static void Main()
{
// Application.EnableVisualStyles();
// Application.SetCompatibleTextRenderingDefault(false);
// Application.Run(new Form1());
cpolinom a = new cpolinom ("", 2);
}
private static List<cpolinom> Table(cpolinom p, cpolinom ir, Multi mul, int w)
{
List<cpolinom> table = new List<cpolinom>();
table.Add(p % ir);
for (int i = 0; i < Math.Pow(2, w) - 2; i++)
table.Add(mul(table[i], p) % ir);
return table;
}
private static List<cpolinom> NAFLRTable(cpolinom p, cpolinom ir, Multi mul, int power, int w)
{
List<cpolinom> table = new List<cpolinom>();
for (int i = 1; i <= power; i += 2)
table.Add(BinaryLR(p, ir, mul, i));
return table;
}
private static List<cpolinom> SlideLRTable(cpolinom p, cpolinom ir, Multi mul, int power, int w)
{
List<cpolinom> table = new List<cpolinom>();
table.Add(BinaryLR(p, ir, mul, power));
for (int i = 0; i < power - 1; i++)
table.Add(mul(table[i], p) % ir);
return table;
}
public static cpolinom CreateRand(int n, int m)
{
cpolinom c = new cpolinom("", m);
for (int i = 0; i < n; i++)
c.Add(Mod(r.Next(), m));
while (c[0] == 0)
c.RemoveAt(0);
return c;
}
public cpolinom InvPolinom(cpolinom n)
{
cpolinom x = new cpolinom("1", n.mod);
cpolinom y = Copy(this);
cpolinom r;
while (true)
{
r = (x * y) % n;
if (r.x[0] == 1 && r.Count == 1)
break;
else
x++;
}
return x;
}
public static cpolinom Point_Multiplication_Affine_Coord_19(cpolinom p, cpolinom ir, Multi mul, BigInteger n, int A, int B, Inverse inv)
{
BigInteger[,] mas_k;
mas_k = Convert_to_DBNS_1(n, A, B);
int lastindex = mas_k.GetLength(0) - 1;
cpolinom t = cpolinom.Copy(p);
cpolinom res = new cpolinom("1", p.mod);
for (int i = 0; i < mas_k[lastindex, 1]; i++)
t = mul(t, t) % ir;
for (int i = 0; i < mas_k[lastindex, 2]; i++)
t = mul(t, mul(t, t)) % ir;
if (mas_k[lastindex, 0] == -1)
res = mul(res, inv(t, ir)) % ir;
else if (mas_k[lastindex, 0] == 1)
res = mul(res, t) % ir;
for (int i = lastindex - 1; i >= 0; i--)
{
BigInteger u = mas_k[i, 1] - mas_k[i + 1, 1];
BigInteger v = mas_k[i, 2] - mas_k[i + 1, 2];
for (int j = 0; j < u; j++)
t = mul(t, t) % ir;
for (int j = 0; j < v; j++)
t = mul(t, mul(t, t)) % ir;
if (mas_k[i, 0] == -1)
res = mul(res, inv(t, ir)) % ir;
else if (mas_k[i, 0] == 1)
res = mul(res, t) % ir;
}
return res;
}
public static cpolinom Point_Multiplication_Affine_Coord_20(cpolinom p, cpolinom ir, Multi mul, BigInteger n, int A, int B, Inverse inv)
{
BigInteger[,] mas_k;
cpolinom t = cpolinom.Copy(p);
cpolinom res = new cpolinom("1", p.mod);
mas_k = Convert_to_DBNS_2(n, A, B);
if (mas_k[0, 0] == -1)
res = inv(t, ir);
else if (mas_k[0, 0] == 1)
res = t;
for (int i = 0; i < mas_k.GetLength(0) - 1; i++)
{
BigInteger u = mas_k[i, 1] - mas_k[i + 1, 1];
BigInteger v = mas_k[i, 2] - mas_k[i + 1, 2];
for (int j = 0; j < u; j++)
res = mul(res, res) % ir;
for (int j = 0; j < v; j++)
res = mul(res, mul(res, res)) % ir;
if (mas_k[i+1, 0] < 0)
res = mul(res, inv(t, ir)) % ir;
else
res = mul(res, t) % ir;
}
for (int i = 0; i < mas_k[mas_k.GetLength(0) - 1, 1]; i++)
res = mul(res, res) % ir;
for (int i = 0; i < mas_k[mas_k.GetLength(0) - 1, 2]; i++)
res = mul(res, mul(res, res)) % ir;
return res;
}
public static List<cpolinom> Primes(int n, int mod)
{
List<cpolinom> r = new List<cpolinom>();
cpolinom t = new cpolinom("", mod);
cpolinom temp = new cpolinom("1 0", mod);
r.Add(Copy(temp));
temp++;
while (temp.Count != n + 2)
{
