Пример #1
0
 public override BigInteger ToBigInteger()
 {
     return(Nat224.ToBigInteger(x));
 }
Пример #2
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 public SecP224R1FieldElement()
 {
     this.x = Nat224.Create();
 }
Пример #3
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 public override bool TestBitZero()
 {
     return(Nat224.GetBit(x, 0) == 1);
 }
Пример #4
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 public static void Square(uint[] x, uint[] z)
 {
     uint[] tt = Nat224.CreateExt();
     Nat224.Square(x, tt);
     Reduce(tt, z);
 }
Пример #5
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 public static void Multiply(uint[] x, uint[] y, uint[] z)
 {
     uint[] tt = Nat224.CreateExt();
     Nat224.Mul(x, y, tt);
     Reduce(tt, z);
 }
Пример #6
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 public override ECFieldElement Multiply(ECFieldElement b)
 {
     uint[] z = Nat224.Create();
     SecP224R1Field.Multiply(x, ((SecP224R1FieldElement)b).x, z);
     return(new SecP224R1FieldElement(z));
 }
Пример #7
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 public override ECFieldElement Sqrt()
 {
     uint[] y = x;
     if (Nat224.IsZero(y) || Nat224.IsOne(y))
     {
         return(this);
     }
     uint[] array = Nat224.Create();
     SecP224K1Field.Square(y, array);
     SecP224K1Field.Multiply(array, y, array);
     uint[] array2 = array;
     SecP224K1Field.Square(array, array2);
     SecP224K1Field.Multiply(array2, y, array2);
     uint[] array3 = Nat224.Create();
     SecP224K1Field.Square(array2, array3);
     SecP224K1Field.Multiply(array3, y, array3);
     uint[] array4 = Nat224.Create();
     SecP224K1Field.SquareN(array3, 4, array4);
     SecP224K1Field.Multiply(array4, array3, array4);
     uint[] array5 = Nat224.Create();
     SecP224K1Field.SquareN(array4, 3, array5);
     SecP224K1Field.Multiply(array5, array2, array5);
     uint[] array6 = array5;
     SecP224K1Field.SquareN(array5, 8, array6);
     SecP224K1Field.Multiply(array6, array4, array6);
     uint[] array7 = array4;
     SecP224K1Field.SquareN(array6, 4, array7);
     SecP224K1Field.Multiply(array7, array3, array7);
     uint[] array8 = array3;
     SecP224K1Field.SquareN(array7, 19, array8);
     SecP224K1Field.Multiply(array8, array6, array8);
     uint[] array9 = Nat224.Create();
     SecP224K1Field.SquareN(array8, 42, array9);
     SecP224K1Field.Multiply(array9, array8, array9);
     uint[] z = array8;
     SecP224K1Field.SquareN(array9, 23, z);
     SecP224K1Field.Multiply(z, array7, z);
     uint[] array10 = array7;
     SecP224K1Field.SquareN(z, 84, array10);
     SecP224K1Field.Multiply(array10, array9, array10);
     uint[] z2 = array10;
     SecP224K1Field.SquareN(z2, 20, z2);
     SecP224K1Field.Multiply(z2, array6, z2);
     SecP224K1Field.SquareN(z2, 3, z2);
     SecP224K1Field.Multiply(z2, y, z2);
     SecP224K1Field.SquareN(z2, 2, z2);
     SecP224K1Field.Multiply(z2, y, z2);
     SecP224K1Field.SquareN(z2, 4, z2);
     SecP224K1Field.Multiply(z2, array2, z2);
     SecP224K1Field.Square(z2, z2);
     uint[] array11 = array9;
     SecP224K1Field.Square(z2, array11);
     if (Nat224.Eq(y, array11))
     {
         return(new SecP224K1FieldElement(z2));
     }
     SecP224K1Field.Multiply(z2, PRECOMP_POW2, z2);
     SecP224K1Field.Square(z2, array11);
     if (Nat224.Eq(y, array11))
     {
         return(new SecP224K1FieldElement(z2));
     }
     return(null);
 }
Пример #8
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        public override ECPoint Add(ECPoint b)
        {
            if (this.IsInfinity)
            {
                return(b);
            }
            if (b.IsInfinity)
            {
                return(this);
            }
            if (this == b)
            {
                return(Twice());
            }

            ECCurve curve = this.Curve;

            SecP224R1FieldElement X1 = (SecP224R1FieldElement)this.RawXCoord, Y1 = (SecP224R1FieldElement)this.RawYCoord;
            SecP224R1FieldElement X2 = (SecP224R1FieldElement)b.RawXCoord, Y2 = (SecP224R1FieldElement)b.RawYCoord;

