public static void Half(uint[] x, uint[] z) { if ((x[0] & 1) == 0) { Nat.ShiftDownBit(5, x, 0, z); } else { uint c = Nat160.Add(x, P, z); Nat.ShiftDownBit(5, z, c); } }
public static void MultiplyAddToExt(uint[] x, uint[] y, uint[] zz) { uint c = Nat160.MulAddTo(x, y, zz); if (c != 0 || (zz[9] == PExt9 && Nat.Gte(10, zz, PExt))) { if (Nat.AddTo(PExtInv.Length, PExtInv, zz) != 0) { Nat.IncAt(10, zz, PExtInv.Length); } } }
public static void Reduce(uint[] xx, uint[] z) { ulong cc = Nat160.Mul33Add(PInv33, xx, 5, xx, 0, z, 0); uint c = Nat160.Mul33DWordAdd(PInv33, cc, z, 0); Debug.Assert(c == 0 || c == 1); if (c != 0 || (z[4] == P4 && Nat160.Gte(z, P))) { Nat.Add33To(5, PInv33, z); } }
public virtual bool Equals(SecP160R1FieldElement other) { if (this == other) { return(true); } if (null == other) { return(false); } return(Nat160.Eq(x, other.x)); }
public override ECPoint Twice() { if (base.IsInfinity) { return(this); } ECCurve curve = Curve; SecP160R2FieldElement secP160R2FieldElement = (SecP160R2FieldElement)base.RawYCoord; if (secP160R2FieldElement.IsZero) { return(curve.Infinity); } SecP160R2FieldElement secP160R2FieldElement2 = (SecP160R2FieldElement)base.RawXCoord; SecP160R2FieldElement secP160R2FieldElement3 = (SecP160R2FieldElement)base.RawZCoords[0]; uint[] array = Nat160.Create(); SecP160R2Field.Square(secP160R2FieldElement.x, array); uint[] array2 = Nat160.Create(); SecP160R2Field.Square(array, array2); uint[] array3 = Nat160.Create(); SecP160R2Field.Square(secP160R2FieldElement2.x, array3); uint x = Nat160.AddBothTo(array3, array3, array3); SecP160R2Field.Reduce32(x, array3); uint[] array4 = array; SecP160R2Field.Multiply(array, secP160R2FieldElement2.x, array4); x = Nat.ShiftUpBits(5, array4, 2, 0u); SecP160R2Field.Reduce32(x, array4); uint[] array5 = Nat160.Create(); x = Nat.ShiftUpBits(5, array2, 3, 0u, array5); SecP160R2Field.Reduce32(x, array5); SecP160R2FieldElement secP160R2FieldElement4 = new SecP160R2FieldElement(array2); SecP160R2Field.Square(array3, secP160R2FieldElement4.x); SecP160R2Field.Subtract(secP160R2FieldElement4.x, array4, secP160R2FieldElement4.x); SecP160R2Field.Subtract(secP160R2FieldElement4.x, array4, secP160R2FieldElement4.x); SecP160R2FieldElement secP160R2FieldElement5 = new SecP160R2FieldElement(array4); SecP160R2Field.Subtract(array4, secP160R2FieldElement4.x, secP160R2FieldElement5.x); SecP160R2Field.Multiply(secP160R2FieldElement5.x, array3, secP160R2FieldElement5.x); SecP160R2Field.Subtract(secP160R2FieldElement5.x, array5, secP160R2FieldElement5.x); SecP160R2FieldElement secP160R2FieldElement6 = new SecP160R2FieldElement(array3); SecP160R2Field.Twice(secP160R2FieldElement.x, secP160R2FieldElement6.x); if (!secP160R2FieldElement3.IsOne) { SecP160R2Field.Multiply(secP160R2FieldElement6.x, secP160R2FieldElement3.x, secP160R2FieldElement6.x); } return(new SecP160K1Point(curve, secP160R2FieldElement4, secP160R2FieldElement5, new ECFieldElement[1] { secP160R2FieldElement6 }, base.IsCompressed)); }
