public override ECFieldElement Sqrt() { uint[] x = this.x; if (Nat224.IsZero(x) || Nat224.IsOne(x)) { return(this); } uint[] z = Nat224.Create(); SecP224K1Field.Square(x, z); SecP224K1Field.Multiply(z, x, z); uint[] numArray3 = z; SecP224K1Field.Square(z, numArray3); SecP224K1Field.Multiply(numArray3, x, numArray3); uint[] numArray4 = Nat224.Create(); SecP224K1Field.Square(numArray3, numArray4); SecP224K1Field.Multiply(numArray4, x, numArray4); uint[] numArray5 = Nat224.Create(); SecP224K1Field.SquareN(numArray4, 4, numArray5); SecP224K1Field.Multiply(numArray5, numArray4, numArray5); uint[] numArray6 = Nat224.Create(); SecP224K1Field.SquareN(numArray5, 3, numArray6); SecP224K1Field.Multiply(numArray6, numArray3, numArray6); uint[] numArray7 = numArray6; SecP224K1Field.SquareN(numArray6, 8, numArray7); SecP224K1Field.Multiply(numArray7, numArray5, numArray7); uint[] numArray8 = numArray5; SecP224K1Field.SquareN(numArray7, 4, numArray8); SecP224K1Field.Multiply(numArray8, numArray4, numArray8); uint[] numArray9 = numArray4; SecP224K1Field.SquareN(numArray8, 0x13, numArray9); SecP224K1Field.Multiply(numArray9, numArray7, numArray9); uint[] numArray10 = Nat224.Create(); SecP224K1Field.SquareN(numArray9, 0x2a, numArray10); SecP224K1Field.Multiply(numArray10, numArray9, numArray10); uint[] numArray11 = numArray9; SecP224K1Field.SquareN(numArray10, 0x17, numArray11); SecP224K1Field.Multiply(numArray11, numArray8, numArray11); uint[] numArray12 = numArray8; SecP224K1Field.SquareN(numArray11, 0x54, numArray12); SecP224K1Field.Multiply(numArray12, numArray10, numArray12); uint[] numArray13 = numArray12; SecP224K1Field.SquareN(numArray13, 20, numArray13); SecP224K1Field.Multiply(numArray13, numArray7, numArray13); SecP224K1Field.SquareN(numArray13, 3, numArray13); SecP224K1Field.Multiply(numArray13, x, numArray13); SecP224K1Field.SquareN(numArray13, 2, numArray13); SecP224K1Field.Multiply(numArray13, x, numArray13); SecP224K1Field.SquareN(numArray13, 4, numArray13); SecP224K1Field.Multiply(numArray13, numArray3, numArray13); SecP224K1Field.Square(numArray13, numArray13); uint[] numArray14 = numArray10; SecP224K1Field.Square(numArray13, numArray14); if (Nat224.Eq(x, numArray14)) { return(new SecP224K1FieldElement(numArray13)); } SecP224K1Field.Multiply(numArray13, PRECOMP_POW2, numArray13); SecP224K1Field.Square(numArray13, numArray14); if (Nat224.Eq(x, numArray14)) { return(new SecP224K1FieldElement(numArray13)); } return(null); }
public static void Square(uint[] x, uint[] z) { uint[] tt = Nat224.CreateExt(); Nat224.Square(x, tt); Reduce(tt, z); }
public override ECPoint Twice() { if (this.IsInfinity) { return(this); } ECCurve curve = this.Curve; SecP224K1FieldElement Y1 = (SecP224K1FieldElement)this.RawYCoord; if (Y1.IsZero) { return(curve.Infinity); } SecP224K1FieldElement X1 = (SecP224K1FieldElement)this.RawXCoord, Z1 = (SecP224K1FieldElement)this.RawZCoords[0]; uint c; uint[] Y1Squared = Nat224.Create(); SecP224K1Field.Square(Y1.x, Y1Squared); uint[] T = Nat224.Create(); SecP224K1Field.Square(Y1Squared, T); uint[] M = Nat224.Create(); SecP224K1Field.Square(X1.x, M); c = Nat224.AddBothTo(M, M, M); SecP224K1Field.Reduce32(c, M); uint[] S = Y1Squared; SecP224K1Field.Multiply(Y1Squared, X1.x, S); c = Nat.ShiftUpBits(7, S, 2, 0); SecP224K1Field.Reduce32(c, S); uint[] t1 = Nat224.Create(); c = Nat.ShiftUpBits(7, T, 3, 0, t1); SecP224K1Field.Reduce32(c, t1); SecP224K1FieldElement X3 = new SecP224K1FieldElement(T); SecP224K1Field.Square(M, X3.x); SecP224K1Field.Subtract(X3.x, S, X3.x); SecP224K1Field.Subtract(X3.x, S, X3.x); SecP224K1FieldElement Y3 = new SecP224K1FieldElement(S); SecP224K1Field.Subtract(S, X3.x, Y3.x); SecP224K1Field.Multiply(Y3.x, M, Y3.x); SecP224K1Field.Subtract(Y3.x, t1, Y3.x); SecP224K1FieldElement Z3 = new SecP224K1FieldElement(M); SecP224K1Field.Twice(Y1.x, Z3.x); if (!Z1.IsOne) { SecP224K1Field.Multiply(Z3.x, Z1.x, Z3.x); } return(new SecP224K1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed)); }
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); } }
public static void Square(uint[] x, uint[] z) { uint[] array = Nat224.CreateExt(); Nat224.Square(x, array); Reduce(array, z); }
public override BigInteger ToBigInteger() { return(Nat224.ToBigInteger(x)); }
public override ECFieldElement Subtract(ECFieldElement b) { uint[] z = Nat224.Create(); SecP224R1Field.Subtract(x, ((SecP224R1FieldElement)b).x, z); return(new SecP224R1FieldElement(z)); }
public override ECPoint Add(ECPoint b) { if (base.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } if (this == b) { return(this.Twice()); } ECCurve curve = this.Curve; SecP224R1FieldElement secP224R1FieldElement = (SecP224R1FieldElement)base.RawXCoord; SecP224R1FieldElement secP224R1FieldElement2 = (SecP224R1FieldElement)base.RawYCoord; SecP224R1FieldElement secP224R1FieldElement3 = (SecP224R1FieldElement)b.RawXCoord; SecP224R1FieldElement secP224R1FieldElement4 = (SecP224R1FieldElement)b.RawYCoord; SecP224R1FieldElement secP224R1FieldElement5 = (SecP224R1FieldElement)base.RawZCoords[0]; SecP224R1FieldElement secP224R1FieldElement6 = (SecP224R1FieldElement)b.RawZCoords[0]; uint[] array = Nat224.CreateExt(); uint[] array2 = Nat224.Create(); uint[] array3 = Nat224.Create(); uint[] array4 = Nat224.Create(); bool isOne = secP224R1FieldElement5.IsOne; uint[] array5; uint[] array6; if (isOne) { array5 = secP224R1FieldElement3.x; array6 = secP224R1FieldElement4.x; } else { array6 = array3; SecP224R1Field.Square(secP224R1FieldElement5.x, array6); array5 = array2; SecP224R1Field.Multiply(array6, secP224R1FieldElement3.x, array5); SecP224R1Field.Multiply(array6, secP224R1FieldElement5.x, array6); SecP224R1Field.Multiply(array6, secP224R1FieldElement4.x, array6); } bool isOne2 = secP224R1FieldElement6.IsOne; uint[] array7; uint[] array8; if (isOne2) { array7 = secP224R1FieldElement.x; array8 = secP224R1FieldElement2.x; } else { array8 = array4; SecP224R1Field.Square(secP224R1FieldElement6.x, array8); array7 = array; SecP224R1Field.Multiply(array8, secP224R1FieldElement.x, array7); SecP224R1Field.Multiply(array8, secP224R1FieldElement6.x, array8); SecP224R1Field.Multiply(array8, secP224R1FieldElement2.x, array8); } uint[] array9 = Nat224.Create(); SecP224R1Field.Subtract(array7, array5, array9); uint[] array10 = array2; SecP224R1Field.Subtract(array8, array6, array10); if (!Nat224.IsZero(array9)) { uint[] array11 = array3; SecP224R1Field.Square(array9, array11); uint[] array12 = Nat224.Create(); SecP224R1Field.Multiply(array11, array9, array12); uint[] array13 = array3; SecP224R1Field.Multiply(array11, array7, array13); SecP224R1Field.Negate(array12, array12); Nat224.Mul(array8, array12, array); uint