static SRP()
{
// initialize N
{
NHex =
//512bit
//"D4C7F8A2B32C11B8FBA9581EC4BA4F1B04215642EF7355E37C0FC0443EF756EA2C6B8EEB755A1C723027663CAA265EF785B8FF6A9B35227A52D86633DBDFCA43";
//256bit
"EEAF0AB9ADB38DD69C33F80AFA8FC5E86072618775FF3C0B9EA2314C9C256576D674DF7496EA81D3383B4813D692C6E0E0D5D8E250B98BE48E495C1D6089DAD15DC7D7B46154D6B6CE8EF4AD69B15D4982559B297BCF1885C529F566660E57EC68EDBC3C05726CC02FD4CBF4976EAA9AFD5138FE8376435B9FC61D2FC0EB06E3".ToLowerInvariant();
N = new BigInteger(NHex, 16);
_nbits = N.bitCount();
Nminus1 = N - 1;
// if (!N.isProbablePrime(80))
// {
// throw new Exception("Warning: N is not prime");
// }
//
// if (!(Nminus1 / 2).isProbablePrime(80))
// {
// throw new Exception("Warning: (N-1)/2 is not prime");
// }
}
// initialize g
{
gHex = "2";
g = new BigInteger(gHex, 16);
}
// initialize k = H(N || g)
{
BigInteger ktmp = new BigInteger(HHex(
(((NHex.Length & 1) == 0) ? "" : "0") + NHex +
new string('0', NHex.Length - gHex.Length) + gHex
), 16);
k = (ktmp < N) ? ktmp : (ktmp % N);
kHex = k.ToString(16).ToLowerInvariant().TrimStart('0');
}
// initialize a, A
{
a = new BigInteger();
a.genRandomBits(36);
A = g.modPow(a, N);
while (A.modInverse(N) == 0)
{
a = new BigInteger();
a.genRandomBits(36);
A = g.modPow(a, N);
}
Ahex = A.ToString(16).ToLowerInvariant().TrimStart('0');
}
}
//***********************************************************************
// Probabilistic prime test based on Solovay-Strassen (Euler Criterion)
//
// p is probably prime if for any a < p (a is not multiple of p),
// a^((p-1)/2) mod p = J(a, p)
//
// where J is the Jacobi symbol.
//
// Otherwise, p is composite.
//
// Returns
// -------
// True if "this" is a Euler pseudoprime to randomly chosen
// bases. The number of chosen bases is given by the "confidence"
// parameter.
//
// False if "this" is definitely NOT prime.
//
//***********************************************************************
public bool SolovayStrassenTest(int confidence)
{
BigInteger thisVal;
if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative
thisVal = -this;
else
thisVal = this;
if (thisVal.dataLength == 1)
{
// test small numbers
if (thisVal.data[0] == 0 || thisVal.data[0] == 1)
return false;
else if (thisVal.data[0] == 2 || thisVal.data[0] == 3)
return true;
}
if ((thisVal.data[0] & 0x1) == 0) // even numbers
return false;
int bits = thisVal.bitCount();
BigInteger a = new BigInteger();
BigInteger p_sub1 = thisVal - 1;
BigInteger p_sub1_shift = p_sub1 >> 1;
for (int round = 0; round < confidence; round++)
{
bool done = false;
while (!done) // generate a < n
{
int testBits = 0;
// make sure "a" has at least 2 bits
while (testBits < 2)
testBits = (int)(UnityEngine.Random.value * bits);
a.genRandomBits(testBits);
int byteLen = a.dataLength;
// make sure "a" is not 0
if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1))
done = true;
}
// check whether a factor exists (fix for version 1.03)
BigInteger gcdTest = a.gcd(thisVal);
if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
return false;
// calculate a^((p-1)/2) mod p
BigInteger expResult = a.modPow(p_sub1_shift, thisVal);
if (expResult == p_sub1)
expResult = -1;
// calculate Jacobi symbol
BigInteger jacob = Jacobi(a, thisVal);
//Console.WriteLine("a = " + a.ToString(10) + " b = " + thisVal.ToString(10));
//Console.WriteLine("expResult = " + expResult.ToString(10) + " Jacob = " + jacob.ToString(10));
// if they are different then it is not prime
