public ProjectivePoint ToProjectivePoint()
{
if (this == AffinePoint.GetInfinitePointForCurve(E))
{
return(new ProjectivePoint(0, 1, 0, E));
}
return(new ProjectivePoint(X, Y, 1, E));
}
public static void SolveDLPRange(int startBitLength, int finishBitLength, int count)
{
Excel.Application excelApp = new Excel.Application();
Excel.Workbook workBook;
Excel.Worksheet workSheet;
workBook = excelApp.Workbooks.Add();
workSheet = (Excel.Worksheet)workBook.Worksheets.get_Item(1);
excelApp.Visible = true;
int row = 1;
for (int i = startBitLength; i <= finishBitLength; i++)
{
var primes = FileUtility.ReadArrayFromFile(String.Format(@"C:\Utility\ECDLPUtility\Сurves\p{0}bits.txt", i));
var arrA = FileUtility.ReadArrayFromFile(String.Format(@"C:\Utility\ECDLPUtility\Сurves\A{0}bits.txt", i));
var arrB = FileUtility.ReadArrayFromFile(String.Format(@"C:\Utility\ECDLPUtility\Сurves\B{0}bits.txt", i));
var arrX = FileUtility.ReadArrayFromFile(String.Format(@"C:\Utility\ECDLPUtility\Points\X{0}bits.txt", i));
var arrY = FileUtility.ReadArrayFromFile(String.Format(@"C:\Utility\ECDLPUtility\Points\Y{0}bits.txt", i));
//var arrOrder = FileUtility.ReadArrayFromFile(String.Format(@"C:\Utility\ECDLPUtility\Points\order{0}bits.txt", i));
//var arrOrderbitslength = FileUtility.ReadArrayFromFile(String.Format(@"C:\Utility\ECDLPUtility\Points\orderbitslength{0}bits.txt", i));
var A = arrA[0];
var B = arrB[0];
var p = primes[0];
var curve = new EllipticCurveUtility.EllipticCurve(A, B, p);
var X = arrX[0];
var Y = arrY[0];
//var order = arrOrder[0];
//var orderBitsLength = arrOrderbitslength[0];
var point = new EllipticCurveUtility.AffinePoint(X, Y, curve);
var rand = new BigIntegerRandom();
for (int j = 0; j < count; j++)
{
var n = rand.Next(0, p - 1);
var P = point.ToProjectivePoint();
var Q = (n * P);
var log = SolveDLP(P, Q);
workSheet.Cells[row, 1] = i.ToString();
workSheet.Cells[row, 2] = curve.ToString();
workSheet.Cells[row, 3] = P.ToString();
workSheet.Cells[row, 4] = Q.ToString();
// workSheet.Cells[row, 5] = order.ToString();
// workSheet.Cells[row, 6] = orderBitsLength.ToString();
workSheet.Cells[row, 7] = TimeInSec.ToString();
workSheet.Cells[row, 8] = n.ToString();
workSheet.Cells[row, 9] = log.ToString();
workSheet.Cells[row, 10] = StepsCount.ToString();
//workSheet.Cells[row, 11] = RhoPollard.GCD.ToString();
row++;
}
}
}
public bool IsOnCurve(AffinePoint P)
{
var x = P.X;
var t = (x * (x * x + A) + B).ModPositive(this.P);
if (BigIntegerExtension.JacobiSymbol(t, this.P) == -1)
{
return(false);
}
return(true);
}
////Функция нахождения порядка кривой в афинных координатах
//public static BigInteger FindOrder(EllipticCurve E)
//{
// var Z = E.P;
// var rand = new Random();
// var startPoint = BasePoint.RandomPoint<PointAffine>(E);
// // Найдем границы по теореме Хассе
// var leftBorder = Z + 1 - 2 * (FieldsOperations.Sqrt(Z));
// var rightBorder = Z + 1 + 2 * (FieldsOperations.Sqrt(Z));
// for (int c = 0; c < NUMBER_OF_ATTEMPTS; c++)
// {
// //Сгенерируем точку на кривой и найдем ее порядок
// var P = BasePoint.RandomPoint<PointAffine>(E);
