// also checks if GCD(result - 1, f) == 1
/// <summary>
/// Gets next prime number that is greater
/// equal than Min, and less, than Max and
/// GCD(number - 1, f) = 1
/// </summary>
/// <param name="Min">Lower bound of interval</param>
/// <param name="Max">Upper bound of interval</param>
/// <param name="f">Number f</param>
/// <returns>Prime long number</returns>
public ULongIntB Next(ULongIntB Min, ULongIntB Max, SLongIntB f)
{
if (Min > Max)
throw new ArgumentException("Lower bound is less, that upper bound!");
if (LongMath.IsEven(f))
throw new ArgumentException("Argument 'f' cannot be even!");
ULongIntB p = new ULongIntB(rand.Next(Min, Max), ConstructorMode.Assign);
ULongIntB t = Max - Min;
if (LongMath.IsEven(p))
++p;
if (p > Max)
p = Min + (p % (t + 1));
while (CryptoMath.TestPrimeMillerRabin(p, RoundsNumber.Rounds25) == PrimeTestResult.Composite
|| (CryptoMath.GCD((SLongIntB)p - 1, f) == 1))
{
++p;
++p;
while (p > Max)
{
p = Min + (p % (t + 1));
if (LongMath.IsEven(p))
++p;
}
}
return p;
}
public void PowerTest3()
{
SLongIntB A = new SLongIntB("-98276598235872");
short r = 12, s = 31;
Assert.AreEqual(LongMath.Exp(A, (ulong)(r + s)), LongMath.Exp(A, (ulong)r) * LongMath.Exp(A, (ulong)s));
}
public static SLongIntB ChineRem(SLongIntB[] coefs, SLongIntB[] modules)
{
if (coefs.Length != modules.Length)
throw new ArgumentException("Input parameters have different sizes.");
int i = 0;
SLongIntB m = modules[i];
SLongIntB x = coefs[i];
SLongIntB U = null;
SLongIntB V = null;
while (i < coefs.Length - 1)
{
++i;
SLongIntB gcd = eXtendedGCD(m, modules[i], out U, out V);
if (gcd != 1)
throw new WrondResultException("Modules are not coprime!");
SLongIntB temp = U*m*coefs[i] + V*modules[i]*x;
m = m*modules[i];
x = temp % m;
x.LongSign = SignTransformer.GetLSign(temp.Sign*m.Sign);
}
return x;
}
/// <summary>
/// Provides all operations needed to
/// get public and private RSA keys. Must
/// be called before other methods of this class
/// </summary>
/// <param name="bitLength">Length of key</param>
public void GenerateRSAKey(BitLength bitLength)
{
key = new RSAKey();
// find prime numbers p and q
CalculatePQ(bitLength);
// n is product of found numbers
key.N = (SLongIntB)(p * q);
--p;
--q;
// eiler number equals (p - 1)*(q - 1)
eilerNumber = (SLongIntB) (p * q);
++p;
++q;
SLongIntB tempEiler = eilerNumber - 1;
SLongIntB e = new SLongIntB(rand.NextPQ(p, q), ConstructorMode.Assign);
while ((CryptoMath.GCD(e, eilerNumber) != 1) || (e > tempEiler))
{
e = new SLongIntB(rand.NextPQ(p, q), ConstructorMode.Assign);
}
key.E = e;
SLongIntB d = null;
CryptoMath.eXGCDInvertedSafe(e, eilerNumber, out d);
key.D = d;
generated = true;
}
public void PowerTest1()
{
SLongIntB A = new SLongIntB("-98276598235872");
SLongIntB B = (SLongIntB)1;
short k = 120;
for (int i = 0; i < (int)k; ++i)
B *= A;
Assert.AreEqual(LongMath.Exp(A, (ulong)k), B);
}
public void TestAddition2()
{
SLongIntB A = new SLongIntB("-982");
SLongIntB B = new SLongIntB(A);
for (int i = 1; i < 1000; ++i)
{
A++;
Assert.AreEqual(A, B + (short)i);
}
}
public void TestAddition1()
{
SLongIntB A = new SLongIntB("-98276598235872687523562056");
SLongIntB B = (SLongIntB)0;
short k = 120;
for (int i = 0; i < (int)k; ++i)
B += A;
Assert.AreEqual(k*A, B);
A *= -1;
B = (SLongIntB)0;
for (int i = 0; i < (int)k; ++i)
B += A;
Assert.AreEqual(k*A, B);
}
public void TestSubstraction2()
{
SLongIntB A = new SLongIntB("239");
SLongIntB B = new SLongIntB(A);
for (int i = 1; i < 1000; ++i)
{
--A;
Assert.AreEqual(A, B - (short)i);
}
}
public void TestSubstraction3()
{
SLongIntB N = new SLongIntB("2945729752935981200000005151659293467923476293623");
RandomLong rand = new RandomLong((ulong)DateTime.Now.Millisecond);
for (int i = 0; i < 1000; ++i)
{
SLongIntB A = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB B = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB C = A - B;
