/**
         * return a sqrt root - the routine verifies that the calculation returns the right value - if
         * none exists it returns null.
         */
        public override ECFieldElement Sqrt()
        {
            /*
             * Raise this element to the exponent 2^254 - 2^222 - 2^94 + 2^62
             *
             * Breaking up the exponent's binary representation into "repunits", we get:
             * { 31 1s } { 1 0s } { 128 1s } { 31 0s } { 1 1s } { 62 0s}
             *
             * We use an addition chain for the beginning: [1], 2, 3, 6, 12, [24], 30, [31]
             */

            uint[] x1 = this.x;
            if (Nat256.IsZero(x1) || Nat256.IsOne(x1))
            {
                return(this);
            }

            uint[] x2 = Nat256.Create();
            SM2P256V1Field.Square(x1, x2);
            SM2P256V1Field.Multiply(x2, x1, x2);
            uint[] x4 = Nat256.Create();
            SM2P256V1Field.SquareN(x2, 2, x4);
            SM2P256V1Field.Multiply(x4, x2, x4);
            uint[] x6 = Nat256.Create();
            SM2P256V1Field.SquareN(x4, 2, x6);
            SM2P256V1Field.Multiply(x6, x2, x6);
            uint[] x12 = x2;
            SM2P256V1Field.SquareN(x6, 6, x12);
            SM2P256V1Field.Multiply(x12, x6, x12);
            uint[] x24 = Nat256.Create();
            SM2P256V1Field.SquareN(x12, 12, x24);
            SM2P256V1Field.Multiply(x24, x12, x24);
            uint[] x30 = x12;
            SM2P256V1Field.SquareN(x24, 6, x30);
            SM2P256V1Field.Multiply(x30, x6, x30);
            uint[] x31 = x6;
            SM2P256V1Field.Square(x30, x31);
            SM2P256V1Field.Multiply(x31, x1, x31);

            uint[] t1 = x24;
            SM2P256V1Field.SquareN(x31, 31, t1);

            uint[] x62 = x30;
            SM2P256V1Field.Multiply(t1, x31, x62);

            SM2P256V1Field.SquareN(t1, 32, t1);
            SM2P256V1Field.Multiply(t1, x62, t1);
            SM2P256V1Field.SquareN(t1, 62, t1);
            SM2P256V1Field.Multiply(t1, x62, t1);
            SM2P256V1Field.SquareN(t1, 4, t1);
            SM2P256V1Field.Multiply(t1, x4, t1);
            SM2P256V1Field.SquareN(t1, 32, t1);
            SM2P256V1Field.Multiply(t1, x1, t1);
            SM2P256V1Field.SquareN(t1, 62, t1);

            uint[] t2 = x4;
            SM2P256V1Field.Square(t1, t2);

            return(Nat256.Eq(x1, t2) ? new SM2P256V1FieldElement(t1) : null);
        }
 public override ECFieldElement Divide(ECFieldElement b)
 {
     //return Multiply(b.Invert());
     uint[] z = Nat256.Create();
     Mod.Invert(SM2P256V1Field.P, ((SM2P256V1FieldElement)b).x, z);
     SM2P256V1Field.Multiply(z, x, z);
     return(new SM2P256V1FieldElement(z));
 }
        public SM2P256V1FieldElement(BigInteger x)
        {
            if (x == null || x.SignValue < 0 || x.CompareTo(Q) >= 0)
            {
                throw new ArgumentException("value invalid for SM2P256V1FieldElement", "x");
            }

            this.x = SM2P256V1Field.FromBigInteger(x);
        }
 public override ECFieldElement Multiply(ECFieldElement b)
 {
     uint[] z = Nat256.Create();
     SM2P256V1Field.Multiply(x, ((SM2P256V1FieldElement)b).x, z);
     return(new SM2P256V1FieldElement(z));
 }
 public override ECFieldElement Subtract(ECFieldElement b)
 {
     uint[] z = Nat256.Create();
     SM2P256V1Field.Subtract(x, ((SM2P256V1FieldElement)b).x, z);
     return(new SM2P256V1FieldElement(z));
 }
 public override ECFieldElement AddOne()
 {
     uint[] z = Nat256.Create();
     SM2P256V1Field.AddOne(x, z);
     return(new SM2P256V1FieldElement(z));
 }
Example #7
0
        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;

            SM2P256V1FieldElement X1 = (SM2P256V1FieldElement)this.RawXCoord, Y1 = (SM2P256V1FieldElement)this.RawYCoord;
            SM2P256V1FieldElement X2 = (SM2P256V1FieldElement)b.RawXCoord, Y2 = (SM2P256V1FieldElement)b.RawYCoord;

            SM2P256V1FieldElement Z1 = (SM2P256V1FieldElement)this.RawZCoords[0];
            SM2P256V1FieldElement Z2 = (SM2P256V1FieldElement)b.RawZCoords[0];

            uint c;

            uint[] tt1 = Nat256.CreateExt();
            uint[] t2  = Nat256.Create();
            uint[] t3  = Nat256.Create();
            uint[] t4  = Nat256.Create();

            bool Z1IsOne = Z1.IsOne;

            uint[] U2, S2;
            if (Z1IsOne)
            {
                U2 = X2.x;
                S2 = Y2.x;
            }
            else
            {
                S2 = t3;
                SM2P256V1Field.Square(Z1.x, S2);

