private static void ZKPCracker()
{
System.Console.WriteLine("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
System.Console.Write("\nn: ");
Integer n = Tools.ToInteger(Console.ReadLine());
Integer p;
while (true)
{
var t = MathI.RandomI();
var y = t.ModPow(2, n);
System.Console.WriteLine($"y: {y.ToHexString()}");
System.Console.Write("z: ");
var z = Tools.ToInteger(Console.ReadLine());
if (y != z || y != -z)
{
p = NumberTheory.GCD(t + z, n);
if (p != 1)
{
break;
}
}
System.Console.WriteLine("___________________");
}
System.Console.WriteLine("\n\nEnd of attack");
var q = n / p;
System.Console.WriteLine($"p: {p.ToHexString()}");
System.Console.WriteLine($"q: {q.ToHexString()}");
System.Console.WriteLine($"Test n: {(p * q).ToHexString()}");
}
public Fraction(long numerator, long denominator)
{
long GreatestCommonDivisor = NumberTheory.GCD(numerator, denominator);
m_numerator = numerator / GreatestCommonDivisor;
m_denominator = denominator / GreatestCommonDivisor;
}
public void GCDTest(long a, long b)
{
//action
long gcd = NumberTheory.GCD(a, b);
//assert
(a % gcd).Should().Be(0L);
(b % gcd).Should().Be(0L);
}
private void f4_button_GetRandomCb_Click(object sender, EventArgs e)
{
BigInteger P = BigInteger.Parse(f4_textP.Text);
RandomNumberGenerator rng = RandomNumberGenerator.Create();
BigInteger Db, Cb = BigIntegerRandomUtils.RandomInRange(rng, 2, P - 1);
while (!(NumberTheory.GCD(Cb, P - 1, out BigInteger x, out BigInteger y) == 1))
{
Cb = BigIntegerRandomUtils.RandomInRange(rng, 2, P - 1);
}
;
f4_textCb.Text = Convert.ToString(Cb);
}
private void f9_button_GetRandomSecret_Click(object sender, EventArgs e)
{
RandomNumberGenerator rng = RandomNumberGenerator.Create();
BigInteger N = BigInteger.Parse(f9_textN.Text);
BigInteger P = BigInteger.Parse(f9_textP.Text);
BigInteger Q = BigInteger.Parse(f9_textQ.Text);
BigInteger fi = (P - 1) * (Q - 1); // Функция Эйлера от N
BigInteger SecretKey = BigIntegerRandomUtils.RandomInRange(rng, 2, N - 1);
while (NumberTheory.GCD(SecretKey, fi, out BigInteger x, out BigInteger y) != 1)
{
SecretKey = BigIntegerRandomUtils.RandomInRange(rng, 2, N - 1);
}
f9_textSecretKey.Text = Convert.ToString(SecretKey);
}
private void f4_button_SetCb_Click(object sender, EventArgs e)
{
f4_textCb.Text = new string(f4_textCb.Text.Where(t => char.IsDigit(t)).ToArray());
if (f4_textCb.TextLength > 0)
{
BigInteger P = BigInteger.Parse(f4_textP.Text);
BigInteger Cb = BigInteger.Parse(f4_textCb.Text);
if ((NumberTheory.GCD(Cb, P - 1, out BigInteger x, out BigInteger y) == 1))
{
f4_textDb.Text = Convert.ToString(NumberTheory.Foo(Cb, P - 1));
f4_textCb.ReadOnly = true;
f4_button_GetRandomCb.Enabled = false;
f4_button_SetCb.Enabled = false;
f4_button_ChangeCb.Enabled = true;
}
}
}
private void f9_button_SetSecretKey_Click(object sender, EventArgs e)
{
f9_textSecretKey.Text = new string(f9_textSecretKey.Text.Where(t => char.IsDigit(t)).ToArray());
BigInteger SecretKey;
BigInteger P = BigInteger.Parse(f9_textP.Text);
BigInteger Q = BigInteger.Parse(f9_textQ.Text);
BigInteger N = BigInteger.Parse(f9_textN.Text);
BigInteger fi = (P - 1) * (Q - 1); // Функция Эйлера от N
if (f9_textSecretKey.TextLength > 0)
{
SecretKey = BigInteger.Parse(f9_textSecretKey.Text);
SecretKey = SecretKey % N;
if (SecretKey > 1 && NumberTheory.GCD(SecretKey, fi, out BigInteger x, out BigInteger y) == 1)
{
f9_textOpenKey.Text = Convert.ToString(NumberTheory.Foo(SecretKey, fi));
f9_button_SetSecretKey.Enabled = false;
f9_button_GetRandomSecret.Enabled = false;
f9_button_ClearSecretKey.Enabled = true;
f9_buttonSign.Enabled = true;
}
}
}
static void Main(String[] args)
{
Console.WriteLine(NumberTheory.GCD(123, 12));
Console.ReadKey();
}
/// <summary>
/// A.1.2.1.2
/// </summary>
/// <param name="L"></param>
/// <param name="N"></param>
/// <param name="firstSeed"></param>
/// <returns></returns>
private PQGenerateResult Generate(int L, int N, BigInteger firstSeed)