public override ECFieldElement Sqrt() { uint[] x = this.x; if (Nat160.IsZero(x) || Nat160.IsOne(x)) { return(this); } uint[] z = Nat160.Create(); SecP160R2Field.Square(x, z); SecP160R2Field.Multiply(z, x, z); uint[] numArray3 = Nat160.Create(); SecP160R2Field.Square(z, numArray3); SecP160R2Field.Multiply(numArray3, x, numArray3); uint[] numArray4 = Nat160.Create(); SecP160R2Field.Square(numArray3, numArray4); SecP160R2Field.Multiply(numArray4, x, numArray4); uint[] numArray5 = Nat160.Create(); SecP160R2Field.SquareN(numArray4, 3, numArray5); SecP160R2Field.Multiply(numArray5, numArray3, numArray5); uint[] numArray6 = numArray4; SecP160R2Field.SquareN(numArray5, 7, numArray6); SecP160R2Field.Multiply(numArray6, numArray5, numArray6); uint[] numArray7 = numArray5; SecP160R2Field.SquareN(numArray6, 3, numArray7); SecP160R2Field.Multiply(numArray7, numArray3, numArray7); uint[] numArray8 = Nat160.Create(); SecP160R2Field.SquareN(numArray7, 14, numArray8); SecP160R2Field.Multiply(numArray8, numArray6, numArray8); uint[] numArray9 = numArray6; SecP160R2Field.SquareN(numArray8, 0x1f, numArray9); SecP160R2Field.Multiply(numArray9, numArray8, numArray9); uint[] numArray10 = numArray8; SecP160R2Field.SquareN(numArray9, 0x3e, numArray10); SecP160R2Field.Multiply(numArray10, numArray9, numArray10); uint[] numArray11 = numArray9; SecP160R2Field.SquareN(numArray10, 3, numArray11); SecP160R2Field.Multiply(numArray11, numArray3, numArray11); uint[] numArray12 = numArray11; SecP160R2Field.SquareN(numArray12, 0x12, numArray12); SecP160R2Field.Multiply(numArray12, numArray7, numArray12); SecP160R2Field.SquareN(numArray12, 2, numArray12); SecP160R2Field.Multiply(numArray12, x, numArray12); SecP160R2Field.SquareN(numArray12, 3, numArray12); SecP160R2Field.Multiply(numArray12, z, numArray12); SecP160R2Field.SquareN(numArray12, 6, numArray12); SecP160R2Field.Multiply(numArray12, numArray3, numArray12); SecP160R2Field.SquareN(numArray12, 2, numArray12); SecP160R2Field.Multiply(numArray12, x, numArray12); uint[] numArray13 = z; SecP160R2Field.Square(numArray12, numArray13); return(!Nat160.Eq(x, numArray13) ? null : new SecP160R2FieldElement(numArray12)); }
public override ECFieldElement Sqrt() { uint[] y = x; if (Nat160.IsZero(y) || Nat160.IsOne(y)) { return(this); } uint[] array = Nat160.Create(); SecP160R2Field.Square(y, array); SecP160R2Field.Multiply(array, y, array); uint[] array2 = Nat160.Create(); SecP160R2Field.Square(array, array2); SecP160R2Field.Multiply(array2, y, array2); uint[] array3 = Nat160.Create(); SecP160R2Field.Square(array2, array3); SecP160R2Field.Multiply(array3, y, array3); uint[] array4 = Nat160.Create(); SecP160R2Field.SquareN(array3, 3, array4); SecP160R2Field.Multiply(array4, array2, array4); uint[] array5 = array3; SecP160R2Field.SquareN(array4, 7, array5); SecP160R2Field.Multiply(array5, array4, array5); uint[] array6 = array4; SecP160R2Field.SquareN(array5, 3, array6); SecP160R2Field.Multiply(array6, array2, array6); uint[] array7 = Nat160.Create(); SecP160R2Field.SquareN(array6, 14, array7); SecP160R2Field.Multiply(array7, array5, array7); uint[] array8 = array5; SecP160R2Field.SquareN(array7, 31, array8); SecP160R2Field.Multiply(array8, array7, array8); uint[] z = array7; SecP160R2Field.SquareN(array8, 62, z); SecP160R2Field.Multiply(z, array8, z); uint[] array9 = array8; SecP160R2Field.SquareN(z, 3, array9); SecP160R2Field.Multiply(array9, array2, array9); uint[] z2 = array9; SecP160R2Field.SquareN(z2, 18, z2); SecP160R2Field.Multiply(z2, array6, z2); SecP160R2Field.SquareN(z2, 2, z2); SecP160R2Field.Multiply(z2, y, z2); SecP160R2Field.SquareN(z2, 3, z2); SecP160R2Field.Multiply(z2, array, z2); SecP160R2Field.SquareN(z2, 6, z2); SecP160R2Field.Multiply(z2, array2, z2); SecP160R2Field.SquareN(z2, 2, z2); SecP160R2Field.Multiply(z2, y, z2); uint[] array10 = array; SecP160R2Field.Square(z2, array10); return((!Nat160.Eq(y, array10)) ? null : new SecP160R2FieldElement(z2)); }
public override ECPoint LookupVar(int index) { uint[] x = Nat160.Create(), y = Nat160.Create(); int pos = index * SECP160R2_FE_INTS * 2; for (int j = 0; j < SECP160R2_FE_INTS; ++j) { x[j] = m_table[pos + j]; y[j] = m_table[pos + SECP160R2_FE_INTS + j]; } return(CreatePoint(x, y)); }
// D.1.4 91 /** * 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 2^158 - 2^29 * * Breaking up the exponent's binary representation into "repunits", we get: * { 129 1s } { 29 0s } * * Therefore we need an addition chain containing 129 (the length of the repunit) We use: * 1, 2, 4, 8, 16, 32, 64, 128, [129] */ uint[] x1 = this.x; if (Nat160.IsZero(x1) || Nat160.IsOne(x1)) { return(this); } uint[] x2 = Nat160.Create(); SecP160R1Field.Square(x1, x2); SecP160R1Field.Multiply(x2, x1, x2); uint[] x4 = Nat160.Create(); SecP160R1Field.SquareN(x2, 2, x4); SecP160R1Field.Multiply(x4, x2, x4); uint[] x8 = x2; SecP160R1Field.SquareN(x4, 4, x8); SecP160R1Field.Multiply(x8, x4, x8); uint[] x16 = x4; SecP160R1Field.SquareN(x8, 8, x16); SecP160R1Field.Multiply(x16, x8, x16); uint[] x32 = x8; SecP160R1Field.SquareN(x16, 16, x32); SecP160R1Field.Multiply(x32, x16, x32); uint[] x64 = x16; SecP160R1Field.SquareN(x32, 32, x64); SecP160R1Field.Multiply(x64, x32, x64); uint[] x128 = x32; SecP160R1Field.SquareN(x64, 64, x128); SecP160R1Field.Multiply(x128, x64, x128); uint[] x129 = x64; SecP160R1Field.Square(x128, x129); SecP160R1Field.Multiply(x129, x1, x129); uint[] t1 = x129; SecP160R1Field.SquareN(t1, 29, t1); uint[] t2 = x128; SecP160R1Field.Square(t1, t2); return(Nat160.Eq(x1, t2) ? new SecP160R1FieldElement(t1) : null); }
public static void SquareN(uint[] x, int n, uint[] z) { Debug.Assert(n > 0); uint[] tt = Nat160.CreateExt(); Nat160.Square(x, tt); Reduce(tt, z); while (--n > 0) { Nat160.Square(z, tt); Reduce(tt, z); } }
public override ECLookupTable CreateCacheSafeLookupTable(ECPoint[] points, int off, int len) { uint[] table = new uint[len * SECP160K1_FE_INTS * 2]; { int pos = 0; for (int i = 0; i < len; ++i) { ECPoint p = points[off + i]; Nat160.Copy(((SecP160R2FieldElement)p.RawXCoord).x, 0, table, pos); pos += SECP160K1_FE_INTS; Nat160.Copy(((SecP160R2FieldElement)p.RawYCoord).x, 0, table, pos); pos += SECP160K1_FE_INTS; } } return(new SecP160K1LookupTable(this, table, len)); }