for (int i = 0; i < r.Count; i++)
{
t = temp % r[i];
if (t.Count == 1 && t[0] == 0)
break;
}
if (t.Count > 1 || (t.Count == 1 && t[0] != 0))
r.Add(Copy(temp));
temp++;
}
return r;
}
public static cpolinom DBNS1LR(cpolinom p, cpolinom ir, Multi mul, BigInteger n, int A, int B, Inverse inv)
{
return methods.Point_Multiplication_Affine_Coord_20(p, ir, mul, n, A, B, inv);
}
public static cpolinom MontgomeryLadder(cpolinom p, cpolinom ir, Multi mul, BigInteger n)
{
cpolinom res = new cpolinom("1", p.mod);
cpolinom t = cpolinom.Copy(p);
string Binary = bif.ToBin(n);
for (int i = 0; i < Binary.Length; i++)
{
if (Binary[i] == '0')
{
t = mul(t, res) % ir;
res = mul(res, res) % ir;
}
else
{
res = mul(res, t) % ir;
t = mul(t, t) % ir;
}
}
return res;
}
public static cpolinom Joye_double_and_add(cpolinom p, cpolinom ir, Multi mul, BigInteger n)
{
cpolinom res = new cpolinom("1", p.mod);
cpolinom t = cpolinom.Copy(p);
string Binary = bif.ToBin(n);
for (int i = Binary.Length - 1; i >= 0 ; i--)
{
if (Binary[i] == '1')
{
res = mul(res, res) % ir;
res = mul(res, t) % ir;
}
else
{
t = mul(t, t) % ir;
t = mul(res, t) % ir;
}
}
return res;
}
public static cpolinom AddSubLR(cpolinom p, cpolinom ir, Multi mul, BigInteger n, Inverse inv)
{
cpolinom res = new cpolinom("1", p.mod);
cpolinom c = cpolinom.Copy(p);
string BinaryT = bif.ToBin(3 * n);
string BinaryN = bif.ToBin(n);
while (BinaryN.Length < BinaryT.Length) BinaryN = "0" + BinaryN;
for (int i = 0; i < BinaryN.Length - 1; i++)
{
res = mul(res, res) % ir;
if (BinaryT[i] != '0' && BinaryN[i] == '0') res = mul(res, c) % ir;
else if (BinaryT[i] == '0' && BinaryN[i] != '0') res = mul(res, inv(c, ir)) % ir;
}
return res;
}
public static cpolinom wNAFSlideLR(cpolinom p, cpolinom ir, Multi mul, BigInteger n, int w, Inverse inv)
{
cpolinom res = new cpolinom("1", p.mod);
List<BigInteger> x = bif.wNAF(n, w);
int pow = 2 * ((int)Math.Pow(2, w) - (int)Math.Pow((-1), w)) / 3 - 1;
List<cpolinom> table = NAFLRTable(p, ir, mul, pow, w);
for (int i = 0; i < x.Count; )
{
List<BigInteger> max = new List<BigInteger>();
if (x[i] == 0)
{
max.Add(0);
max.Add(1);
}
else
max = FindLargest2(x, i, w);
for (int d = 0; d < max[1]; d++)
res = mul(res, res) % ir;
if (max[0] > 0)
res = mul(res, table[(int)(bif.Abs(x[i]) / 2)]) % ir;
else if (max[0] < 0)
res = mul(res, inv(table[(int)(bif.Abs(x[i]) / 2)], ir)) % ir;
i = i + (int)max[1];
}
return res;
}
public static cpolinom SlideRL(cpolinom p, cpolinom ir, Multi mul, BigInteger n, int w)
{
int power = (int)Math.Pow(2, w - 1);
List<cpolinom> table = SlideRLTable(p, ir, mul, power, w);
cpolinom res = new cpolinom("1", p.mod);
cpolinom temp = cpolinom.Copy(p);
string binary = bif.ToBin(n);
while(binary.Length > 0)
{
int index = binary.Length - 1;
if (binary.Length < w || binary[index - w + 1] == '0')
{
if (binary[index] == '1')
res = mul(res, temp) % ir;
for (int j = 0; j < table.Count; j++)
table[j] = mul(table[j], table[j]) % ir;
temp = mul(temp, temp) % ir;
binary = binary.Remove(index, 1);
}
else
{
int c = Convert.ToInt32(binary.Substring(index - w + 1, w), 2);
res = mul(res, table[c - power]) % ir;
temp = mul(temp, table[table.Count - 1]) % ir;
for (int k = 0; k < w; k++)
for (int j = 0; j < table.Count; j++)
table[j] = mul(table[j], table[j]) % ir;
binary = binary.Remove(index - w + 1, w);
}
}
return res;
}
public static cpolinom BinaryRL(cpolinom p, cpolinom ir, Multi mul, BigInteger n)