            SecP224R1FieldElement Z1 = (SecP224R1FieldElement)this.RawZCoords[0];
            SecP224R1FieldElement Z2 = (SecP224R1FieldElement)b.RawZCoords[0];

            uint c;

            uint[] tt1 = Nat224.CreateExt();
            uint[] t2  = Nat224.Create();
            uint[] t3  = Nat224.Create();
            uint[] t4  = Nat224.Create();

            bool Z1IsOne = Z1.IsOne;

            uint[] U2, S2;
            if (Z1IsOne)
            {
                U2 = X2.x;
                S2 = Y2.x;
            }
            else
            {
                S2 = t3;
                SecP224R1Field.Square(Z1.x, S2);

                U2 = t2;
                SecP224R1Field.Multiply(S2, X2.x, U2);

                SecP224R1Field.Multiply(S2, Z1.x, S2);
                SecP224R1Field.Multiply(S2, Y2.x, S2);
            }

            bool Z2IsOne = Z2.IsOne;

            uint[] U1, S1;
            if (Z2IsOne)
            {
                U1 = X1.x;
                S1 = Y1.x;
            }
            else
            {
                S1 = t4;
                SecP224R1Field.Square(Z2.x, S1);

                U1 = tt1;
                SecP224R1Field.Multiply(S1, X1.x, U1);

                SecP224R1Field.Multiply(S1, Z2.x, S1);
                SecP224R1Field.Multiply(S1, Y1.x, S1);
            }

            uint[] H = Nat224.Create();
            SecP224R1Field.Subtract(U1, U2, H);

            uint[] R = t2;
            SecP224R1Field.Subtract(S1, S2, R);

            // Check if b == this or b == -this
            if (Nat224.IsZero(H))
            {
                if (Nat224.IsZero(R))
                {
                    // this == b, i.e. this must be doubled
                    return(this.Twice());
                }

                // this == -b, i.e. the result is the point at infinity
                return(curve.Infinity);
            }

            uint[] HSquared = t3;
            SecP224R1Field.Square(H, HSquared);

            uint[] G = Nat224.Create();
            SecP224R1Field.Multiply(HSquared, H, G);

            uint[] V = t3;
            SecP224R1Field.Multiply(HSquared, U1, V);

            SecP224R1Field.Negate(G, G);
            Nat224.Mul(S1, G, tt1);

            c = Nat224.AddBothTo(V, V, G);
            SecP224R1Field.Reduce32(c, G);

            SecP224R1FieldElement X3 = new SecP224R1FieldElement(t4);

            SecP224R1Field.Square(R, X3.x);
            SecP224R1Field.Subtract(X3.x, G, X3.x);

            SecP224R1FieldElement Y3 = new SecP224R1FieldElement(G);

            SecP224R1Field.Subtract(V, X3.x, Y3.x);
            SecP224R1Field.MultiplyAddToExt(Y3.x, R, tt1);
            SecP224R1Field.Reduce(tt1, Y3.x);

            SecP224R1FieldElement Z3 = new SecP224R1FieldElement(H);

            if (!Z1IsOne)
            {
                SecP224R1Field.Multiply(Z3.x, Z1.x, Z3.x);
            }
            if (!Z2IsOne)
            {
                SecP224R1Field.Multiply(Z3.x, Z2.x, Z3.x);
            }

            ECFieldElement[] zs = new ECFieldElement[] { Z3 };

            return(new SecP224R1Point(curve, X3, Y3, zs, IsCompressed));
        }
Пример #9
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 public override ECFieldElement Square()
 {
     uint[] z = Nat224.Create();
     SecP224K1Field.Square(x, z);
     return(new SecP224K1FieldElement(z));
 }
Пример #10
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 public static void Square(uint[] x, uint[] z)
 {
     uint[] array = Nat224.CreateExt();
     Nat224.Square(x, array);
     Reduce(array, z);
 }
Пример #11
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        public override ECPoint Twice()
        {
            if (this.IsInfinity)
            {
                return(this);
            }

            ECCurve curve = this.Curve;

            SecP224R1FieldElement Y1 = (SecP224R1FieldElement)this.RawYCoord;

            if (Y1.IsZero)
            {
                return(curve.Infinity);
            }

            SecP224R1FieldElement X1 = (SecP224R1FieldElement)this.RawXCoord, Z1 = (SecP224R1FieldElement)this.RawZCoords[0];

            uint c;

            uint[] t1 = Nat224.Create();
            uint[] t2 = Nat224.Create();

            uint[] Y1Squared = Nat224.Create();
            SecP224R1Field.Square(Y1.x, Y1Squared);

            uint[] T = Nat224.Create();
            SecP224R1Field.Square(Y1Squared, T);

            bool Z1IsOne = Z1.IsOne;

            uint[] Z1Squared = Z1.x;
            if (!Z1IsOne)
            {
                Z1Squared = t2;
                SecP224R1Field.Square(Z1.x, Z1Squared);
            }

