public static Polynom operator *(Polynom A, double number)
{
// умножение на число
Polynom B = new Polynom(A.polynomCoefs.Length);
for (int i = 0; i < B.polynomCoefs.Length; i++)
{
B.polynomCoefs[i] = A.polynomCoefs[i] * number;
}
return B;
}
public static Polynom operator ^(Polynom A, int power)
{
// пох что оператор ^ должен делать XOR, тут это возведение в степень
Polynom B;
B = new Polynom(1);
B.polynomCoefs[0] = 1;
for (int i = 0; i < power; i++)
{
B = B * A;
}
return(B);
}
public static Polynom operator *(Polynom A, Polynom B)
{
// умножение
int maxResultLength = (A.polynomCoefs.Length - 1) + (B.polynomCoefs.Length - 1) + 1;
Polynom C = new Polynom(maxResultLength);
for (int i = 0; i < A.polynomCoefs.Length; i++)
{
for (int k = 0; k < B.polynomCoefs.Length; k++)
{
C.polynomCoefs[i + k] += A.polynomCoefs[i] * B.polynomCoefs[k];
}
}
return C;
}
public static Polynom operator *(Polynom A, Polynom B)
{
// умножение
int maxResultLength = (A.polynomCoefs.Length - 1) + (B.polynomCoefs.Length - 1) + 1;
Polynom C = new Polynom(maxResultLength);
for (int i = 0; i < A.polynomCoefs.Length; i++)
{
for (int k = 0; k < B.polynomCoefs.Length; k++)
{
C.polynomCoefs[i + k] += A.polynomCoefs[i] * B.polynomCoefs[k];
}
}
return(C);
}
public static void BruteDecomposition(Polynom pol, int maxCoef)
{
int maxPow = pol.polynomCoefs.Length;
Stopwatch timer = new Stopwatch();
int attempts = 0;
Console.WriteLine("----------------------------------------------");
Console.WriteLine("trying to decompose polynome: " + pol);
Console.WriteLine("----------------------------------------------");
Console.WriteLine("maxCoef: " + maxCoef);
Console.WriteLine("maxPow: " + maxPow);
Console.WriteLine("----------------------------------------------");
Console.WriteLine("+++++++");
for (int i = 2; i <= maxPow; i++)
{
int length1 = i;
int length2 = maxPow - i + 2;
//
timer.Start();
for (int k1 = 1; k1 < Math.Pow(maxCoef, length1); k1++)
{
for (int k2 = 1; k2 < Math.Pow(maxCoef, length2); k2++)
{
attempts++;
Polynom pol1 = new Polynom(k1, maxCoef);
Polynom pol2 = new Polynom(k2, maxCoef);
if (pol == pol1.Composition(pol2))
{
Console.WriteLine("p1: " + pol1);
Console.WriteLine("p2: " + pol2);
Console.WriteLine("+++++++");
}
}
}
}
timer.Stop();
Console.WriteLine("Attempts: " + attempts);
Console.WriteLine("Total time: " + Math.Round((double)timer.ElapsedMilliseconds / 1000, 2) + " sec");
}
public static void BruteDecomposition(Polynom pol, int maxCoef)
{
int maxPow = pol.polynomCoefs.Length;
Stopwatch timer = new Stopwatch();
int attempts = 0;
Console.WriteLine("----------------------------------------------");
Console.WriteLine("trying to decompose polynome: " + pol);
Console.WriteLine("----------------------------------------------");
Console.WriteLine("maxCoef: " + maxCoef);
Console.WriteLine("maxPow: " + maxPow);
Console.WriteLine("----------------------------------------------");
Console.WriteLine("+++++++");
for (int i = 2; i <= maxPow; i++)
{
int length1 = i;
int length2 = maxPow - i + 2;
//
timer.Start();
for (int k1 = 1; k1 < Math.Pow(maxCoef, length1); k1++)
{
for (int k2 = 1; k2 < Math.Pow(maxCoef, length2); k2++)
{
attempts++;
Polynom pol1 = new Polynom(k1, maxCoef);
Polynom pol2 = new Polynom(k2, maxCoef);
if (pol == pol1.Composition(pol2))
{
Console.WriteLine("p1: " + pol1);
Console.WriteLine("p2: " + pol2);
Console.WriteLine("+++++++");
}
}
}
}
timer.Stop();
Console.WriteLine("Attempts: " + attempts);
Console.WriteLine("Total time: " + Math.Round((double)timer.ElapsedMilliseconds/1000, 2) + " sec");
}
public static Polynom operator +(Polynom A, Polynom B)
{
// сложение
if (B.polynomCoefs.Length > A.polynomCoefs.Length)
{
Polynom tmp = A;
A = B;
B = tmp;
}
Polynom C = new Polynom(A.polynomCoefs.Length);
for (int i = 0; i < C.polynomCoefs.Length; i++)
{
