예제 #1
0
파일: xtr.cpp 프로젝트: bonjorno7/GAME
void XTR_FindPrimesAndGenerator(RandomNumberGenerator &rng, Integer &p, Integer &q, GFP2Element &g, unsigned int pbits, unsigned int qbits)
{
	CRYPTOPP_ASSERT(qbits > 9);	// no primes exist for pbits = 10, qbits = 9
	CRYPTOPP_ASSERT(pbits > qbits);

	const Integer minQ = Integer::Power2(qbits - 1);
	const Integer maxQ = Integer::Power2(qbits) - 1;
	const Integer minP = Integer::Power2(pbits - 1);
	const Integer maxP = Integer::Power2(pbits) - 1;

top:

	Integer r1, r2;
	do
	{
		(void)q.Randomize(rng, minQ, maxQ, Integer::PRIME, 7, 12);
		// Solution always exists because q === 7 mod 12.
		(void)SolveModularQuadraticEquation(r1, r2, 1, -1, 1, q);
		// I believe k_i, r1 and r2 are being used slightly different than the
		// paper's algorithm. I believe it is leading to the failed asserts.
		// Just make the assert part of the condition.
		if(!p.Randomize(rng, minP, maxP, Integer::PRIME, CRT(rng.GenerateBit() ?
			r1 : r2, q, 2, 3, EuclideanMultiplicativeInverse(p, 3)), 3 * q)) { continue; }
	} while (((p % 3U) != 2) || (((p.Squared() - p + 1) % q).NotZero()));

	// CRYPTOPP_ASSERT((p % 3U) == 2);
	// CRYPTOPP_ASSERT(((p.Squared() - p + 1) % q).IsZero());

	GFP2_ONB<ModularArithmetic> gfp2(p);
	GFP2Element three = gfp2.ConvertIn(3), t;

	while (true)
	{
		g.c1.Randomize(rng, Integer::Zero(), p-1);
		g.c2.Randomize(rng, Integer::Zero(), p-1);
		t = XTR_Exponentiate(g, p+1, p);
		if (t.c1 == t.c2)
			continue;
		g = XTR_Exponentiate(g, (p.Squared()-p+1)/q, p);
		if (g != three)
			break;
	}

	if (XTR_Exponentiate(g, q, p) != three)
		goto top;

	// CRYPTOPP_ASSERT(XTR_Exponentiate(g, q, p) == three);
}
예제 #2
0
bool XTR_DH::Agree(byte *agreedValue, const byte *privateKey, const byte *otherPublicKey, bool validateOtherPublicKey) const
{
	GFP2Element w(otherPublicKey, PublicKeyLength());
	if (validateOtherPublicKey)
	{
		GFP2_ONB<ModularArithmetic> gfp2(m_p);
		GFP2Element three = gfp2.ConvertIn(3);
		if (w.c1.IsNegative() || w.c2.IsNegative() || w.c1 >= m_p || w.c2 >= m_p || w == three)
			return false;
		if (XTR_Exponentiate(w, m_q, m_p) != three)
			return false;
	}
	Integer s(privateKey, PrivateKeyLength());
	GFP2Element z = XTR_Exponentiate(w, s, m_p);
	z.Encode(agreedValue, AgreedValueLength());
	return true;
}
예제 #3
0
bool XTR_DH::Validate(RandomNumberGenerator &rng, unsigned int level) const
{
	bool pass = true;
	pass = pass && m_p > Integer::One() && m_p.IsOdd();
	pass = pass && m_q > Integer::One() && m_q.IsOdd();
	GFP2Element three = GFP2_ONB<ModularArithmetic>(m_p).ConvertIn(3);
	pass = pass && !(m_g.c1.IsNegative() || m_g.c2.IsNegative() || m_g.c1 >= m_p || m_g.c2 >= m_p || m_g == three);
	if (level >= 1)
		pass = pass && ((m_p.Squared()-m_p+1)%m_q).IsZero();
	if (level >= 2)
	{
		pass = pass && VerifyPrime(rng, m_p, level-2) && VerifyPrime(rng, m_q, level-2);
		pass = pass && XTR_Exponentiate(m_g, (m_p.Squared()-m_p+1)/m_q, m_p) != three;
		pass = pass && XTR_Exponentiate(m_g, m_q, m_p) == three;
	}
	return pass;
}
예제 #4
0
파일: xtr.cpp 프로젝트: Andy-Amoy/cryptopp
void XTR_FindPrimesAndGenerator(RandomNumberGenerator &rng, Integer &p, Integer &q, GFP2Element &g, unsigned int pbits, unsigned int qbits)
{
	assert(qbits > 9);	// no primes exist for pbits = 10, qbits = 9
	assert(pbits > qbits);

	const Integer minQ = Integer::Power2(qbits - 1);
	const Integer maxQ = Integer::Power2(qbits) - 1;
	const Integer minP = Integer::Power2(pbits - 1);
	const Integer maxP = Integer::Power2(pbits) - 1;

	Integer r1, r2;
	do
	{
		bool qFound = q.Randomize(rng, minQ, maxQ, Integer::PRIME, 7, 12);
		CRYPTOPP_UNUSED(qFound); assert(qFound);
		bool solutionsExist = SolveModularQuadraticEquation(r1, r2, 1, -1, 1, q);
		CRYPTOPP_UNUSED(solutionsExist); assert(solutionsExist);
	} while (!p.Randomize(rng, minP, maxP, Integer::PRIME, CRT(rng.GenerateBit()?r1:r2, q, 2, 3, EuclideanMultiplicativeInverse(p, 3)), 3*q));
	assert(((p.Squared() - p + 1) % q).IsZero());

	GFP2_ONB<ModularArithmetic> gfp2(p);
	GFP2Element three = gfp2.ConvertIn(3), t;

	while (true)
	{
		g.c1.Randomize(rng, Integer::Zero(), p-1);
		g.c2.Randomize(rng, Integer::Zero(), p-1);
		t = XTR_Exponentiate(g, p+1, p);
		if (t.c1 == t.c2)
			continue;
		g = XTR_Exponentiate(g, (p.Squared()-p+1)/q, p);
		if (g != three)
			break;
	}
	assert(XTR_Exponentiate(g, q, p) == three);
}
예제 #5
0
void XTR_DH::GeneratePublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const
{
	Integer x(privateKey, PrivateKeyLength());
	GFP2Element y = XTR_Exponentiate(m_g, x, m_p);
	y.Encode(publicKey, PublicKeyLength());
}