private static BigInteger[] GeneratePrimes(int lengthBits, int count)
{
BigInteger start = BigInteger.Pow(2, lengthBits - 1);
BigInteger finish = BigInteger.Pow(2, lengthBits) - 1;
BigInteger range = finish - start + 1;
var list = new List <BigInteger>();
var checkedNumbers = new List <BigInteger>();
BigIntegerRandom rand = new BigIntegerRandom();
while (checkedNumbers.Count < range && list.Count < count)
{
var shift = rand.Next(0, range);
var temp = start + shift;
if (!checkedNumbers.Contains(temp))
{
if (BigIntegerPrimeTest.MillerRabinTest(temp) && temp != 2)
{
list.Add(temp);
}
checkedNumbers.Add(temp);
}
}
return(list.ToArray <BigInteger>());
//listOfArraysOfPrimes.Add(list.ToArray<BigInteger>());
}
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 void GeneratehAndxInFiles(int startBitsLength, int finishBitsLength, int rangeCount)
{
BigIntegerRandom rand = new BigIntegerRandom();
for (int i = startBitsLength; i <= finishBitsLength; i++)
{
string primesPath = String.Format(@"..\..\..\TestUtility\primes{0}bits.txt", i);
BigInteger[] primes = FileUtility.ReadArrayFromFile(primesPath);
string generatorsPath = String.Format(@"..\..\..\TestUtility\generators{0}bits.txt", i);
BigInteger[] generators = FileUtility.ReadArrayFromFile(generatorsPath);
var listH = new List <BigInteger>();
var listX = new List <BigInteger>();
for (int j = 0; j < primes.Length && j < rangeCount; j++)
{
var p = primes[j];
var g = generators[j];
var x = rand.Next(0, p - 1);
var h = BigInteger.ModPow(g, x, p);
listH.Add(h);
listX.Add(x);
}
string hPath = String.Format(@"..\..\..\TestUtility\h{0}bits.txt", i);
FileUtility.WriteArrayInFile(hPath, listH.ToArray <BigInteger>());
string xPath = String.Format(@"..\..\..\TestUtility\x{0}bits.txt", i);
FileUtility.WriteArrayInFile(xPath, listX.ToArray <BigInteger>());
}
}
public static void SolveDLPRange(int startBitLength, int finishBitLength, int count)
{
BigIntegerRandom rand = new BigIntegerRandom();
for (int i = startBitLength; i <= finishBitLength; i++)
{
var primes = FileUtility.ReadArrayFromFile(String.Format(@"..\..\..\TestUtility\primes{0}bits.txt", i));
var generators = FileUtility.ReadArrayFromFile(String.Format(@"..\..\..\TestUtility\generators{0}bits.txt", i));
var text = "";
for (int j = 0; j < count; j++)
{
var p = primes[j];
var g = generators[j];
var log = rand.Next(0, p - 1);
var h = BigInteger.ModPow(g, log, p);
var startTime = System.Diagnostics.Stopwatch.StartNew();
var x = DLPAlgorithm.BabyStepGiantStep.SolveDLP(g, h, p);
startTime.Stop();
var resultTime = startTime.Elapsed;
string elapsedTime = String.Format("{0:00}:{1:00}:{2:00}.{3:000}",
resultTime.Hours,
resultTime.Minutes,
resultTime.Seconds,
resultTime.Milliseconds);
var line = i.ToString() + " " + p.ToString() + " " + g.ToString() + " " + h.ToString() + " " + log.ToString() + " " + x.ToString() + " " + elapsedTime;
text += line + Environment.NewLine + Environment.NewLine;
}
FileUtility.WriteStringInFile(String.Format(@"..\..\..\DLPUtility\rhopollard{0}bits.txt", i), text);
}
}
public static void TestBabyStepGiantStep(int startBitLength, int finishBitLength, int count)
{
BigIntegerRandom rand = new BigIntegerRandom();
for (int i = startBitLength; i <= finishBitLength; i++)
{
int tempI = 27;
BigInteger a = 19;
BigInteger b = 7;
BigInteger p = 121572721;
var curve = new EllipticCurveUtility.EllipticCurve(a, b, p);
BigInteger x = 42812350;
BigInteger y = 114715677;
BigInteger order = 1820539;
var point = new EllipticCurveUtility.AffinePoint(x, y, curve);
var text = "";
for (int j = 0; j < count; j++)