if (i < B.polynomCoefs.Length)
{
C.polynomCoefs[i] = A.polynomCoefs[i] + B.polynomCoefs[i];
}
else
{
C.polynomCoefs[i] = A.polynomCoefs[i];
}
}
return(C);
}
static void Main(string[] args)
{
//тестовые значения
int a = 257;
int b = 18;
int nRoots = 1;
int nBase;
int xr;
Polynom sx;
// если есть входные аргументы, юзаем их
if (args.Length != 0)
{
a = Convert.ToInt32(args[0]);
b = Convert.ToInt32(args[1]);
nRoots = Convert.ToInt32(args[2]);
}
else
{
Console.WriteLine("no arguments passed, using test values...");
}
// генерим полином и закрытый ключ
int sqrt = Convert.ToInt32(Math.Floor(Math.Pow(a < b ? a : b, (double)1 / nRoots)));
Random rnd = new Random();
sqrt = rnd.Next(2, sqrt + 1);
nBase = Convert.ToInt32(Math.Pow(sqrt, nRoots));
int n = rnd.Next(1, 10); // хз какой диапазон брать
xr = sqrt - n;
sx = (new Polynom(new double[] { n, 1 })) ^ nRoots;
// преобразумем числа в полиномы
Polynom p1 = new Polynom(a, nBase);
Polynom p2 = new Polynom(b, nBase);
// композиция с S(x)
Polynom c1 = p1.Composition(sx);
Polynom c2 = p2.Composition(sx);
// результат деления
Polynom[] divP = (p1 / p2);
Polynom[] divC = (c1 / c2);
// вывод в консоль
Console.WriteLine("----------------------------------------------");
Console.WriteLine("p1: " + p1);
Console.WriteLine("p2: " + p2);
Console.WriteLine("s(x): " + sx);
Console.WriteLine("nBase: " + nBase);
Console.WriteLine("xr: " + xr);
Console.WriteLine("----------------------------------------------");
Console.WriteLine("c1: " + c1);
Console.WriteLine("c2: " + c2);
Console.WriteLine("----------------------------------------------");
Console.WriteLine("p1 + p2: " + (p1 + p2));
Console.WriteLine("(p1 + p2)(nBase): " + (p1 + p2).Value(nBase));
Console.WriteLine("c1 + c2: " + (c1 + c2));
Console.WriteLine("(c1 + c2)(xr): " + (c1 + c2).Value(xr));
Console.WriteLine("----------------------------------------------");
Console.WriteLine("p1 * p2: " + (p1 * p2));
Console.WriteLine("(p1 * p2)(nBase): " + (p1 * p2).Value(nBase));
Console.WriteLine("c1 * c2: " + (c1 * c2));
Console.WriteLine("(c1 * c2)(xr): " + (c1 * c2).Value(xr));
Console.WriteLine("----------------------------------------------");
Console.WriteLine("p1 / p2: " + divP[0]);
Console.WriteLine("remainder:\t" + divP[1]);
Console.WriteLine("(p1 / p2)(nBase): " + Math.Round(divP[0].Value(nBase), 2));
Console.WriteLine("remainder:\t" + Math.Round(divP[1].Value(nBase), 2) + "/" + b);
Console.WriteLine("c1 / c2: " + divC[0]);
Console.WriteLine("remainder:\t" + divC[1]);
Console.WriteLine("(c1 / c2)(xr): " + Math.Round(divC[0].Value(xr), 2));
Console.WriteLine("remainder:\t" + Math.Round(divC[1].Value(xr), 2) + "/" + b);
Console.WriteLine("----------------------------------------------");
BruteDecomposition(c1, nBase);
Console.ReadKey();
}
public static Polynom operator +(Polynom A, Polynom B)
{
// сложение
if(B.polynomCoefs.Length > A.polynomCoefs.Length)
{
Polynom tmp = A;
A = B;
B = tmp;
}
Polynom C = new Polynom(A.polynomCoefs.Length);
for (int i = 0; i < C.polynomCoefs.Length; i++)
{
if(i < B.polynomCoefs.Length)
{
C.polynomCoefs[i] = A.polynomCoefs[i] + B.polynomCoefs[i];
}
else
{
C.polynomCoefs[i] = A.polynomCoefs[i];
}
}
return C;
}
public Polynom Composition(Polynom p2)
{
// вычисление композиции
Polynom resultPolynom = new Polynom((p2.polynomCoefs.Length - 1) * (this.polynomCoefs.Length - 1) + 1);
for (int i = 0; i < this.polynomCoefs.Length; i++)
{
resultPolynom += (p2 ^ i) * this.polynomCoefs[i];
}
return resultPolynom;
}
public static Polynom operator ^(Polynom A, int power)
{
// пох что оператор ^ должен делать XOR, тут это возведение в степень
Polynom B;
B = new Polynom(1);
B.polynomCoefs[0] = 1;
for (int i = 0; i < power; i++ )
{
B = B * A;
}
return B;
}
public static Polynom[] operator /(Polynom A, Polynom B)
{
// деление
// возвращает массив из результата и остатка