            SecP224R1Field.Subtract(X1.x, Z1Squared, t1);

            uint[] M = t2;
            SecP224R1Field.Add(X1.x, Z1Squared, M);
            SecP224R1Field.Multiply(M, t1, M);
            c = Nat224.AddBothTo(M, M, M);
            SecP224R1Field.Reduce32(c, M);

            uint[] S = Y1Squared;
            SecP224R1Field.Multiply(Y1Squared, X1.x, S);
            c = Nat.ShiftUpBits(7, S, 2, 0);
            SecP224R1Field.Reduce32(c, S);

            c = Nat.ShiftUpBits(7, T, 3, 0, t1);
            SecP224R1Field.Reduce32(c, t1);

            SecP224R1FieldElement X3 = new SecP224R1FieldElement(T);

            SecP224R1Field.Square(M, X3.x);
            SecP224R1Field.Subtract(X3.x, S, X3.x);
            SecP224R1Field.Subtract(X3.x, S, X3.x);

            SecP224R1FieldElement Y3 = new SecP224R1FieldElement(S);

            SecP224R1Field.Subtract(S, X3.x, Y3.x);
            SecP224R1Field.Multiply(Y3.x, M, Y3.x);
            SecP224R1Field.Subtract(Y3.x, t1, Y3.x);

            SecP224R1FieldElement Z3 = new SecP224R1FieldElement(M);

            SecP224R1Field.Twice(Y1.x, Z3.x);
            if (!Z1IsOne)
            {
                SecP224R1Field.Multiply(Z3.x, Z1.x, Z3.x);
            }

            return(new SecP224R1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed));
        }
Пример #12
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 public static void Reduce32(uint x, uint[] z)
 {
     if ((x != 0 && Nat224.Mul33WordAdd(6803u, x, z, 0) != 0) || (z[6] == uint.MaxValue && Nat224.Gte(z, P)))
     {
         Nat.Add33To(7, 6803u, z);
     }
 }
Пример #13
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 public static void Multiply(uint[] x, uint[] y, uint[] z)
 {
     uint[] array = Nat224.CreateExt();
     Nat224.Mul(x, y, array);
     Reduce(array, z);
 }
Пример #14
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 public SecP224K1FieldElement()
 {
     x = Nat224.Create();
 }
Пример #15
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 public override ECFieldElement AddOne()
 {
     uint[] z = Nat224.Create();
     SecP224R1Field.AddOne(x, z);
     return(new SecP224R1FieldElement(z));
 }
Пример #16
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        /**
         * return a sqrt root - the routine verifies that the calculation returns the right value - if
         * none exists it returns null.
         */
        public override ECFieldElement Sqrt()
        {
            /*
             * Q == 8m + 5, so we use Pocklington's method for this case.
             *
             * First, raise this element to the exponent 2^221 - 2^29 - 2^9 - 2^8 - 2^6 - 2^4 - 2^1 (i.e. m + 1)
             *
             * Breaking up the exponent's binary representation into "repunits", we get:
             * { 191 1s } { 1 0s } { 19 1s } { 2 0s } { 1 1s } { 1 0s} { 1 1s } { 1 0s} { 3 1s } { 1 0s}
             *
             * Therefore we need an addition chain containing 1, 3, 19, 191 (the lengths of the repunits)
             * We use: [1], 2, [3], 4, 8, 11, [19], 23, 42, 84, 107, [191]
             */

            uint[] x1 = this.x;
            if (Nat224.IsZero(x1) || Nat224.IsOne(x1))
            {
                return(this);
            }

            uint[] x2 = Nat224.Create();
            SecP224K1Field.Square(x1, x2);
            SecP224K1Field.Multiply(x2, x1, x2);
            uint[] x3 = x2;
            SecP224K1Field.Square(x2, x3);
            SecP224K1Field.Multiply(x3, x1, x3);
            uint[] x4 = Nat224.Create();
            SecP224K1Field.Square(x3, x4);
            SecP224K1Field.Multiply(x4, x1, x4);
            uint[] x8 = Nat224.Create();
            SecP224K1Field.SquareN(x4, 4, x8);
            SecP224K1Field.Multiply(x8, x4, x8);
            uint[] x11 = Nat224.Create();
            SecP224K1Field.SquareN(x8, 3, x11);
            SecP224K1Field.Multiply(x11, x3, x11);
            uint[] x19 = x11;
            SecP224K1Field.SquareN(x11, 8, x19);
            SecP224K1Field.Multiply(x19, x8, x19);
            uint[] x23 = x8;
            SecP224K1Field.SquareN(x19, 4, x23);
            SecP224K1Field.Multiply(x23, x4, x23);
            uint[] x42 = x4;
            SecP224K1Field.SquareN(x23, 19, x42);
            SecP224K1Field.Multiply(x42, x19, x42);
            uint[] x84 = Nat224.Create();
            SecP224K1Field.SquareN(x42, 42, x84);
            SecP224K1Field.Multiply(x84, x42, x84);
            uint[] x107 = x42;
            SecP224K1Field.SquareN(x84, 23, x107);
            SecP224K1Field.Multiply(x107, x23, x107);
            uint[] x191 = x23;
            SecP224K1Field.SquareN(x107, 84, x191);
            SecP224K1Field.Multiply(x191, x84, x191);