if (expResult != jacob)
return false;
}
return true;
}
public static void AuthStep2(
string vHex,
string uHex,
string AHex,
string bHex,
string BHex,
out string m1serverHex,
out string m2Hex)
{
BigInteger v = new BigInteger(vHex, 16);
BigInteger u = new BigInteger(uHex, 16);
BigInteger A = new BigInteger(AHex, 16);
BigInteger b = new BigInteger(bHex, 16);
//BigInteger B = new BigInteger(BHex, 16); REMOVED WARNING JOE
// S - common exponential value
// S = (A * v^u) ^ b (mod N)
BigInteger S = ((v.modPow(u, N) * A) % N).modPow(b, N);
// K - the strong cryptographically session key
// K = H(S)
string KHex = HHex(S.ToHexString()).TrimStart('0');
// m2 - expected client's proof as computed by the server
m1serverHex = HHex(
AHex +
BHex +
KHex).TrimStart('0');
// m2 - server's proof that it has the correct key
m2Hex = HHex(
AHex +
m1serverHex +
KHex).TrimStart('0');
}
//***********************************************************************
// Probabilistic prime test based on Rabin-Miller's
//
// for any p > 0 with p - 1 = 2^s * t
//
// p is probably prime (strong pseudoprime) if for any a < p,
// 1) a^t mod p = 1 or
// 2) a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1
//
// Otherwise, p is composite.
//
// Returns
// -------
// True if "this" is a strong pseudoprime to randomly chosen
// bases. The number of chosen bases is given by the "confidence"
// parameter.
//
// False if "this" is definitely NOT prime.
//
//***********************************************************************
public bool RabinMillerTest(int confidence)
{
BigInteger thisVal;
if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative
thisVal = -this;
else
thisVal = this;
if (thisVal.dataLength == 1)
{
// test small numbers
if (thisVal.data[0] == 0 || thisVal.data[0] == 1)
return false;
else if (thisVal.data[0] == 2 || thisVal.data[0] == 3)
return true;
}
if ((thisVal.data[0] & 0x1) == 0) // even numbers
return false;
// calculate values of s and t
BigInteger p_sub1 = thisVal - (new BigInteger(1));
int s = 0;
for (int index = 0; index < p_sub1.dataLength; index++)
{
uint mask = 0x01;
for (int i = 0; i < 32; i++)
{
if ((p_sub1.data[index] & mask) != 0)
{
index = p_sub1.dataLength; // to break the outer loop
break;
}
mask <<= 1;
s++;
}
}
BigInteger t = p_sub1 >> s;
int bits = thisVal.bitCount();
BigInteger a = new BigInteger();
System.Random r = new System.Random ();
for (int round = 0; round < confidence; round++)
{
bool done = false;
while (!done) // generate a < n
{
int testBits = 0;
// make sure "a" has at least 2 bits
while (testBits < 2)
testBits = (int)(r.NextDouble() * bits);
a.genRandomBits(testBits);
int byteLen = a.dataLength;
// make sure "a" is not 0
if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1))
done = true;
}
// check whether a factor exists (fix for version 1.03)
BigInteger gcdTest = a.gcd(thisVal);
if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
return false;
BigInteger b = a.modPow(t, thisVal);
/*
Console.WriteLine("a = " + a.ToString(10));
Console.WriteLine("b = " + b.ToString(10));
Console.WriteLine("t = " + t.ToString(10));
Console.WriteLine("s = " + s);
*/
bool result = false;
if (b.dataLength == 1 && b.data[0] == 1) // a^t mod p = 1
result = true;
for (int j = 0; result == false && j < s; j++)
{
if (b == p_sub1) // a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1
{
result = true;
break;
}
b = (b * b) % thisVal;
}
if (result == false)
return false;
}
return true;
}