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');
}
}
/// <summary>
/// Generate a new SRP verifier. Password is the plaintext password.
/// </summary>
/// <returns>The verifier.</returns>
/// <param name="password">Password.</param>
//original: (didn't work with 3.5 .Net compiler and was annoying to keep switching to 4.0
//public static Meteor.Verifier GenerateVerifier(string password, string identity = null, string salt = null)
public static Meteor.Verifier GenerateVerifier(string password, string identity, string salt)
{
if (identity == null)
{
BigInteger i = new BigInteger ();
i.genRandomBits (36);
identity = i.ToString(16).ToLowerInvariant().TrimStart('0');
}
if (salt == null)
{
BigInteger s = new BigInteger ();
s.genRandomBits (36);
salt = s.ToString(16).ToLowerInvariant().TrimStart('0');
}
string x = Hash (salt + Hash (identity + ":" + password));
BigInteger xi = new BigInteger (x, 16);
BigInteger v = g.modPow (xi, N);
return new Meteor.Verifier () {
identity = identity,
salt = salt,
verifier = v.ToString(16).ToLowerInvariant().TrimStart('0')
};
}
public static void AuthStep1(
string vHex,
string AHex,
out string bHex,
out string BHex,
out string uHex)
{
BigInteger v = new BigInteger(vHex, 16);
//BigInteger A = new BigInteger(AHex, 16); REMOVED WARNING
BigInteger b;
// b - ephemeral private key
// b = random between 2 and N-1
{
b = new BigInteger();
//[TODO] perhaps here use a better random generator
b.genRandomBits(_nbits);
if (b >= N)
{
b = b % Nminus1;
}
if (b < 2)
{
b = 2;
}
}
bHex = b.ToHexString();
// B = public key
// B = kv + g^b (mod N)
BigInteger B = (v * k + g.modPow(b, N)) % N;
BHex = B.ToHexString();
BigInteger u;
// u - scrambling parameter
// u = H (A || B)
{
int nlen = 2 * ((_nbits + 7) >> 3);
BigInteger utmp = new BigInteger(HHex(
new string('0', nlen - AHex.Length) + AHex +
new string('0', nlen - BHex.Length) + BHex
), 16);
u = (utmp < N) ? utmp : (utmp % Nminus1);
}
uHex = u.ToHexString();
}
//***********************************************************************
// Generates a random number with the specified number of bits such
// that gcd(number, this) = 1
//***********************************************************************
public BigInteger genCoPrime(int bits)
{
bool done = false;
BigInteger result = new BigInteger();
while (!done)
{
result.genRandomBits(bits);
//Console.WriteLine(result.ToString(16));
// gcd test
BigInteger g = result.gcd(this);
if (g.dataLength == 1 && g.data[0] == 1)
done = true;
}
return result;
}
//***********************************************************************
// Generates a positive BigInteger that is probably prime.
//***********************************************************************
public static BigInteger genPseudoPrime(int bits, int confidence)
{
BigInteger result = new BigInteger();
bool done = false;
while (!done)
{
result.genRandomBits(bits);
result.data[0] |= 0x01; // make it odd
// prime test
done = result.isProbablePrime(confidence);
}
return result;
}
//***********************************************************************
// 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;
}
//***********************************************************************
// 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;
}