{
var n = rand.Next(0, p - 1);
var Q = (n * point.ToProjectivePoint()).ToAffinePoint();
var startTime = System.Diagnostics.Stopwatch.StartNew();
var log = ECDLPAlgorithm.BabyStepGiantStep.SolveDLP(point.ToProjectivePoint(), Q.ToProjectivePoint());
startTime.Stop();
var resultTime = startTime.Elapsed;
string elapsedTime = String.Format("{0:00}:{1:00}:{2:00}.{3:000}",
resultTime.Hours,
resultTime.Minutes,
resultTime.Seconds,
resultTime.Milliseconds);
var line = tempI.ToString() + " " + n.ToString() + " " + log.ToString() + " " + elapsedTime;
text += line + Environment.NewLine + Environment.NewLine;
//FileUtility.WriteStringInFile(String.Format(@"..\..\..\ECDLPUtility\babystepgiantstep{0}bits.txt", tempI), text);
text = "";
//startTime = System.Diagnostics.Stopwatch.StartNew();
//log = ECDLPAlgorithm.RhoPollard.SolveDLP(point, Q);
//startTime.Stop();
//resultTime = startTime.Elapsed;
//elapsedTime = String.Format("{0:00}:{1:00}:{2:00}.{3:000}",
// resultTime.Hours,
// resultTime.Minutes,
// resultTime.Seconds,
// resultTime.Milliseconds);
//line = tempI.ToString() + " " + n.ToString() + " " + log.ToString() + " " + elapsedTime;
//text += line + Environment.NewLine + Environment.NewLine;
FileUtility.WriteStringInFile(String.Format(@"..\..\..\ECDLPUtility\rhopollard{0}bits.txt", tempI), text);
}
//FileUtility.WriteStringInFile(String.Format(@"..\..\..\ECDLPUtility\babystepgiantstep{0}bits.txt", tempI), text);
}
//var excelFile = new ExcelFile();
//excelFile.ExcelFilePath = String.Format(@"D:\BabyStepGiantStep.xlsx");
//excelFile.OpenExcel();
//foreach(var dataColumn in dataSheet)
//{
// excelFile.AddDataToExcel(dataColumn);
//}
//excelFile.CloseExcel();
}
//public static void TestIndexCalculus(int startBitLength, int finishBitLength, int count)
//{
// BigIntegerRandom rand = new BigIntegerRandom();
// for (int i = startBitLength; i <= finishBitLength; i++)
// {
// Console.WriteLine(i + " bits");
// var primes = FileUtility.ReadArrayFromFile(String.Format(@"..\..\..\TestUtility\primes{0}bits.txt", i));
// var generators = FileUtility.ReadArrayFromFile(String.Format(@"..\..\..\TestUtility\generators{0}bits.txt", i));
// var text = "";
// for (int j = 0; j < count; j++)
// {
// var p = primes[j];
// var g = generators[j];
// var log = rand.Next(0, p - 1);
// var h = BigInteger.ModPow(g, log, p);
// System.Diagnostics.Stopwatch startTime = System.Diagnostics.Stopwatch.StartNew();
// var x = DLPAlgorithm.IndexCalculus.SolveDLP(g, h, p);
// var resultTime = startTime.Elapsed;
// Console.WriteLine(IndexCalculus.FactorBaseSize + " = " + IndexCalculus.ReducedFactorBaseSize);
// Console.WriteLine(x + " = " + log);
// Console.WriteLine(resultTime);
// Console.WriteLine();
// }
// }
//}
public static void TestIndexCalculus(int startBitLength, int finishBitLength, int count)
{
BigIntegerRandom rand = new BigIntegerRandom();
int k = 1;
int step = 20;
int start = 100;
int cofLinearCount = 4;
for (int i = startBitLength; i <= finishBitLength; i++)
{
var primes = FileUtility.ReadArrayFromFile(String.Format(@"..\..\..\TestUtility\primes{0}bits.txt", i));
var generators = FileUtility.ReadArrayFromFile(String.Format(@"..\..\..\TestUtility\generators{0}bits.txt", i));
var text = "";
for (int j = 0; j < count; j++)
{
var p = primes[j];
var g = generators[j];
var log = rand.Next(0, p - 1);
var h = BigInteger.ModPow(g, log, p);
IndexCalculus.LinearEquatationsCount = cofLinearCount * IndexCalculus.FactorBaseSize;
System.Diagnostics.Stopwatch startTime = null;
BigInteger x = -1;
BigInteger startFactBase = 1;