{
cpolinom res = new cpolinom("1", p.mod);
cpolinom t = cpolinom.Copy(p);
string Binary = bif.ToBin(n);
for (int i = Binary.Length - 1; i >= 0; i--)
{
if (Binary[i] == '1')
res = mul(t, res) % ir;
t = mul(t, t) % ir;
}
return res;
}
public static cpolinom BinaryLR(cpolinom p, cpolinom ir, Multi mul, BigInteger n)
{
cpolinom res = new cpolinom("1", p.mod);
cpolinom t = cpolinom.Copy(p);
string Binary = bif.ToBin(n);
for (int i = 0; i < Binary.Length; i++)
{
res = mul(res, res) % ir;
if (Binary[i] == '1')
res = mul(t, res) % ir;
}
return res;
}
public cpolinom Inverve(cpolinom a)
{
cpolinom b = new cpolinom("", a.mod);
for (int i = 0; i < a.Count; i++)
b.Insert(0, a[i]);
return b;
}
public static cpolinom meth7_2(cpolinom p, cpolinom ir, Multi mul, BigInteger n, Inverse inv)
{
cpolinom res = new cpolinom("1", p.mod);
cpolinom c = cpolinom.Copy(p);
BigInteger k = n;
while (k >= 1)
{
BigInteger temp = 0;
if (k % 2 != 0)
{
temp = 2 - k % 4;
k -= temp;
}
if (temp == 1) res = mul(res, c) % ir;
else if (temp == -1) res = mul(res, inv(c, ir)) % ir;
k = k / 2;
c = mul(c, c) % ir;
}
return res;
}
public static cpolinom NAFBinaryLR(cpolinom p, cpolinom ir, Multi mul, BigInteger n, Inverse inv)
{
cpolinom res = new cpolinom("1", p.mod);
cpolinom c = cpolinom.Copy(p);
List<BigInteger> x = bif.NAF(n);
for (int i = x.Count - 1; i > -1; i--)
{
res = mul(res, res) % ir;
if (x[i] == 1) res = mul(res, c) % ir;
else if (x[i] == -1) res = mul(res, inv(c, ir)) % ir;
}
return res;
}
public static cpolinom WindowRL(cpolinom p, cpolinom ir, Multi mul, BigInteger n, int w)
{
List<cpolinom> table = Table(p, ir, mul, w);
cpolinom res = new cpolinom("1", p.mod);
List<string> bins = windows(bif.ToBin(n), w);
for (int i = bins.Count - 1; i > -1; i--)
{
int c = Convert.ToInt32(bins[i], 2);
if (c != 0) res = mul(res, table[c - 1]) % ir;
for (int k = 0; k < w; k++)
for (int j = 0; j < table.Count; j++)
table[j] = mul(table[j], table[j])%ir;
}
return res;
}
public static cpolinom NAFBinaryRL(cpolinom p, cpolinom ir, Multi mul, BigInteger n, Inverse inv)
{
cpolinom res = new cpolinom("1", p.mod);
cpolinom c = cpolinom.Copy(p);
List<BigInteger> x = bif.NAF(n);
for (int i = 0; i < x.Count; i++)
{
if (x[i] == 1) res = mul(res, c) % ir;
else if (x[i] == -1) res = mul(res, inv(c, ir)) % ir;
c = mul(c, c) % ir;
}
return res;
}
public static cpolinom SlideLR(cpolinom p, cpolinom ir, Multi mul, BigInteger n, int w)
{
int power = (int)Math.Pow(2, w - 1);
List<cpolinom> table = SlideLRTable(p, ir, mul, power, w);
cpolinom res = new cpolinom("1", p.mod);
string binary = bif.ToBin(n);
while (binary.Length > 0)
{
if (binary.Length < w || binary[0] == '0')
{
res = mul(res, res) % ir;
if (binary[0] == '1')
res = mul(res, p) % ir;
binary = binary.Remove(0, 1);
}
else
{
int c = Convert.ToInt32(binary.Substring(0, w), 2);
for (int k = 0; k < w; k++)
res = mul(res, res) % ir;
res = mul(res, table[c - power]) % ir;
binary = binary.Remove(0, w);
}
}
return res;
}
public static cpolinom DBNS2RL(cpolinom p, cpolinom ir, Multi mul, BigInteger n, Inverse inv)
{
List<int[]> x = ToDBNS2RL(n);
cpolinom res = new cpolinom("1", p.mod);
cpolinom t = cpolinom.Copy(p);
for (int i = x.Count - 1; i > -1; i--)
{
for (int j = 0; j < x[i][1]; j++)
t = mul(t, t) % ir;
for (int j = 0; j < x[i][2]; j++)
t = mul(t, mul(t, t)) % ir;
if (x[i][0] == 1)
res = mul(res, t) % ir;