public override ECPoint Twice() { if (base.IsInfinity) { return(this); } ECCurve curve = this.Curve; SecP160R2FieldElement rawYCoord = (SecP160R2FieldElement)base.RawYCoord; if (rawYCoord.IsZero) { return(curve.Infinity); } SecP160R2FieldElement rawXCoord = (SecP160R2FieldElement)base.RawXCoord; SecP160R2FieldElement element3 = (SecP160R2FieldElement)base.RawZCoords[0]; uint[] z = Nat160.Create(); SecP160R2Field.Square(rawYCoord.x, z); uint[] numArray2 = Nat160.Create(); SecP160R2Field.Square(z, numArray2); uint[] numArray3 = Nat160.Create(); SecP160R2Field.Square(rawXCoord.x, numArray3); SecP160R2Field.Reduce32(Nat160.AddBothTo(numArray3, numArray3, numArray3), numArray3); uint[] numArray4 = z; SecP160R2Field.Multiply(z, rawXCoord.x, numArray4); SecP160R2Field.Reduce32(Nat.ShiftUpBits(5, numArray4, 2, 0), numArray4); uint[] numArray5 = Nat160.Create(); SecP160R2Field.Reduce32(Nat.ShiftUpBits(5, numArray2, 3, 0, numArray5), numArray5); SecP160R2FieldElement x = new SecP160R2FieldElement(numArray2); SecP160R2Field.Square(numArray3, x.x); SecP160R2Field.Subtract(x.x, numArray4, x.x); SecP160R2Field.Subtract(x.x, numArray4, x.x); SecP160R2FieldElement y = new SecP160R2FieldElement(numArray4); SecP160R2Field.Subtract(numArray4, x.x, y.x); SecP160R2Field.Multiply(y.x, numArray3, y.x); SecP160R2Field.Subtract(y.x, numArray5, y.x); SecP160R2FieldElement element6 = new SecP160R2FieldElement(numArray3); SecP160R2Field.Twice(rawYCoord.x, element6.x); if (!element3.IsOne) { SecP160R2Field.Multiply(element6.x, element3.x, element6.x); } return(new SecP160K1Point(curve, x, y, new ECFieldElement[] { element6 }, base.IsCompressed)); }
public override ECPoint Lookup(int index) { uint[] x = Nat160.Create(), y = Nat160.Create(); int pos = 0; for (int i = 0; i < m_size; ++i) { uint MASK = (uint)(((i ^ index) - 1) >> 31); for (int j = 0; j < SECP160R2_FE_INTS; ++j) { x[j] ^= m_table[pos + j] & MASK; y[j] ^= m_table[pos + SECP160R2_FE_INTS + j] & MASK; } pos += (SECP160R2_FE_INTS * 2); } return(CreatePoint(x, y)); }
public virtual ECPoint Lookup(int index) { uint[] x = Nat160.Create(), y = Nat160.Create(); int pos = 0; for (int i = 0; i < m_size; ++i) { uint MASK = (uint)(((i ^ index) - 1) >> 31); for (int j = 0; j < SECP160R2_FE_INTS; ++j) { x[j] ^= m_table[pos + j] & MASK; y[j] ^= m_table[pos + SECP160R2_FE_INTS + j] & MASK; } pos += (SECP160R2_FE_INTS * 2); } return(m_outer.CreateRawPoint(new SecP160R2FieldElement(x), new SecP160R2FieldElement(y), false)); }
public override ECFieldElement Sqrt() { uint[] y = x; if (Nat160.IsZero(y) || Nat160.IsOne(y)) { return(this); } uint[] array = Nat160.Create(); SecP160R1Field.Square(y, array); SecP160R1Field.Multiply(array, y, array); uint[] array2 = Nat160.Create(); SecP160R1Field.SquareN(array, 2, array2); SecP160R1Field.Multiply(array2, array, array2); uint[] array3 = array; SecP160R1Field.SquareN(array2, 4, array3); SecP160R1Field.Multiply(array3, array2, array3); uint[] array4 = array2; SecP160R1Field.SquareN(array3, 8, array4); SecP160R1Field.Multiply(array4, array3, array4); uint[] array5 = array3; SecP160R1Field.SquareN(array4, 16, array5); SecP160R1Field.Multiply(array5, array4, array5); uint[] array6 = array4; SecP160R1Field.SquareN(array5, 32, array6); SecP160R1Field.Multiply(array6, array5, array6); uint[] array7 = array5; SecP160R1Field.SquareN(array6, 64, array7); SecP160R1Field.Multiply(array7, array6, array7); uint[] array8 = array6; SecP160R1Field.Square(array7, array8); SecP160R1Field.Multiply(array8, y, array8); uint[] z = array8; SecP160R1Field.SquareN(z, 29, z); uint[] array9 = array7; SecP160R1Field.Square(z, array9); if (!Nat160.Eq(y, array9)) { return(null); } return(new SecP160R1FieldElement(z)); }