//хрень короче, можно проще сделать (наверно)
Polynom tmpA = new Polynom((double[]) A.polynomCoefs.Clone());
int lengthA = A.polynomCoefs.Length;
int highCoefA = A.polynomCoefs.Length - 1;
int highCoefB = B.polynomCoefs.Length - 1;
Polynom[] C = new Polynom[2];
C[0] = new Polynom(highCoefA - highCoefB + 1);
while(highCoefA >= highCoefB)
{
if (tmpA.polynomCoefs[highCoefA] != 0)
{
double coef = tmpA.polynomCoefs[highCoefA] / B.polynomCoefs[highCoefB];
int exp = highCoefA - highCoefB;
Polynom tmp = new Polynom(new double[lengthA]);
tmp.polynomCoefs[exp] = coef;
C[0] += tmp;
tmp = tmp * B;
tmpA -= tmp;
}
highCoefA -= 1;
}
C[1] = tmpA;
return C;
}
public static Polynom operator -(Polynom A, Polynom B)
{
// вычитание
//лень нормально делать
for (int i = 0; i < B.polynomCoefs.Length; i++)
{
B.polynomCoefs[i] = -B.polynomCoefs[i];
}
if (B.polynomCoefs.Length > A.polynomCoefs.Length)
{
Polynom tmp = A;
A = B;
B = tmp;
}
Polynom C = new Polynom(A.polynomCoefs.Length);
for (int i = 0; i < C.polynomCoefs.Length; i++)
{
if (i < B.polynomCoefs.Length)
{
C.polynomCoefs[i] = A.polynomCoefs[i] + B.polynomCoefs[i];
}
else
{
C.polynomCoefs[i] = A.polynomCoefs[i];
}
}
return C;
}
static void Main(string[] args)
{
//тестовые значения
int a = 257;
int b = 18;
int nRoots = 1;
int nBase;
int xr;
Polynom sx;
// если есть входные аргументы, юзаем их
if(args.Length !=0)
{
a = Convert.ToInt32(args[0]);
b = Convert.ToInt32(args[1]);
nRoots = Convert.ToInt32(args[2]);
}
else
{
Console.WriteLine("no arguments passed, using test values...");
}
// генерим полином и закрытый ключ
int sqrt = Convert.ToInt32(Math.Floor(Math.Pow(a < b ? a : b, (double)1 / nRoots)));
Random rnd = new Random();
sqrt = rnd.Next(2, sqrt + 1);
nBase = Convert.ToInt32(Math.Pow(sqrt, nRoots));
int n = rnd.Next(1, 10); // хз какой диапазон брать
xr = sqrt - n;
sx = (new Polynom(new double[] { n, 1 })) ^ nRoots;
// преобразумем числа в полиномы
Polynom p1 = new Polynom(a, nBase);
Polynom p2 = new Polynom(b, nBase);
// композиция с S(x)
Polynom c1 = p1.Composition(sx);
Polynom c2 = p2.Composition(sx);
// результат деления
Polynom[] divP = (p1 / p2);
Polynom[] divC = (c1 / c2);
// вывод в консоль
Console.WriteLine("----------------------------------------------");
Console.WriteLine("p1: " + p1);
Console.WriteLine("p2: " + p2);
Console.WriteLine("s(x): " + sx);
Console.WriteLine("nBase: " + nBase);
Console.WriteLine("xr: " + xr);
Console.WriteLine("----------------------------------------------");
Console.WriteLine("c1: " + c1);
Console.WriteLine("c2: " + c2);
Console.WriteLine("----------------------------------------------");
Console.WriteLine("p1 + p2: " + (p1 + p2));
Console.WriteLine("(p1 + p2)(nBase): " + (p1 + p2).Value(nBase));
Console.WriteLine("c1 + c2: " + (c1 + c2));
Console.WriteLine("(c1 + c2)(xr): " + (c1 + c2).Value(xr));
Console.WriteLine("----------------------------------------------");
Console.WriteLine("p1 * p2: " + (p1 * p2));
Console.WriteLine("(p1 * p2)(nBase): " + (p1 * p2).Value(nBase));
Console.WriteLine("c1 * c2: " + (c1 * c2));
Console.WriteLine("(c1 * c2)(xr): " + (c1 * c2).Value(xr));
Console.WriteLine("----------------------------------------------");
Console.WriteLine("p1 / p2: " + divP[0]);
Console.WriteLine("remainder:\t" + divP[1]);
Console.WriteLine("(p1 / p2)(nBase): " +Math.Round( divP[0].Value(nBase),2));
Console.WriteLine("remainder:\t" + Math.Round(divP[1].Value(nBase), 2) + "/" + b);
Console.WriteLine("c1 / c2: " + divC[0]);
Console.WriteLine("remainder:\t" + divC[1]);
Console.WriteLine("(c1 / c2)(xr): " + Math.Round(divC[0].Value(xr),2));
Console.WriteLine("remainder:\t" + Math.Round(divC[1].Value(xr),2) + "/" + b);
Console.WriteLine("----------------------------------------------");
BruteDecomposition(c1,nBase);
Console.ReadKey();
}