Assert.AreEqual(C + B, A);
Assert.AreEqual(LongMath.Abs(C - A), B);
Assert.AreEqual(C - 0, C);
Assert.AreEqual(C - C, (SLongIntB)0);
}
}
public void TestSquare2()
{
SLongIntB N = new SLongIntB("2945729752935981200000005151659293467923476293623");
RandomLong rand = new RandomLong((ulong)DateTime.Now.Millisecond);
for (int i = 0; i < 1000; ++i)
{
SLongIntB temp = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
Assert.AreEqual(temp*temp, LongMath.Sqr(temp));
}
}
public void TestSubstraction1()
{
SLongIntB N = new SLongIntB("2945729752935981200000005151659293467923476293623");
RandomLong rand = new RandomLong((ulong)DateTime.Now.Millisecond);
for (int i = 0; i < 1000; ++i)
{
SLongIntB A = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB B = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB C = A + B;
Assert.AreEqual(C - B, A, C.ToString() + " " + B.ToString());
Assert.AreEqual(C - A, B, C.ToString() + " " + A.ToString());
Assert.AreEqual(C - 0, C);
Assert.AreEqual(C - C, (SLongIntB)0);
}
}
public void TestShifts2()
{
SLongIntB A = new SLongIntB("-98276598235872");
SLongIntB B = new SLongIntB(A);
for (int i = 1; i < 11; ++i)
{
SLongIntB C = new SLongIntB(A);
C.ShR((uint)i);
B /= 2;
Assert.AreEqual(C, B);
}
}
public void TestShifts4()
{
SLongIntB A = new SLongIntB("-98276598235872");
SLongIntB B = new SLongIntB(A);
A.Mod2n(10);
ushort b = B % 1024;
Assert.AreEqual(A, (SLongIntB)b);
}
public RSAPrivateKey(SLongIntB dKey, SLongIntB nKey)
{
d = new SLongIntB(dKey);
n = new SLongIntB(nKey);
}
public void TestDivision1()
{
SLongIntB N = new SLongIntB("2945729752935981200000005151659293467923476293623");
RandomLong rand = new RandomLong((ulong)DateTime.Now.Millisecond);
for (int i = 0; i < 1000; ++i)
{
SLongIntB A = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB B = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB C = A*B;
if (C == 0)
continue;
Assert.AreEqual(C / B, A);
Assert.AreEqual(C / A, B);
}
}
/// <summary>
/// Divides input number by 2 while can
/// </summary>
/// <param name="A">Input number</param>
/// <param name="k">Number of times, that value is diveded by 2</param>
public static void SelfTwoFact(SLongIntB A, out int k)
{
k = 0;
if (A == 0)
return;
while (LongMath.IsEven(A))
{
A.Shr();
++k;
}
}
/// <summary>
/// Calculates square of input signed number N times by modulo
/// </summary>
/// <param name="a">Input number</param>
/// <param name="n">Number of times to calculate square</param>
/// <param name="m">Modulo</param>
/// <returns>[ a ^ (2*n) ] % m</returns>
public static SLongIntB NSquareMod(SLongIntB a, uint n, SLongIntB m)
{
SLongIntB res = a % m;
for (int i = 0; i < n; ++i)
res = LongMath.Sqr(res) % m;
return res;
}
//[Test()]
public void TestExtendedGCD()
{
SLongIntB N = new SLongIntB("2945729752935981200000005151659293467923476293623");
RandomLong rand = new RandomLong((ulong)DateTime.Now.Millisecond);
SLongIntB U = null, V = null;
for (int i = 0; i < 1000; ++i)
{
SLongIntB temp1 = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB temp2 = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB gcd = CryptoMath.eXtendedGCD(temp1, temp2, out U, out V);
SLongIntB gcdB = CryptoMath.GCD(temp1, temp2);
Assert.AreEqual(gcd, temp1*U + temp2*V);
Assert.AreEqual(gcd, gcdB, temp1.ToString() + " " + temp2.ToString() + " " + gcd.ToString() + " " + gcdB.ToString());
}
}
/// <summary>
/// Calculates square of input signed number by modulo
/// </summary>
/// <param name="a">Input number</param>
/// <param name="m">Modulo</param>
/// <returns>(a*a) % m</returns>
public static SLongIntB SquareMod(SLongIntB a, SLongIntB m)
{
return LongMath.Sqr(a) % m;
}
public void TestDivision2()
{
SLongIntB N = new SLongIntB("2945729752935981200000005151659293467923476293623");
RandomLong rand = new RandomLong((ulong)DateTime.Now.Millisecond);