public override ECFieldElement Sqrt() { uint[] x = this.x; if (Nat160.IsZero(x) || Nat160.IsOne(x)) { return(this); } uint[] z = Nat160.Create(); SecP160R1Field.Square(x, z); SecP160R1Field.Multiply(z, x, z); uint[] numArray3 = Nat160.Create(); SecP160R1Field.SquareN(z, 2, numArray3); SecP160R1Field.Multiply(numArray3, z, numArray3); uint[] numArray4 = z; SecP160R1Field.SquareN(numArray3, 4, numArray4); SecP160R1Field.Multiply(numArray4, numArray3, numArray4); uint[] numArray5 = numArray3; SecP160R1Field.SquareN(numArray4, 8, numArray5); SecP160R1Field.Multiply(numArray5, numArray4, numArray5); uint[] numArray6 = numArray4; SecP160R1Field.SquareN(numArray5, 0x10, numArray6); SecP160R1Field.Multiply(numArray6, numArray5, numArray6); uint[] numArray7 = numArray5; SecP160R1Field.SquareN(numArray6, 0x20, numArray7); SecP160R1Field.Multiply(numArray7, numArray6, numArray7); uint[] numArray8 = numArray6; SecP160R1Field.SquareN(numArray7, 0x40, numArray8); SecP160R1Field.Multiply(numArray8, numArray7, numArray8); uint[] numArray9 = numArray7; SecP160R1Field.Square(numArray8, numArray9); SecP160R1Field.Multiply(numArray9, x, numArray9); uint[] numArray10 = numArray9; SecP160R1Field.SquareN(numArray10, 0x1d, numArray10); uint[] numArray11 = numArray8; SecP160R1Field.Square(numArray10, numArray11); return(!Nat160.Eq(x, numArray11) ? null : new SecP160R1FieldElement(numArray10)); }
public override BigInteger ToBigInteger() { return(Nat160.ToBigInteger(x)); }
public SecP160R2FieldElement() { this.x = Nat160.Create(); }
public override bool TestBitZero() { return(Nat160.GetBit(x, 0) == 1); }
public override ECFieldElement Multiply(ECFieldElement b) { uint[] z = Nat160.Create(); SecP160R2Field.Multiply(x, ((SecP160R2FieldElement)b).x, z); return(new SecP160R2FieldElement(z)); }
// D.1.4 91 /** * 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 2^158 - 2^30 - 2^12 - 2^10 - 2^7 - 2^6 - 2^5 - 2^1 - 2^0 * * Breaking up the exponent's binary representation into "repunits", we get: { 127 1s } { 1 * 0s } { 17 1s } { 1 0s } { 1 1s } { 1 0s } { 2 1s } { 3 0s } { 3 1s } { 1 0s } { 1 1s } * * Therefore we need an Addition chain containing 1, 2, 3, 17, 127 (the lengths of the repunits) * We use: [1], [2], [3], 4, 7, 14, [17], 31, 62, 124, [127] */ uint[] x1 = this.x; if (Nat160.IsZero(x1) || Nat160.IsOne(x1)) { return(this); } uint[] x2 = Nat160.Create(); SecP160R2Field.Square(x1, x2); SecP160R2Field.Multiply(x2, x1, x2); uint[] x3 = Nat160.Create(); SecP160R2Field.Square(x2, x3); SecP160R2Field.Multiply(x3, x1, x3); uint[] x4 = Nat160.Create(); SecP160R2Field.Square(x3, x4); SecP160R2Field.Multiply(x4, x1, x4); uint[] x7 = Nat160.Create(); SecP160R2Field.SquareN(x4, 3, x7); SecP160R2Field.Multiply(x7, x3, x7); uint[] x14 = x4; SecP160R2Field.SquareN(x7, 7, x14); SecP160R2Field.Multiply(x14, x7, x14); uint[] x17 = x7; SecP160R2Field.SquareN(x14, 