private int countPointInner(long start, long end)
{
var count = 0;
var pLong = (long)p;
if (end >= pLong)
{
end = pLong;
}
for (long x = start; x < end; x++)
{
var z = (long)ExtraBigIntegerExtensions.Mod(x * x * x + a * x + b, p);
if (z == 0)
{
count++;
}
else
{
var legendreSymbol = BigIntegerExtensions.jacobi(z, pLong);
if (legendreSymbol == 1)
{
count += 2;
}
}
}
return(count);
}
public void CreateBasis()
{
BigInteger x = 0;
var y = Math.Sqrt((double)ExtraBigIntegerExtensions.Mod(x * x * x + a * x + b, p));
while (x < p && ((long)(y * tenExp) % tenExp != 0))
{
x++;
y = Math.Sqrt((double)ExtraBigIntegerExtensions.Mod(x * x * x + a * x + b, p));
}
Basis = CreatePoint(x, (BigInteger)y);
}
/// <summary>
/// Возвращает объект LenstraFactorizationResult,
/// если находится какое-то число, то все осатльные потоки прекращаются
/// </summary>
/// <param name="n">Число, у которого требуется найти делитель</param>
/// <param name="token">Токен отмены</param>
public LenstraFactorizationResult GetDividerWithCancel(BigInteger n, Random random, CancellationToken token)
{
var startTime = DateTime.Now;
BigInteger g, x, y, a, b;
int k = 0;
do
{
x = BigIntegerExtensions.GetNextRandom(random, n);
y = BigIntegerExtensions.GetNextRandom(random, n);
a = BigIntegerExtensions.GetNextRandom(random, n);
k++;
b = ExtraBigIntegerExtensions.Mod(y * y - x * x * x - a * x, n);
g = BigInteger.GreatestCommonDivisor(n, 4 * a * a * a + 27 * b * b);
} while (g == n);
EllepticCurve ec = null;
try
{
if (g != 1)
{
throw new GcdFoundException(g);
}
ec = new EllepticCurve(a, b, n);
var p0 = new PointOfEC
{
EllepticCurve = ec,
X = x,
Y = y
};
ec.LenstraStartingPoint = p0;
var P = new PointOfEC(p0);
BigInteger p = 2;
while (p < B1 && !token.IsCancellationRequested)
{
var pr = p;
while (pr < B1)
{
P = ec.Mult(p, P);
pr *= p;
}
p = BigIntegerExtensions.NextPrimaryMillerRabin(p);
}
}
catch (GcdFoundException exc)
{
Console.WriteLine("Поток {0} молодец: {1} = {2} * {3}",
Task.CurrentId, n, exc.GreatestCommonDivisor, n / exc.GreatestCommonDivisor);
return(new LenstraFactorizationResult
{
EllepticCurve = ec,
TargetNumber = n,
Divider = exc.GreatestCommonDivisor,
WastedTime = DateTime.Now - startTime
});
}
if (token.IsCancellationRequested)
{
Console.WriteLine("Поток {0} остановлен", Task.CurrentId);
}
else
{
Console.WriteLine("Поток {0} не смог", Task.CurrentId);
}
return(new LenstraFactorizationResult
{
EllepticCurve = ec,
TargetNumber = n,
WastedTime = DateTime.Now - startTime
});
}
/// <summary> Возвращает объект LenstraFactorizationResult </summary>
/// <param name="n">Число, у которого требуется найти делитель</param>
public LenstraFactorizationResult GetDivider(BigInteger n, Random random)
{
var startTime = DateTime.Now;
BigInteger g, x, y, a, b;
int k = 0;
do
{
x = BigIntegerExtensions.GetNextRandom(random, n);
y = BigIntegerExtensions.GetNextRandom(random, n);
a = BigIntegerExtensions.GetNextRandom(random, n);
k++;
b = ExtraBigIntegerExtensions.Mod(y * y - x * x * x - a * x, n);
g = BigInteger.GreatestCommonDivisor(n, 4 * a * a * a + 27 * b * b);
} while (g == n);
//убираем влияние выбора рандомного числа на время работы алгоритма
//startTime = startTime + new TimeSpan(0, 0, 0, k*3);
EllepticCurve ec = null;
try
{
if (g != 1)
{
throw new GcdFoundException(g);
}
ec = new EllepticCurve(a, b, n);
var p0 = new PointOfEC
{
EllepticCurve = ec,
X = x,
Y = y
};
ec.LenstraStartingPoint = p0;
var P = new PointOfEC(p0);
BigInteger p = 2;
while (p < B1)
{
var pr = p;
while (pr < B1)
{
P = ec.Mult(p, P);
pr *= p;
}
p = BigIntegerExtensions.NextPrimaryMillerRabin(p);
}
}
catch (GcdFoundException exc)
{
Console.WriteLine("Поток {0} молодец: {1} = {2} * {3}",
Task.CurrentId, n, exc.GreatestCommonDivisor, n / exc.GreatestCommonDivisor);
return(new LenstraFactorizationResult
{
EllepticCurve = ec,
TargetNumber = n,
Divider = exc.GreatestCommonDivisor,
WastedTime = DateTime.Now - startTime
});
}
return(new LenstraFactorizationResult
{
EllepticCurve = ec,
TargetNumber = n,
WastedTime = DateTime.Now - startTime
});
}
/// <summary> Содержит ли ЭК точку? </summary>
/// <param name="X">координата Х</param>
/// <param name="Y">координата Y</param>
/// <returns></returns>
public bool ContainsPoint(BigInteger X, BigInteger Y)
{
return(ExtraBigIntegerExtensions.Mod(Y * Y, p) == ExtraBigIntegerExtensions.Mod(X * X * X + a * X + b, p));
}
/// <summary> Сумма двух точек эллиптической кривой </summary>
/// <param name="point1"> Первая точка</param>
/// <param name="point2"> Вторая точка</param>
public PointOfEC Sum(PointOfEC point1, PointOfEC point2)
{
if (point1.Equals(point2.Invariant()))
{
return new PointOfEC()
{
EllepticCurve = this,
IsInfinity = true
}
}
;
if (point1.IsInfinity)
{
return(point2);
}
if (point2.IsInfinity)
{
return(point1);
}
var lamdZnam = point2.X - point1.X >= BigInteger.Zero ? point2.X - point1.X : point2.X - point1.X + p;
if (lamdZnam != 0 && BigInteger.GreatestCommonDivisor(lamdZnam, p) > 1)
{
throw new GcdFoundException(BigInteger.GreatestCommonDivisor(lamdZnam, p));
}
point1.X = point1.X % p;
point2.X = point2.X % p;
point1.Y = point1.Y % p;
point2.Y = point2.Y % p;
BigInteger lambda;
if (!point1.Equals(point2))
{
lambda = BigInteger.Multiply(point2.Y - point1.Y, ExtraBigIntegerExtensions.Inverse(point2.X - point1.X, p));
}
else
{
lambda = (3 * point1.X * point1.X + a) * ExtraBigIntegerExtensions.Inverse(2 * point2.Y, p);
}
lambda = lambda % p;
var x = lambda * lambda - point1.X - point2.X;
var y = lambda * (point1.X - x) - point1.Y;
var result = new PointOfEC()
{
EllepticCurve = this,
X = x % p,
Y = y % p
};
return(new PointOfEC()
{
//указать явно
//IsInfinity = false,
EllepticCurve = this,
X = result.X >= BigInteger.Zero ? result.X : result.X + p,
Y = result.Y >= BigInteger.Zero ? result.Y : result.Y + p
});
}