// var M = E.FindPointOrder(P);
// startPoint = P;
// if (M == 0)
// continue;
// int countOfDevided = 0;
// var order = BigInteger.Zero;
// //Найдем число делителей порядка точки в границах
// for (var i = leftBorder; i < rightBorder; )
// {
// if (i % M == 0)
// {
// order = i;
// i += M;
// countOfDevided++;
// if (countOfDevided > 1)
// break;
// }
// else
// {
// i++;
// }
// }
// //Если оно равно единице, то порядок кривой - делитель порядка точки
// if (countOfDevided == 1)
// {
// E.Order = order;
// return order;
// }
// }
// return 0;
//}
public static BigInteger FindPointOrder(AffinePoint P)
{
var point = P;
//var rand = new Random();
var rand = new BigIntegerRandom();
BigInteger M = 0;
//Создаем список точек
var A = new List <AffinePoint>();
var Q = (P.E.P + 1) * point;
A.Add(new AffinePoint());
A[0].X = 0;
A[0].Y = 0;
A[0].Z = 1;
A[0].E = P.E;
A.Add(point);
var max = BigInteger.One;
int count = 0;
for (; count < P.E.P; count++)
{
M = 0;
// генерерируем число m
var m = BigIntegerExtension.Sqrt(BigIntegerExtension.Sqrt(P.E.P)) + 1 + rand.Next(0, P.E.P);
if (m > max)
{
//дозаполняем список
for (BigInteger i = 0; i < m - max; i++)
{
A.Add(point + A[A.Count - 1]);
}
max = m;
}
var k = -m - 1;
int j = 0;
bool flag = true;
var twoMP = (2 * m) * point;
var temp = Q + (k * twoMP);
k++;
//вычисляем параметры k и j
for (; k < m && flag; k++)
{
if (k < 0 && k != -m)
{
temp = temp - twoMP;
}
else
{
temp = temp + twoMP;
}
for (j = 0; j < A.Count && flag; j++)
{
if (temp == A[j])
{
j = -j;
flag = false;
break;
}
if (temp == (-A[j]))
{
flag = false;
break;
}
}
}
k--;
M = (P.E.P + 1 + 2 * m * k + j);
if ((M * point) == P.E.GetInfiniteAffinePoint() && M != 0)
{
break;
}
}
if (count == P.E.P)
{
return(0);
}
// Раскладываем число M ро-методом Полларда
List <BigInteger> factorsM;
try
{
factorsM = BigIntegerExtension.PollardsAlg(BigInteger.Abs(M));
}
catch (Exception)
{
return(0);
}
// Проверяем простые делители числа M
for (int i = 0; i < factorsM.Count;)
{
BigInteger temp = M / factorsM[i];
if (M != factorsM[i] && M % factorsM[i] == 0 && (temp * point) == P.E.GetInfiniteAffinePoint())
{
M = temp;
i = 0;
}
else
{
i++;
}
}
//P.Order = M;
return(M);
}
public static AffinePoint Double(AffinePoint P)
{
return(P + P);
}
//чувака
private static AffinePoint X2(AffinePoint point)
{
BigInteger A = 3 * point.X * point.X + point.E.A * point.Z * point.Z;
A = BigInteger.Remainder(A, point.E.P);
if (A < 0)
{
while (A < 0)
{
A += point.E.P;
}
}
BigInteger B = 2 * point.Y * point.Z;
B = BigInteger.Remainder(B, point.E.P);
if (B < 0)
{
while (B < 0)
{
B += point.E.P;
}
}
BigInteger X = B * (A * A - 4 * point.X * point.Y * B);
X = BigInteger.Remainder(X, point.E.P);
if (X < 0)
{
while (X < 0)
{
X += point.E.P;
}
}
BigInteger Y = A * (6 * point.Y * point.X * B - A * A) - 2 * point.Y * point.Y * B * B;
Y = BigInteger.Remainder(Y, point.E.P);
if (Y < 0)
{
while (Y < 0)
{
Y += point.E.P;
}
}
BigInteger Z = B * B * B;
Z = BigInteger.Remainder(Z, point.E.P);
if (Z < 0)
{
while (Z < 0)
{
Z += point.E.P;
}
}
return(new AffinePoint(X, Y, Z, point.E));
}