else if (x[i][0] == -1)
res = mul(res, inv(t, ir)) % ir;
}
return res;
}
public static cpolinom DBNS2LR(cpolinom p, cpolinom ir, Multi mul, BigInteger n, Inverse inv)
{
List<int[]> x = ToDBNS2LR(n);
cpolinom res = cpolinom.Copy(p);
for (int i = x.Count - 1; i > 0 ; i--)
{
for (int j = 0; j < x[i][1]; j++)
res = mul(res, res) % ir;
for (int j = 0; j < x[i][2]; j++)
res = mul(res, mul(res, res)) % ir;
if (x[i][0] == 1)
res = mul(res, p) % ir;
else if (x[i][0] == -1)
res = mul(res, inv(p, ir)) % ir;
}
for (int j = 0; j < x[0][1]; j++)
res = mul(res, res) % ir;
for (int j = 0; j < x[0][2]; j++)
res = mul(res, mul(res, res)) % ir;
return res;
}
public static cpolinom NAFWindowLR(cpolinom p, cpolinom ir, Multi mul, BigInteger n, int w, Inverse inv)
{
cpolinom res = new cpolinom("1", p.mod);
List<BigInteger> x = bif.NAF(n);
int pow = (int)Math.Pow(2, w - 1);
List<cpolinom> table = NAFLRTable(p, ir, mul, pow, w);
for (int i = x.Count - 1; i > -1 ; i--)
{
res = mul(res, res) % ir;
if (x[i] > 0)
res = mul(res, table[(int)(x[i] / 2)]) % ir;
else if (x[i] < 0)
res = mul(res, inv(table[(int)(-x[i] / 2)], ir)) % ir;
}
return res;
}
public static cpolinom wNAFSlideRL(cpolinom p, cpolinom ir, Multi mul, BigInteger n, int w, Inverse inv)
{
cpolinom res = new cpolinom("1", p.mod);
List<BigInteger> x = bif.wNAF(n, w);
int pow = 2 * ((int)Math.Pow(2, w) - (int)Math.Pow((-1), w)) / 3 - 1;
List<cpolinom> table = NAFRLTable(p, ir, mul, pow, w);
for (int i = x.Count - 1; i > -1; )
{
List<BigInteger> max = FindLargest1(x, i, w);
if (max[0] > 0)
res = mul(res, table[(int)(bif.Abs(x[i]) / 2)]) % ir;
else if (max[0] < 0)
res = mul(res, inv(table[(int)(bif.Abs(x[i]) / 2)], ir)) % ir;
for (int d = 0; d < max[1]; d++)
for (int j = 0; j < table.Count; j++)
table[j] = mul(table[j], table[j]) % ir;
i = i - (int)max[1];
}
return res;
}
public static cpolinom WindowLR(cpolinom p, cpolinom ir, Multi mul, BigInteger n, int w)
{
List<cpolinom> table = Table(p, ir, mul, w);
cpolinom res = new cpolinom("1", p.mod);
List<string> bins = windows(bif.ToBin(n), w);
for (int i = 0; i < bins.Count; i++)
{
for (int k = 0; k < w; k++)
res = mul(res, res) % ir;
int c = Convert.ToInt32(bins[i], 2);
if (c != 0) res = mul(res, table[c - 1]) % ir;
}
return res;
}
public cpolinom ParseString(string str)
{
this.pointer = 0;
int baseField = ParseNumber(str, '(', '^');
int powerField = ParseNumber(str, '^', ')');
bool firstNumber = true;
cpolinom polinom = new cpolinom("", baseField);
List<int> coefficients = new List<int>();
while ((this.pointer >= str.Length) == false)
{
int coefficient = ParseCoefficients(str);
int power = ParsePower(str);
if (firstNumber == true)
{
polinom = new cpolinom(power, baseField);
firstNumber = false;
}
polinom[power] = coefficient;
}
return Inverve(polinom);
}
public static cpolinom NAFWindowRL(cpolinom p, cpolinom ir, Multi mul, BigInteger n, int w, Inverse inv)
{
cpolinom res = new cpolinom("1", p.mod);
List<BigInteger> x = bif.NAF(n);
int pow = (int)Math.Pow(2, w - 1);
List<cpolinom> table = NAFRLTable(p, ir, mul, pow, w);
for (int i = 1; i < pow; i += 2)
table.Add(BinaryRL(p, ir, mul, i));
for (int i = 0; i < x.Count; i++)
{
if (x[i] > 0)
res = mul(res, table[(int)(x[i] / 2)]) % ir;
else if (x[i] < 0)
res = mul(res, inv(table[(int)(-x[i] / 2)], ir)) % ir;
for (int j = 0; j < table.Count; j++)
table[j] = mul(table[j], table[j]) % ir;
}
return res;
}