{
// 1
if (!DSAHelper.VerifyLenPair(L, N))
{
return(new PQGenerateResult("Bad L, N pair"));
}
// 2
var qResult = PrimeGen186_4.ShaweTaylorRandomPrime(N, firstSeed, _sha);
if (!qResult.Success)
{
return(new PQGenerateResult("Failed to generate q from ShaweTaylor"));
}
var q = qResult.Prime;
var qSeed = qResult.PrimeSeed;
var qCounter = qResult.PrimeGenCounter;
// 3
var pLen = L.CeilingDivide(2) + 1;
var pResult = PrimeGen186_4.ShaweTaylorRandomPrime(pLen, qSeed, _sha);
if (!pResult.Success)
{
return(new PQGenerateResult("Failed to generate p0 from ShaweTaylor"));
}
var p0 = pResult.Prime;
var pSeed = pResult.PrimeSeed;
var pCounter = pResult.PrimeGenCounter;
// 4, 5
var outLen = _sha.HashFunction.OutputLen;
var iterations = L.CeilingDivide(outLen) - 1;
var oldCounter = pCounter;
// 6, 7
BigInteger x = 0;
for (var i = 0; i <= iterations; i++)
{
x += _sha.HashNumber(pSeed + i).ToBigInteger() * NumberTheory.Pow2(i * outLen);
}
// 8
pSeed += iterations + 1;
// 9
x = NumberTheory.Pow2(L - 1) + (x % NumberTheory.Pow2(L - 1));
// 10
var t = x.CeilingDivide(2 * q * p0);
do
{
// 11
if (2 * t * q * p0 + 1 > NumberTheory.Pow2(L))
{
t = NumberTheory.Pow2(L - 1).CeilingDivide(2 * q * p0);
}
// 12, 13
var p = 2 * t * q * p0 + 1;
pCounter++;
// 14, 15
BigInteger a = 0;
for (var i = 0; i <= iterations; i++)
{
a += _sha.HashNumber(pSeed + i).ToBigInteger() * NumberTheory.Pow2(i * outLen);
}
// 16
pSeed += iterations + 1;
// 17
a = 2 + (a % (p - 3));
// 18
var z = BigInteger.ModPow(a, 2 * t * q, p);
// 19
if (1 == NumberTheory.GCD(z - 1, p) && 1 == BigInteger.ModPow(z, p0, p))
{
return(new PQGenerateResult(p, q, new DomainSeed(firstSeed, pSeed, qSeed), new Counter(pCounter, qCounter)));
}
// 20
if (pCounter > 4 * L + oldCounter)
{
return(new PQGenerateResult("Too many iterations"));
}
// 21
t++;
// 22
} while (true);
}
public override object Evaluate()
{
return((Complex)NumberTheory.GCD(Expressions.Select(x => x.EvaluateAsInt64()).ToArray()));
}
private PrimeGeneratorResult GeneratePrimes(PrimeGeneratorParameters param)
{
// 1, 2, 3 performed by guards
// 4, 4.1
var i = 0;
BigInteger p = 0;
var pqLowerBound = GetBound(param.Modulus);
do
{
do
{
// 4.2
if (p != 0 && _kat)
{
return(new PrimeGeneratorResult("Given p less than sqrt(2) * 2 ^ (n/2) - 1, need to get a new random number."));
}
p = _entropyProvider.GetEntropy(param.Modulus / 2).ToPositiveBigInteger();
// 4.3
if (_performAShift)
{
p += (param.A - p).PosMod(8);
}
else if (p.IsEven)
{
p++;
}
// 4.4
} while (p < pqLowerBound);
// 4.5
if (NumberTheory.GCD(p - 1, param.PublicE) == 1)
{
if (PrimeGeneratorHelper.MillerRabin(_primeTestMode, param.Modulus, p, false))
{
break;
}
}
// 4.6, 4.7
i++;
if (i >= _iBoundForP * (param.Modulus / 2))
{
return(new PrimeGeneratorResult("Too many iterations for p"));
}
if (_kat)
{
return(new PrimeGeneratorResult("Given p is not prime"));
}
} while (!_kat);
// 5, 5.1
i = 0;
BigInteger q = 0;
do
{
do
{
// 5.2
if (q != 0 && _kat)
{
return(new PrimeGeneratorResult("Given q less than sqrt(2) * 2 ^ (n/2) - 1, need to get a new random number."));
}
q = _entropyProvider.GetEntropy(param.Modulus / 2).ToPositiveBigInteger();
// 5.3
if (_performBShift)
{
q += (param.B - q).PosMod(8);
}
else if (q.IsEven)
{
q++;
}
// 5.4
// 5.5
} while (BigInteger.Abs(p - q) <= NumberTheory.Pow2(param.Modulus / 2 - 100) || q < pqLowerBound);
// 5.6
if (NumberTheory.GCD(q - 1, param.PublicE) == 1)
{
if (PrimeGeneratorHelper.MillerRabin(_primeTestMode, param.Modulus, q, false))
{
break;
}
}
// 5.7, 5.8
i++;
if (i >= _iBoundForQ * (param.Modulus / 2))
{
return(new PrimeGeneratorResult("Too many iterations for q"));
}
if (_kat)
{
return(new PrimeGeneratorResult("Given q is not prime"));
}
} while (!_kat);
var auxValues = new AuxiliaryResult();
var primePair = new PrimePair {
P = p, Q = q
};
return(new PrimeGeneratorResult(primePair, auxValues));
}