while (x == -1)
{
startTime = System.Diagnostics.Stopwatch.StartNew();
startFactBase = IndexCalculus.FactorBaseSize;
x = DLPAlgorithm.IndexCalculus.SolveDLP(g, h, p);
if (x == -1)
{
IndexCalculus.FactorBaseSize += 5;
}
}
startTime.Stop();
var resultTime = startTime.Elapsed;
string elapsedTime = String.Format("{0:00}:{1:00}:{2:00}.{3:000}",
resultTime.Hours,
resultTime.Minutes,
resultTime.Seconds,
resultTime.Milliseconds);
var line = i.ToString() + " bits, p = " + p.ToString() + ", g = " + g.ToString() +
", h = " + h.ToString() + " , log = " + log.ToString() + " , x = " + x.ToString() +
" , time = " + elapsedTime + " , startFactorBaseSize = " + startFactBase +
" , reducedFactorBaseSize = " + IndexCalculus.ReducedFactorBaseSize;
text += line + Environment.NewLine + Environment.NewLine;
k++;
}
FileUtility.WriteStringInFile(String.Format(@"..\..\..\IndexCalculusUtility\indexcalculus{0}bits.txt", i), text);
}
}
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++;
}
}
}
/// <summary>
/// Функция генерирует два случайных числа a и b меньше P, возвращает true в случае подлинности подписи
/// </summary>
/// <param name="P">Опубликованное простое число</param>
/// <param name="G">Порождающий элемент</param>
/// <param name="X">Закрытый ключ</param>
/// <param name="Z">Подписанное сообщение</param>
/// <param name="M">Неподписанное сообщение</param>
/// <returns></returns>
static bool Bob(BigInteger P, BigInteger G, BigInteger X, BigInteger Z, BigInteger M)
{
BigInteger A = BigIntegerRandom.GenerateRandom(0, P, new Random());
Thread.Sleep(5);
BigInteger B = BigIntegerRandom.GenerateRandom(0, P, new Random());
BigInteger C = (BigInteger.ModPow(BigInteger.ModPow(Z, A, P) * BigInteger.ModPow(G, X * B, P), 1, P));
BigInteger D_Bob = BigInteger.ModPow(BigInteger.ModPow(M, A, P) * BigInteger.ModPow(G, B, P), 1, P);
BigInteger D_Alice = Alice(C, P, X);
return(D_Alice == D_Bob);
}
private void OnGenerateXBtnClick(object sender, RoutedEventArgs e)
{
int p = 1, g = 1;
bool isValid = int.TryParse(pTxtBox.Text, out p) && int.TryParse(gTxtBox.Text, out g);
if (isValid)
{
var rand = new BigIntegerRandom();
var x = rand.Next(0, p - 1);
var h = BigInteger.ModPow(g, x, p);
xTxtBox.Text = x.ToString();
hTxtBox.Text = h.ToString();
}
}
public static EllipticCurve GenerateEllipticCurve(BigInteger p)
{
BigIntegerRandom rand = new BigIntegerRandom();
BigInteger a, b;
bool condition;
do
{
a = rand.Next(0, p);
b = rand.Next(0, p);
condition = (4 * BigInteger.ModPow(a, 3, p) + 27 * BigInteger.ModPow(b, 2, p) % p) != 0 && a != 0 && b != 0;
} while (!condition);
return(new EllipticCurve(a, b, p));
}
public static void GeneratePrimesInFiles(int startBitsLength, int finishBitsLength, int rangeCount)
{
BigIntegerRandom rand = new BigIntegerRandom();
List <Task> taskList = new List <Task>();
for (int i = startBitsLength; i <= finishBitsLength; i++)
{
string primesPath = String.Format(@"..\..\..\TestUtility\primes{0}bits.txt", i);
var tempI = i;
taskList.Add(new Task(() => PrimeThreadFunc(primesPath, tempI, rangeCount)));
}
foreach (var t in taskList)
{
t.Start();
}
Task.WaitAll(taskList.ToArray());
}
public static void GenerateGeneratorsInFiles(int startBitsLength, int finishBitsLength)
{
BigIntegerRandom rand = new BigIntegerRandom();
List <Task> taskList = new List <Task>();
for (int i = startBitsLength; i <= finishBitsLength; i++)
{
var tempI = i;
BigInteger[] primes = FileUtility.ReadArrayFromFile(String.Format(@"..\..\..\TestUtility\primes{0}bits.txt", tempI));
