public static BigInteger Solve(BigInteger a, BigInteger b, BigInteger p)
{
BigInteger H = BigMath.Sqrt(p) + 1;
//c = a^H mod p
BigInteger c = BigMath.Pow(a, H);
c = c % p;
//TODO sorted needed + -> change
Dictionary <BigInteger, BigInteger> table1 = new Dictionary <BigInteger, BigInteger>();
for (BigInteger u = 1; u <= H; u++)
{
table1.Add(u, BigMath.Pow(c, u) % p);
}
Dictionary <BigInteger, BigInteger> table2 = new Dictionary <BigInteger, BigInteger>();
for (BigInteger v = 0; v <= H; v++)
{
table2.Add(v, b * BigMath.Pow(a, v) % p);
foreach (KeyValuePair <BigInteger, BigInteger> t1 in table1)
{
if (table1[t1.Key] == table2[v])
{
return((H * t1.Key - v) % (p - 1));
}
}
}
return(-1);
}
public static BigInteger Solve(BigInteger _a, BigInteger _b, BigInteger p)
{
BigInteger r = _a, q = _b;
BigInteger x = 1, a = 0, b = 0;
BigInteger X = x, A = a, B = b;
for (int iterator = 1; iterator < p; iterator++)
{
RefreshValues(ref x, ref a, ref b, r, q, p);
RefreshValues(ref X, ref A, ref B, r, q, p); //2i - 2
RefreshValues(ref X, ref A, ref B, r, q, p);
if (x == X)
{
BigInteger m = (a - A).Mod(p - 1), // + +
n = (B - b).Mod(p - 1);
if (m == 0)
{
return(-1);
}
BigInteger gcd = BigMath.GCD_EuclideanExtended(m, p - 1, out BigInteger mu, out BigInteger pu);
Console.WriteLine(gcd);
BigInteger temp = (mu * n).Mod(p - 1);
for (BigInteger w = 0; w <= gcd; w++)
{
BigInteger result = ((temp + w * (p - 1)) / gcd).Mod(p - 1);
if (BigMath.Pow(r, result) % p == q)
{
return(result);
}
else if (w % 2 == 0 && BigMath.Pow(-r, result).Mod(p) == q)
{
return(result);
}
//if (w % 2 == 0) //sqrt(x^2y) = abs(x^y) = (+-)x^y
//{
// result = ((temp + w * (p - 1)) / gcd).Mod(p - 1);
// Console.WriteLine(result);
// if (BigMath.Pow(r, result) % p == q)
// {
// return result;
// }
//}
}
return(-1);
}
}
return(-1);
}
//TODO add button on main window
public static bool CheckResult(BigInteger a, BigInteger b, BigInteger p, BigInteger x)
{
if (x < 0)
{
return(false);
}
bool isSubstitutionCorrect = BigMath.Pow(a, x) % p == b;
return(isSubstitutionCorrect);
}
private void GenerateNumbers(int p_digits, int a_digits, int b_digits, out BigInteger p, out BigInteger a, out BigInteger b)
{
do
{
p = BigMath.Random(p_digits);
}while (!IsPGood(p));
do
{
a = BigMath.Random(a_digits);
}while (!IsAGood(a, p));
b = BigMath.Random(b_digits, p);
}
public static BigInteger Solve(BigInteger a, BigInteger b, BigInteger p)
{
BigInteger counter = 0;
BigInteger sum = 0;
for (int j = 1; j <= p - 2; j++)
{
sum += BigInteger.Pow(b, j) / (BigInteger.Pow(a, j) - 1);
counter++;
}
//sum <= (sum) < sum + counter, because / is about integer division
for (BigInteger i = 0; i <= counter; i++)
{
BigInteger result = (sum + i) % (p - 1);
if (BigMath.Pow(a, result) % p == b)
{
return(result);
}
}
return(-1);
}
public static BigInteger Solve(BigInteger a, BigInteger b, BigInteger p)
{
//1 find dividers of (р-1)
Dictionary <BigInteger, int> q_alpha = BigMath.Q_Alpha(p - 1);
//2 table r
BigInteger q;
// get index throught the loop
BigInteger[][] r = new BigInteger[q_alpha.Count][];
for (int q_index = 0; q_index < q_alpha.Count; q_index++)
{
q = q_alpha.ElementAt(q_index).Key;
r[q_index] = new BigInteger[(int)q]; //TODO change
for (int j = 0; j < q; j++)
{
r[q_index][j] = BigMath.Pow(a, (j * (p - 1) / q)) % p; // r +
}
}
//3 system х
Dictionary <BigInteger, BigInteger> q_x = new Dictionary <BigInteger, BigInteger>();
for (int q_index = 0; q_index < q_alpha.Count; q_index++)
{
q = q_alpha.ElementAt(q_index).Key;
BigInteger[] xi = new BigInteger[q_alpha[q]];
BigInteger temp; // b^power OR b*a^power
for (int al = 0; al < q_alpha[q]; al++)
{
if (al == 0)
{
temp = BigMath.Pow(b, (p - 1) / q) % p;
for (int j = 0; j < q; j++)
{
if (r[q_index][j] == temp) //search in table r
{
xi[al] = j; //x0 +
}
}
}
else
{
BigInteger power = xi[0];
for (int i = 1; i < al; i++)
{
power += xi[i] * (int)BigMath.Pow(q, i);
}
if (power == 1)
{
temp = b / a;
}
else
{
temp = b * BigMath.Pow(a, -power);//a^(-x0-x1..)
}
temp = BigMath.Pow(temp, (p - 1) / (BigMath.Pow(q, al + 1))); //(b*a)^(...)
temp = temp % p; //(mod p)
for (int j = 0; j < q; j++)
{
if (r[q_index][j] == temp) //search in table r
{
xi[al] = j; //xi +
}
}
}
}
BigInteger x = xi[0];
for (int i = 1; i < xi.Length; i++)
{
x += xi[i] * BigMath.Pow(q, i);
}
x = x % (BigMath.Pow(q, q_alpha[q]));
q_x.Add(q, x); // x, q +
}
//4 solve system х by Chinese remainder Th
BigInteger X = 0;
BigInteger M0 = 1;
BigInteger[] Mi = new BigInteger[q_x.Count];
BigInteger[] Yi = new BigInteger[q_x.Count];
BigInteger[] mi = new BigInteger[q_x.Count];
int counter = 0;
foreach (var qx in q_x)
{
mi[counter] = BigMath.Pow(qx.Key, q_alpha[qx.Key]);
M0 *= mi[counter];
counter++;
}
counter = 0;
foreach (var qx in q_x)
{
Mi[counter] = M0 / mi[counter];
counter++;
}
counter = 0;
foreach (var qx in q_x)
{
for (int i = 1; i < mi[counter]; i++)
{
if ((Mi[counter] * i - qx.Value) % mi[counter] == 0)
{
Yi[counter] = i;
break;
}
}
X += Mi[counter] * Yi[counter];
counter++;
}
return(X);
}
private bool IsPGood(BigInteger p) //needs to be prime
{
return(BigMath.IsPrime(p));
}
private bool IsAGood(BigInteger a, BigInteger p)
{
return(a > 1 && BigMath.OrderOfMagnitude(a) <= BigMath.OrderOfMagnitude(p - 1));
}