x = Nat224.AddBothTo(array13, array13, array12); SecP224R1Field.Reduce32(x, array12); SecP224R1FieldElement secP224R1FieldElement7 = new SecP224R1FieldElement(array4); SecP224R1Field.Square(array10, secP224R1FieldElement7.x); SecP224R1Field.Subtract(secP224R1FieldElement7.x, array12, secP224R1FieldElement7.x); SecP224R1FieldElement secP224R1FieldElement8 = new SecP224R1FieldElement(array12); SecP224R1Field.Subtract(array13, secP224R1FieldElement7.x, secP224R1FieldElement8.x); SecP224R1Field.MultiplyAddToExt(secP224R1FieldElement8.x, array10, array); SecP224R1Field.Reduce(array, secP224R1FieldElement8.x); SecP224R1FieldElement secP224R1FieldElement9 = new SecP224R1FieldElement(array9); if (!isOne) { SecP224R1Field.Multiply(secP224R1FieldElement9.x, secP224R1FieldElement5.x, secP224R1FieldElement9.x); } if (!isOne2) { SecP224R1Field.Multiply(secP224R1FieldElement9.x, secP224R1FieldElement6.x, secP224R1FieldElement9.x); } ECFieldElement[] zs = new ECFieldElement[] { secP224R1FieldElement9 }; return(new SecP224R1Point(curve, secP224R1FieldElement7, secP224R1FieldElement8, zs, base.IsCompressed)); } if (Nat224.IsZero(array10)) { return(this.Twice()); } return(curve.Infinity); }
public override ECFieldElement Square() { uint[] z = Nat224.Create(); SecP224K1Field.Square(x, z); return(new SecP224K1FieldElement(z)); }
public static void Reduce(uint[] xx, uint[] z) { ulong y = Nat224.Mul33Add(6803u, xx, 7, xx, 0, z, 0); if (Nat224.Mul33DWordAdd(6803u, y, z, 0) != 0u || (z[6] == 4294967295u && Nat224.Gte(z, SecP224K1Field.P))) { Nat.Add33To(7, 6803u, z); } }
public override ECPoint Twice() { if (base.IsInfinity) { return(this); } ECCurve curve = this.Curve; SecP224R1FieldElement secP224R1FieldElement = (SecP224R1FieldElement)base.RawYCoord; if (secP224R1FieldElement.IsZero) { return(curve.Infinity); } SecP224R1FieldElement secP224R1FieldElement2 = (SecP224R1FieldElement)base.RawXCoord; SecP224R1FieldElement secP224R1FieldElement3 = (SecP224R1FieldElement)base.RawZCoords[0]; uint[] array = Nat224.Create(); uint[] array2 = Nat224.Create(); uint[] array3 = Nat224.Create(); SecP224R1Field.Square(secP224R1FieldElement.x, array3); uint[] array4 = Nat224.Create(); SecP224R1Field.Square(array3, array4); bool isOne = secP224R1FieldElement3.IsOne; uint[] array5 = secP224R1FieldElement3.x; if (!isOne) { array5 = array2; SecP224R1Field.Square(secP224R1FieldElement3.x, array5); } SecP224R1Field.Subtract(secP224R1FieldElement2.x, array5, array); uint[] array6 = array2; SecP224R1Field.Add(secP224R1FieldElement2.x, array5, array6); SecP224R1Field.Multiply(array6, array, array6); uint x = Nat224.AddBothTo(array6, array6, array6); SecP224R1Field.Reduce32(x, array6); uint[] array7 = array3; SecP224R1Field.Multiply(array3, secP224R1FieldElement2.x, array7); x = Nat.ShiftUpBits(7, array7, 2, 0u); SecP224R1Field.Reduce32(x, array7); x = Nat.ShiftUpBits(7, array4, 3, 0u, array); SecP224R1Field.Reduce32(x, array); SecP224R1FieldElement secP224R1FieldElement4 = new SecP224R1FieldElement(array4); SecP224R1Field.Square(array6, secP224R1FieldElement4.x); SecP224R1Field.Subtract(secP224R1FieldElement4.x, array7, secP224R1FieldElement4.x); SecP224R1Field.Subtract(secP224R1FieldElement4.x, array7, secP224R1FieldElement4.x); SecP224R1FieldElement secP224R1FieldElement5 = new