string generatorsPath = String.Format(@"..\..\..\TestUtility\generators{0}bits.txt", tempI);
taskList.Add(new Task(() => GenerateGenerators(generatorsPath, primes)));
}
foreach (var t in taskList)
{
t.Start();
}
Task.WaitAll(taskList.ToArray());
}
public static void TestRhoPollard(int startBitLength, int finishBitLength, int count)
{
BigIntegerRandom rand = new BigIntegerRandom();
// var dataSheet = new List<string[]>();
for (int i = startBitLength; i <= finishBitLength; i++)
{
var primes = FileUtility.ReadArrayFromFile(String.Format(@"..\..\..\TestUtility\primes{0}bits.txt", i));
var generators = FileUtility.ReadArrayFromFile(String.Format(@"..\..\..\TestUtility\generators{0}bits.txt", i));
var text = "";
for (int j = 0; j < count; j++)
{
var p = primes[j];
var g = generators[j];
var log = rand.Next(0, p - 1);
var h = BigInteger.ModPow(g, log, p);
var startTime = System.Diagnostics.Stopwatch.StartNew();
var x = DLPAlgorithm.RhoPollard.SolveDLP(g, h, p);
startTime.Stop();
var resultTime = startTime.Elapsed;
string elapsedTime = String.Format("{0:00}:{1:00}:{2:00}.{3:000}",
resultTime.Hours,
resultTime.Minutes,
resultTime.Seconds,
resultTime.Milliseconds);
var line = i.ToString() + " " + p.ToString() + " " + g.ToString() + " " + h.ToString() + " " + log.ToString() + " " + x.ToString() + " " + elapsedTime;
text += line + Environment.NewLine + Environment.NewLine;
//var dataColumn = new string[] { i.ToString(), p.ToString(), g.ToString(), h.ToString(), log.ToString(), x.ToString(), elapsedTime };
//dataSheet.Add(dataColumn);
}
FileUtility.WriteStringInFile(String.Format(@"..\..\..\DLPUtility\rhopollard{0}bits.txt", i), text);
}
//var excelFile = new ExcelFile();
//excelFile.ExcelFilePath = String.Format(@"D:\BabyStepGiantStep.xlsx");
//excelFile.OpenExcel();
//foreach(var dataColumn in dataSheet)
//{
// excelFile.AddDataToExcel(dataColumn);
//}
//excelFile.CloseExcel();
}
private void OnGeneratePBtnClick(object sender, RoutedEventArgs e)
{
int bitsLength = 1;
bool isValid = int.TryParse(bitsLengthTxtBox.Text, out bitsLength);
if (isValid)
{
var rand = new BigIntegerRandom();
BigInteger start = BigInteger.Pow(2, bitsLength - 1);
BigInteger finish = BigInteger.Pow(2, bitsLength) - 1;
BigInteger range = finish - start + 1;
BigInteger p = 1;
do
{
var shift = rand.Next(0, range);
p = start + shift;
}while (BigIntegerPrimeTest.MillerRabinTest(p));
pTxtBox.Text = p.ToString();
}
}
public AffinePoint GetRandomAffinePoint()
{
BigIntegerRandom rand = new BigIntegerRandom();
var start = rand.Next(0, P);
var x = start;
BigInteger t;
do
{
t = (x * (x * x + A) + B).ModPositive(P);
if (BigIntegerExtension.JacobiSymbol(t, P) != -1)
{
return(new AffinePoint(x, BigIntegerExtension.Sqrt(t).ModPositive(P), this));
}
if (x > P - 1)
{
x = -1;
}
x++;
}while (x != start);
return(GetInfiniteAffinePoint());
}
static void Main(string[] args)
{
int Nice = 0;
int NotNice = 0;
BigIntegerRandom BIR = new BigIntegerRandom();
DigitalSignature NewSignature = new DigitalSignature(64); //p,g
//Console.WriteLine("i=={0,3} G=={1}", i,NewSignature.G);
BigInteger X;
do
{
X = BIR.GenerateSimple(64);
if (GCDEX.GetX(X, NewSignature.P - 1) > 0)
{
break;
}
} while (true);
//Закрытый ключ
BigInteger M = BigInteger.Parse("465498132"); //Исходное сообщение
BigInteger Z = BigInteger.ModPow(M, X, NewSignature.P); //Подписанное сообщение
for (int i = 0; i < 10; i++)
{
if (Bob(NewSignature.P, NewSignature.G, X, Z, M))
{
Nice++;
}
else
{
NotNice++;
}
}
Console.WriteLine("Nice=={0}\nNotNice=={1}", Nice, NotNice);
}
////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);
}
