^(L1) X < 2^L. w[0] |= (byte) 0x80; } BigInteger X = new BigInteger(1, w); // 11.4 c = X mod 2q. BigInteger c = X.mod(q.shiftLeft(1)); // 11.5 p = X - (c - 1). Comment: p 1 (mod 2q). BigInteger p = X.subtract(c.subtract(ONE)); // 11.6 If (p < 2^(L-1)), then go to step 11.9 if (p.bitLength() != L) { continue; } // 11.7 Test whether or not p is prime as specified in Appendix C.3. if (isProbablePrime(p)) { // 11.8 If p is determined to be prime, then return VALID and the values of p, q and // (optionally) the values of domain_parameter_seed and counter. if (usageIndex >= 0) { BigInteger g = calculateGenerator_FIPS186_3_Verifiable(d, p, q, seed, usageIndex); if (g != null) { return new DSAParameters(p, q, g, new DSAValidationParameters(seed, counter, usageIndex)); } } BigInteger g = calculateGenerator_FIPS186_3_Unverifiable(p, q, random); return new DSAParameters(p, q, g, new DSAValidationParameters(seed, counter)); } // 11.9 offset = offset + n + 1. Comment: Increment offset; then, as part of // the loop in step 11, increment counter; if // counter < 4L, repeat steps 11.1 through 11.8. // Note: 'offset' value already incremented in inner loop } // 12. Go to step 5. } } private boolean isProbablePrime(BigInteger x) { /* * TODO Use Primes class for FIPS 186-4 C.3 primality checking - but it breaks existing * tests using FixedSecureRandom */ // return !Primes.hasAnySmallFactors(x) && Primes.isMRProbablePrime(x, random, iterations); return x.isProbablePrime(certainty); } private static BigInteger calculateGenerator_FIPS186_3_Unverifiable(BigInteger p, BigInteger q, SecureRandom r) { return calculateGenerator_FIPS186_2(p, q, r); } private static BigInteger calculateGenerator_FIPS186_3_Verifiable(Digest d, BigInteger p, BigInteger q, byte[] seed, int index) { // A.2.3 Verifiable Canonical Generation of the Generator g BigInteger e = p.subtract(ONE).divide(q); byte[] ggen = Hex.decodeStrict("6767656E"); // 7. U = domain_parameter_seed || "ggen" || index || count. byte[] U = new byte[seed.length + ggen.length + 1 + 2]; System.arraycopy(seed, 0, U, 0, seed.length); System.arraycopy(ggen, 0, U, seed.length, ggen.length); U[U.length - 3] = (byte) index; byte[] w = new byte[d.getDigestSize()]; for (int count = 1; count < (1 << 16); ++count) { inc(U); hash(d, U, w, 0); BigInteger W = new BigInteger(1, w); BigInteger g = W.modPow(e, p); if (g.compareTo(TWO) >= 0) { return g; } } return null; } private static void hash(Digest d, byte[] input, byte[] output, int outputPos) { d.update(input, 0, input.length); d.doFinal(output, outputPos); } private static int getDefaultN(int L) { return L > 1024 ? 256 : 160; } private static int getMinimumIterations(int L) { // Values based on FIPS 186-4 C.3 Table C.1 return L <= 1024 ? 40 : (48 + 8 * ((L - 1) / 1024)); } private static void inc(byte[] buf) { for (int i = buf.length - 1; i >= 0; --i) { byte b = (byte) ((buf[i] + 1) & 0xff); buf[i] = b; if (b != 0) { break; } } } }