public static void FirstStep(DLPInput input, BigInteger[] factorBase, ref List <List <BigInteger> > coefficients, ref List <BigInteger> constantTerms)
{
var rand = new BigIntegerRandom();
for (int i = 1; i < input.order; i++)
{
//var k = rand.Next(0, input.order);
//while (k == 0)
//{
// k = rand.Next(0, input.order);
//}
var k = input.order - i;
var temp = BigInteger.ModPow(input.g, k, input.p);
var factorBaseFactorizationExponents = Factorization.GetFactorBaseFactorizationExponents(temp, factorBase);
if (factorBaseFactorizationExponents != null)
{
coefficients.Add(factorBaseFactorizationExponents.ToList());
constantTerms.Add(k);
//bool isLinearIndependent = GaussianElimination.IsLinearIndependent(coefficients, input.order);
//if (!isLinearIndependent)
// coefficients.RemoveAt(coefficients.Count - 1);
//else
// constantTerms.Add(k);
}
//if (coefficients.Count == factorBase.Length)
if (coefficients.Count == LinearEquatationsCount)
{
return;
}
}
}
public static BigInteger SolveDLP(BigInteger g, BigInteger h, BigInteger p)
{
var order = p - 1;
var input = new DLPInput(g, h, p, order);
var factorBase = BigIntegerExtension.GetFactorBase(FactorBaseSize);
var coefficients = new List <List <BigInteger> >();
var constantTerms = new List <BigInteger>();
FirstStep(input, factorBase, ref coefficients, ref constantTerms);
Console.WriteLine("First step done");
var factorBaseLogs = SecondStep(input, ref factorBase, Converter.ToTwoDimensionalBigIntegerArray(coefficients), constantTerms.ToArray());
Console.WriteLine("Second step done");
if (factorBaseLogs == null)
{
return(-1);
}
for (int i = 0; i < factorBaseLogs.Length; i++)
{
var l = factorBaseLogs[i];
BigInteger pow = -1;
if (l != -1)
{
pow = BigInteger.ModPow(g, l, p);
}
var pr = factorBase[i];
Console.WriteLine(pow + " = " + pr);
}
var x = ThirdStep(input, factorBase, factorBaseLogs);
Console.WriteLine("Third step done");
ReducedFactorBaseSize = factorBase.Length;
return(x);
}
public static BigInteger ThirdStep(DLPInput input, BigInteger[] factorBase, BigInteger[] factorBaseLogs)
{
for (BigInteger k = 1; k < input.order; k++)
{
var temp = (input.h * BigInteger.ModPow(input.g, k, input.p)).ModPositive(input.p);
var factorBaseFactorizationExponents = Factorization.GetFactorBaseFactorizationExponents(temp, factorBase);
if (factorBaseFactorizationExponents != null)
{
BigInteger x = 0;
int i = 0;
foreach (var log in factorBaseLogs)
{
x += log * factorBaseFactorizationExponents[i++];
}
x -= k;
return(x.ModPositive(input.order));
}
}
return(-1);
}
public static BigInteger[] SecondStep(DLPInput input, ref BigInteger[] factorBase, BigInteger[][] coefficients, BigInteger[] constantTerms)
{
return(GaussianElimination.SolveSystemOfLinearEquatations(input, ref factorBase, coefficients, constantTerms));
}