SecP224R1FieldElement(array7); SecP224R1Field.Subtract(array7, secP224R1FieldElement4.x, secP224R1FieldElement5.x); SecP224R1Field.Multiply(secP224R1FieldElement5.x, array6, secP224R1FieldElement5.x); SecP224R1Field.Subtract(secP224R1FieldElement5.x, array, secP224R1FieldElement5.x); SecP224R1FieldElement secP224R1FieldElement6 = new SecP224R1FieldElement(array6); SecP224R1Field.Twice(secP224R1FieldElement.x, secP224R1FieldElement6.x); if (!isOne) { SecP224R1Field.Multiply(secP224R1FieldElement6.x, secP224R1FieldElement3.x, secP224R1FieldElement6.x); } return(new SecP224R1Point(curve, secP224R1FieldElement4, secP224R1FieldElement5, new ECFieldElement[] { secP224R1FieldElement6 }, base.IsCompressed)); }
public static void Reduce32(uint x, uint[] z) { long num = 0L; if (x != 0) { long num2 = x; num = ((long)((ulong)num)) + (z[0] - num2); z[0] = (uint)num; num = num >> 0x20; if (num != 0L) { num += z[1]; z[1] = (uint)num; num = num >> 0x20; num += z[2]; z[2] = (uint)num; num = num >> 0x20; } num = ((long)((ulong)num)) + (z[3] + num2); z[3] = (uint)num; num = num >> 0x20; } if (((num != 0L) && (Nat.IncAt(7, z, 4) != 0)) || ((z[6] == uint.MaxValue) && Nat224.Gte(z, P))) { AddPInvTo(z); } }
public static void Reduce(uint[] xx, uint[] z) { long num = xx[10]; long num2 = xx[11]; long num3 = xx[12]; long num4 = xx[13]; long num5 = (xx[7] + num2) - 1L; long num6 = xx[8] + num3; long num7 = xx[9] + num4; long num8 = 0L; num8 = ((long)((ulong)num8)) + (xx[0] - num5); long num9 = (uint)num8; num8 = num8 >> 0x20; num8 = ((long)((ulong)num8)) + (xx[1] - num6); z[1] = (uint)num8; num8 = num8 >> 0x20; num8 = ((long)((ulong)num8)) + (xx[2] - num7); z[2] = (uint)num8; num8 = num8 >> 0x20; num8 = ((long)((ulong)num8)) + ((xx[3] + num5) - ((ulong)num)); long num10 = (uint)num8; num8 = num8 >> 0x20; num8 = ((long)((ulong)num8)) + ((xx[4] + num6) - ((ulong)num2)); z[4] = (uint)num8; num8 = num8 >> 0x20; num8 = ((long)((ulong)num8)) + ((xx[5] + num7) - ((ulong)num3)); z[5] = (uint)num8; num8 = num8 >> 0x20; num8 = ((long)((ulong)num8)) + ((xx[6] + num) - ((ulong)num4)); z[6] = (uint)num8; num8 = num8 >> 0x20; num8 += 1L; num10 += num8; num9 -= num8; z[0] = (uint)num9; num8 = num9 >> 0x20; if (num8 != 0L) { num8 += z[1]; z[1] = (uint)num8; num8 = num8 >> 0x20; num8 += z[2]; z[2] = (uint)num8; num10 += num8 >> 0x20; } z[3] = (uint)num10; num8 = num10 >> 0x20; if (((num8 != 0L) && (Nat.IncAt(7, z, 4) != 0)) || ((z[6] == uint.MaxValue) && Nat224.Gte(z, P))) { AddPInvTo(z); } }
public override ECFieldElement Invert() { uint[] z = Nat224.Create(); Mod.Invert(SecP224R1Field.P, x, z); return(new SecP224R1FieldElement(z)); }
public SecP224R1FieldElement() { this.x = Nat224.Create(); }
/** * 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); }
public override bool TestBitZero() { return(Nat224.GetBit(x, 0) == 1); }
public override ECFieldElement Add(ECFieldElement b) { uint[] z = Nat224.Create(); SecP224K1Field.Add(x, ((SecP224K1FieldElement)b).x, z); return(new SecP224K1FieldElement(z)); }
public override ECFieldElement AddOne() { uint[] z = Nat224.Create(); SecP224R1Field.AddOne(x, z); return(new SecP224R1FieldElement(z)); }
public override ECFieldElement RandomFieldElement(SecureRandom r) { uint[] x = Nat224.Create(); SecP224K1Field.Random(r, x); return(new SecP224K1FieldElement(x)); }