                U2 = t2;
                SM2P256V1Field.Multiply(S2, X2.x, U2);

                SM2P256V1Field.Multiply(S2, Z1.x, S2);
                SM2P256V1Field.Multiply(S2, Y2.x, S2);
            }

            bool Z2IsOne = Z2.IsOne;

            uint[] U1, S1;
            if (Z2IsOne)
            {
                U1 = X1.x;
                S1 = Y1.x;
            }
            else
            {
                S1 = t4;
                SM2P256V1Field.Square(Z2.x, S1);

                U1 = tt1;
                SM2P256V1Field.Multiply(S1, X1.x, U1);

                SM2P256V1Field.Multiply(S1, Z2.x, S1);
                SM2P256V1Field.Multiply(S1, Y1.x, S1);
            }

            uint[] H = Nat256.Create();
            SM2P256V1Field.Subtract(U1, U2, H);

            uint[] R = t2;
            SM2P256V1Field.Subtract(S1, S2, R);

            // Check if b == this or b == -this
            if (Nat256.IsZero(H))
            {
                if (Nat256.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;
            SM2P256V1Field.Square(H, HSquared);

            uint[] G = Nat256.Create();
            SM2P256V1Field.Multiply(HSquared, H, G);

            uint[] V = t3;
            SM2P256V1Field.Multiply(HSquared, U1, V);

            SM2P256V1Field.Negate(G, G);
            Nat256.Mul(S1, G, tt1);

            c = Nat256.AddBothTo(V, V, G);
            SM2P256V1Field.Reduce32(c, G);

            SM2P256V1FieldElement X3 = new SM2P256V1FieldElement(t4);

            SM2P256V1Field.Square(R, X3.x);
            SM2P256V1Field.Subtract(X3.x, G, X3.x);

            SM2P256V1FieldElement Y3 = new SM2P256V1FieldElement(G);

            SM2P256V1Field.Subtract(V, X3.x, Y3.x);
            SM2P256V1Field.MultiplyAddToExt(Y3.x, R, tt1);
            SM2P256V1Field.Reduce(tt1, Y3.x);

            SM2P256V1FieldElement Z3 = new SM2P256V1FieldElement(H);

            if (!Z1IsOne)
            {
                SM2P256V1Field.Multiply(Z3.x, Z1.x, Z3.x);
            }
            if (!Z2IsOne)
            {
                SM2P256V1Field.Multiply(Z3.x, Z2.x, Z3.x);
            }

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

            return(new SM2P256V1Point(curve, X3, Y3, zs, IsCompressed));
        }
Example #8
0
        public override ECPoint Twice()
        {
            if (this.IsInfinity)
            {
                return(this);
            }

            ECCurve curve = this.Curve;

            SM2P256V1FieldElement Y1 = (SM2P256V1FieldElement)this.RawYCoord;

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

            SM2P256V1FieldElement X1 = (SM2P256V1FieldElement)this.RawXCoord, Z1 = (SM2P256V1FieldElement)this.RawZCoords[0];

            uint c;

            uint[] t1 = Nat256.Create();
            uint[] t2 = Nat256.Create();

            uint[] Y1Squared = Nat256.Create();
            SM2P256V1Field.Square(Y1.x, Y1Squared);

            uint[] T = Nat256.Create();
            SM2P256V1Field.Square(Y1Squared, T);

            bool Z1IsOne = Z1.IsOne;

            uint[] Z1Squared = Z1.x;
            if (!Z1IsOne)
            {
                Z1Squared = t2;
                SM2P256V1Field.Square(Z1.x, Z1Squared);
            }

            SM2P256V1Field.Subtract(X1.x, Z1Squared, t1);

            uint[] M = t2;
            SM2P256V1Field.Add(X1.x, Z1Squared, M);
            SM2P256V1Field.Multiply(M, t1, M);
            c = Nat256.AddBothTo(M, M, M);
            SM2P256V1Field.Reduce32(c, M);

            uint[] S = Y1Squared;
            SM2P256V1Field.Multiply(Y1Squared, X1.x, S);
            c = Nat.ShiftUpBits(8, S, 2, 0);
            SM2P256V1Field.Reduce32(c, S);

            c = Nat.ShiftUpBits(8, T, 3, 0, t1);
            SM2P256V1Field.Reduce32(c, t1);

            SM2P256V1FieldElement X3 = new SM2P256V1FieldElement(T);

            SM2P256V1Field.Square(M, X3.x);
            SM2P256V1Field.Subtract(X3.x, S, X3.x);
            SM2P256V1Field.Subtract(X3.x, S, X3.x);

            SM2P256V1FieldElement Y3 = new SM2P256V1FieldElement(S);

            SM2P256V1Field.Subtract(S, X3.x, Y3.x);
            SM2P256V1Field.Multiply(Y3.x, M, Y3.x);
            SM2P256V1Field.Subtract(Y3.x, t1, Y3.x);

            SM2P256V1FieldElement Z3 = new SM2P256V1FieldElement(M);

            SM2P256V1Field.Twice(Y1.x, Z3.x);
            if (!Z1IsOne)
            {
                SM2P256V1Field.Multiply(Z3.x, Z1.x, Z3.x);
            }

            return(new SM2P256V1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed));
        }