for (int i = 0; i < 1000; ++i)
{
SLongIntB A = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB B = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
if (B == 0)
continue;
if ((B * (A / B)) + (A % B) != A)
{
Console.WriteLine(A);
Console.WriteLine(B);
Console.WriteLine((A/B).ToString());
Console.WriteLine((A%B).ToString());
}
Assert.AreEqual((B * (A / B)) + (A % B), A, string.Join(" ",
new string[]{ A.ToString(), B.ToString(), (A/B).ToString(), (A%B).ToString() }));
}
}
public static SLongIntB LCM(SLongIntB A, SLongIntB B)
{
return (A*B) / GCD(A, B);
}
/// <summary>
/// Calculates Jacobi symbol for long numbers A and B - (A/B)
/// </summary>
/// <param name="A"></param>
/// <param name="B"></param>
/// <returns></returns>
public static int JacobiSymbol(SLongIntB a, SLongIntB b)
{
if (b.IsZero())
{
if (a == 1 || a == -1)
return 1;
else
return 0;
}
if (LongMath.IsEven(a) && LongMath.IsEven(b))
return 0;
SLongIntB A = new SLongIntB(a);
SLongIntB B = new SLongIntB(b);
sbyte[] mods = new sbyte[] { 0, 1, 0, -1, 0, -1, 0, 1 };
int v = 0;
SelfTwoFact(B, out v);
int k = 1;
if (v % 2 == 1)
k = mods[A[0] & 7];
LongMath.SelfAbs(B);
if (A < 0)
k = -k;
while (A > 0)
{
SelfTwoFact(A, out v);
if (v % 2 == 1)
k = mods[B[0] & 7] * k;
if ((A[0] & B[0] & 2) != 0)
k = -k;
SLongIntB r = LongMath.Abs(A);
A.Assign(B % r);
B.Assign(r);
}
if (B > 1)
return 0;
else
return k;
}
public void TestMul1()
{
SLongIntB N = new SLongIntB("2945729752935981200000005151659293467923476293623");
RandomLong rand = new RandomLong((ulong)DateTime.Now.Millisecond);
for (int i = 0; i < 1000; ++i)
{
SLongIntB temp1 = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB temp2 = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB temp3 = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
Assert.AreEqual((temp1*temp2)*temp3, temp1*(temp2*temp3));
}
}
public static void TwoFact(SLongIntB A, out SLongIntB u, out int k)
{
k = 0;
u = new SLongIntB(A);
if (A == 0)
return;
while (LongMath.IsEven(u))
{
++k;
u.Shr();
}
}
public void TestBinaryDecimalCast()
{
SLongIntB A = new SLongIntB("-20976982698769825692774362798672976276668754000000000000000765700000000");
SLongIntD B = (SLongIntD)A;
Assert.AreEqual(A.ToString(), B.ToString());
Assert.AreEqual((SLongIntD)A, B);
Assert.AreEqual(A, (SLongIntB)B);
}
public void TestPower()
{
SLongIntB N = new SLongIntB("2945");
RandomLong rand = new RandomLong((ulong)DateTime.Now.Millisecond);
Random rand32 = new Random(DateTime.Now.Millisecond);
SLongIntB m = new SLongIntB("98696766574783");
for (int i = 0; i < 100; ++i)
{
SLongIntB temp = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
int power = rand32.Next(ushort.MaxValue) % 10000;
Assert.AreEqual(CryptoMath.ExpMod5((ULongIntB)temp, (ULongIntB)power, (ULongIntB)m), LongMath.Exp((ULongIntB)temp, (ulong)power) % (ULongIntB)m,
temp.ToString() + "^" + power.ToString());
}
}
public static SLongIntB StupidGCD(SLongIntB a, SLongIntB b)
{
while (b != 0)
{
SLongIntB r = a % b;
a.Assign(b);
b.Assign(r);
}
return a;
}
public void TestShiftRight()
{
SLongIntB N = new SLongIntB("2945729752935981200000005151659293467923476293623");
RandomLong rand = new RandomLong((ulong)DateTime.Now.Millisecond);
for (int i = 0; i < 1000; ++i)
{
SLongIntB temp1 = new SLongIntB(rand.Next(N), ConstructorMode.Assign);
SLongIntB temp3 = new SLongIntB(temp1);
temp1.Shr();
SLongIntB temp2 = new SLongIntB(temp1);
temp2.Shl();
Assert.AreEqual(temp1 * 2, temp2);
Assert.AreEqual(temp1, temp3 / 2);
}
}
public RSAPublicKey(SLongIntB eKey, SLongIntB nKey)
{
e = new SLongIntB(eKey);
n = new SLongIntB(nKey);
}
public void TestShifts1()
{
SLongIntB A = new SLongIntB("-98276598235872");
SLongIntB B = new SLongIntB(A);
for (int i = 0; i < 10; ++i)
{
A.Shr();
B /= 2;
Assert.AreEqual(A, B);
}
for (int i = 0; i < 10; ++i)
{
A.Shl();
B *= 2;
Assert.AreEqual(A, B);
}
}