public override ECFieldElement Multiply(ECFieldElement b) { uint[] z = Nat224.Create(); SecP224R1Field.Multiply(x, ((SecP224R1FieldElement)b).x, z); return(new SecP224R1FieldElement(z)); }
public static void Square(uint[] x, uint[] z) { uint[] zz = Nat224.CreateExt(); Nat224.Square(x, zz); Reduce(zz, z); }
public static void Reduce32(uint x, uint[] z) { if ((x != 0 && Nat224.Mul33WordAdd(6803u, x, z, 0) != 0) || (z[6] == 4294967295u && Nat224.Gte(z, P))) { Nat.Add33To(7, 6803u, z); } }
public static void Multiply(uint[] x, uint[] y, uint[] z) { uint[] zz = Nat224.CreateExt(); Nat224.Mul(x, y, zz); Reduce(zz, z); }
public static void Multiply(uint[] x, uint[] y, uint[] z) { uint[] array = Nat224.CreateExt(); Nat224.Mul(x, y, array); Reduce(array, z); }
public static void Reduce(uint[] xx, uint[] z) { ulong y = Nat224.Mul33Add(0x1a93, xx, 7, xx, 0, z, 0); if ((Nat224.Mul33DWordAdd(0x1a93, y, z, 0) != 0) || ((z[6] == uint.MaxValue) && Nat224.Gte(z, P))) { Nat.Add33To(7, 0x1a93, z); } }
public static void Multiply(uint[] x, uint[] y, uint[] z) { uint[] tt = Nat224.CreateExt(); Nat224.Mul(x, y, tt); Reduce(tt, z); }
public static void Reduce32(uint x, uint[] z) { if (((x != 0) && (Nat224.Mul33WordAdd(0x1a93, x, z, 0) != 0)) || ((z[6] == uint.MaxValue) && Nat224.Gte(z, P))) { Nat.Add33To(7, 0x1a93, z); } }
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; SecP224K1FieldElement X1 = (SecP224K1FieldElement)this.RawXCoord, Y1 = (SecP224K1FieldElement)this.RawYCoord; SecP224K1FieldElement X2 = (SecP224K1FieldElement)b.RawXCoord, Y2 = (SecP224K1FieldElement)b.RawYCoord; SecP224K1FieldElement Z1 = (SecP224K1FieldElement)this.RawZCoords[0]; SecP224K1FieldElement Z2 = (SecP224K1FieldElement)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; SecP224K1Field.Square(Z1.x, S2); U2 = t2; SecP224K1Field.Multiply(S2, X2.x, U2); SecP224K1Field.Multiply(S2, Z1.x, S2); SecP224K1Field.Multiply(S2, Y2.x, S2); } bool Z2IsOne = Z2.IsOne; uint[] U1, S1; if (Z2IsOne) { U1 = X1.x; S1 = Y1.x; } else { S1 = t4; SecP224K1Field.Square(Z2.x, S1); U1 = tt1; SecP224K1Field.Multiply(S1, X1.x, U1); SecP224K1Field.Multiply(S1, Z2.x, S1); SecP224K1Field.Multiply(S1, Y1.x, S1); } uint[] H = Nat224.Create(); SecP224K1Field.Subtract(U1, U2, H); uint[] R = t2; SecP224K1Field.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; SecP224K1Field.Square(H, HSquared); uint[] G = Nat224.Create(); SecP224K1Field.Multiply(HSquared, H, G); uint[] V = t3; SecP224K1Field.Multiply(HSquared, U1, V); SecP224K1Field.Negate(G, G); Nat224.Mul(S1, G, tt1); c = Nat224.AddBothTo(V, V, G); SecP224K1Field.Reduce32(c, G); SecP224K1FieldElement X3 = new SecP224K1FieldElement(t4); SecP224K1Field.Square(R, X3.x); SecP224K1Field.Subtract(X3.x, G, X3.x); SecP224K1FieldElement Y3 = new SecP224K1FieldElement(G); SecP224K1Field.Subtract(V, X3.x, Y3.x); SecP224K1Field.MultiplyAddToExt(Y3.x, R, tt1); SecP224K1Field.Reduce(tt1, Y3.x); SecP224K1FieldElement Z3 = new SecP224K1FieldElement(H); if (!Z1IsOne) { SecP224K1Field.Multiply(Z3.x, Z1.x, Z3.x); } if (!Z2IsOne) { SecP224K1Field.Multiply(Z3.x, Z2.x, Z3.x); } ECFieldElement[] zs = new ECFieldElement[] { Z3 }; return(new SecP224K1Point(curve, X3, Y3, zs, IsCompressed)); }
public override ECFieldElement Negate() { uint[] z = Nat224.Create(); SecP224K1Field.Negate(this.x, z); return(new SecP224K1FieldElement(z)); }