            uint[] t1 = x191;
            SecP224K1Field.SquareN(t1, 20, t1);
            SecP224K1Field.Multiply(t1, x19, t1);
            SecP224K1Field.SquareN(t1, 3, t1);
            SecP224K1Field.Multiply(t1, x1, t1);
            SecP224K1Field.SquareN(t1, 2, t1);
            SecP224K1Field.Multiply(t1, x1, t1);
            SecP224K1Field.SquareN(t1, 4, t1);
            SecP224K1Field.Multiply(t1, x3, t1);
            SecP224K1Field.Square(t1, t1);

            uint[] t2 = x84;
            SecP224K1Field.Square(t1, t2);

            if (Nat224.Eq(x1, t2))
            {
                return(new SecP224K1FieldElement(t1));
            }

            /*
             * If the first guess is incorrect, we multiply by a precomputed power of 2 to get the second guess,
             * which is ((4x)^(m + 1))/2 mod Q
             */
            SecP224K1Field.Multiply(t1, PRECOMP_POW2, t1);

            SecP224K1Field.Square(t1, t2);

            if (Nat224.Eq(x1, t2))
            {
                return(new SecP224K1FieldElement(t1));
            }

            return(null);
        }
Пример #17
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 public override ECFieldElement Subtract(ECFieldElement b)
 {
     uint[] z = Nat224.Create();
     SecP224R1Field.Subtract(x, ((SecP224R1FieldElement)b).x, z);
     return(new SecP224R1FieldElement(z));
 }
Пример #18
0
 public override ECFieldElement Add(ECFieldElement b)
 {
     uint[] z = Nat224.Create();
     SecP224K1Field.Add(x, ((SecP224K1FieldElement)b).x, z);
     return(new SecP224K1FieldElement(z));
 }
Пример #19
0
        public static void Reduce(uint[] xx, uint[] z)
        {
            long xx10 = xx[10], xx11 = xx[11], xx12 = xx[12], xx13 = xx[13];

            const long n = 1;

            long t0 = (long)xx[7] + xx11 - n;
            long t1 = (long)xx[8] + xx12;
            long t2 = (long)xx[9] + xx13;

            long cc = 0;

            cc += (long)xx[0] - t0;
            long z0 = (uint)cc;

            cc >>= 32;
            cc  += (long)xx[1] - t1;
            z[1] = (uint)cc;
            cc >>= 32;
            cc  += (long)xx[2] - t2;
            z[2] = (uint)cc;
            cc >>= 32;
            cc  += (long)xx[3] + t0 - xx10;
            long z3 = (uint)cc;

            cc >>= 32;
            cc  += (long)xx[4] + t1 - xx11;
            z[4] = (uint)cc;
            cc >>= 32;
            cc  += (long)xx[5] + t2 - xx12;
            z[5] = (uint)cc;
            cc >>= 32;
            cc  += (long)xx[6] + xx10 - xx13;
            z[6] = (uint)cc;
            cc >>= 32;
            cc  += n;

            Debug.Assert(cc >= 0);

            z3 += cc;

            z0  -= cc;
            z[0] = (uint)z0;
            cc   = z0 >> 32;
            if (cc != 0)
            {
                cc  += (long)z[1];
                z[1] = (uint)cc;
                cc >>= 32;
                cc  += (long)z[2];
                z[2] = (uint)cc;
                z3  += cc >> 32;
            }
            z[3] = (uint)z3;
            cc   = z3 >> 32;

            Debug.Assert(cc == 0 || cc == 1);

            if ((cc != 0 && Nat.IncAt(7, z, 4) != 0) ||
                (z[6] == P6 && Nat224.Gte(z, P)))
            {
                AddPInvTo(z);
            }
        }
Пример #20
0
 public override ECFieldElement Invert()
 {
     uint[] z = Nat224.Create();
     Mod.Invert(SecP224K1Field.P, x, z);
     return(new SecP224K1FieldElement(z));
 }