3, x17); SecP160R2Field.Multiply(x17, x3, x17); uint[] x31 = Nat160.Create(); SecP160R2Field.SquareN(x17, 14, x31); SecP160R2Field.Multiply(x31, x14, x31); uint[] x62 = x14; SecP160R2Field.SquareN(x31, 31, x62); SecP160R2Field.Multiply(x62, x31, x62); uint[] x124 = x31; SecP160R2Field.SquareN(x62, 62, x124); SecP160R2Field.Multiply(x124, x62, x124); uint[] x127 = x62; SecP160R2Field.SquareN(x124, 3, x127); SecP160R2Field.Multiply(x127, x3, x127); uint[] t1 = x127; SecP160R2Field.SquareN(t1, 18, t1); SecP160R2Field.Multiply(t1, x17, t1); SecP160R2Field.SquareN(t1, 2, t1); SecP160R2Field.Multiply(t1, x1, t1); SecP160R2Field.SquareN(t1, 3, t1); SecP160R2Field.Multiply(t1, x2, t1); SecP160R2Field.SquareN(t1, 6, t1); SecP160R2Field.Multiply(t1, x3, t1); SecP160R2Field.SquareN(t1, 2, t1); SecP160R2Field.Multiply(t1, x1, t1); uint[] t2 = x2; SecP160R2Field.Square(t1, t2); return(Nat160.Eq(x1, t2) ? new SecP160R2FieldElement(t1) : null); }
public override ECPoint Twice() { if (this.IsInfinity) { return(this); } ECCurve curve = this.Curve; SecP160R2FieldElement Y1 = (SecP160R2FieldElement)this.RawYCoord; if (Y1.IsZero) { return(curve.Infinity); } SecP160R2FieldElement X1 = (SecP160R2FieldElement)this.RawXCoord, Z1 = (SecP160R2FieldElement)this.RawZCoords[0]; uint c; uint[] t1 = Nat160.Create(); uint[] t2 = Nat160.Create(); uint[] Y1Squared = Nat160.Create(); SecP160R2Field.Square(Y1.x, Y1Squared); uint[] T = Nat160.Create(); SecP160R2Field.Square(Y1Squared, T); bool Z1IsOne = Z1.IsOne; uint[] Z1Squared = Z1.x; if (!Z1IsOne) { Z1Squared = t2; SecP160R2Field.Square(Z1.x, Z1Squared); } SecP160R2Field.Subtract(X1.x, Z1Squared, t1); uint[] M = t2; SecP160R2Field.Add(X1.x, Z1Squared, M); SecP160R2Field.Multiply(M, t1, M); c = Nat160.AddBothTo(M, M, M); SecP160R2Field.Reduce32(c, M); uint[] S = Y1Squared; SecP160R2Field.Multiply(Y1Squared, X1.x, S); c = Nat.ShiftUpBits(5, S, 2, 0); SecP160R2Field.Reduce32(c, S); c = Nat.ShiftUpBits(5, T, 3, 0, t1); SecP160R2Field.Reduce32(c, t1); SecP160R2FieldElement X3 = new SecP160R2FieldElement(T); SecP160R2Field.Square(M, X3.x); SecP160R2Field.Subtract(X3.x, S, X3.x); SecP160R2Field.Subtract(X3.x, S, X3.x); SecP160R2FieldElement Y3 = new SecP160R2FieldElement(S); SecP160R2Field.Subtract(S, X3.x, Y3.x); SecP160R2Field.Multiply(Y3.x, M, Y3.x); SecP160R2Field.Subtract(Y3.x, t1, Y3.x); SecP160R2FieldElement Z3 = new SecP160R2FieldElement(M); SecP160R2Field.Twice(Y1.x, Z3.x); if (!Z1IsOne) { SecP160R2Field.Multiply(Z3.x, Z1.x, Z3.x); } return(new SecP160R2Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed)); }
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; SecP160R2FieldElement X1 = (SecP160R2FieldElement)this.RawXCoord, Y1 = (SecP160R2FieldElement)this.RawYCoord; SecP160R2FieldElement X2 = (SecP160R2FieldElement)b.RawXCoord, Y2 = (SecP160R2FieldElement)b.RawYCoord; SecP160R2FieldElement Z1 = (SecP160R2FieldElement)this.RawZCoords[0]; SecP160R2FieldElement Z2 = (SecP160R2FieldElement)b.RawZCoords[0]; uint c; uint[] tt1 = Nat160.CreateExt(); uint[] t2 = Nat160.Create(); uint[] t3 = Nat160.Create(); uint[] t4 = Nat160.Create(); bool Z1IsOne = Z1.IsOne; uint[] U2, S2; if (Z1IsOne) { U2 = X2.x; S2 = Y2.x; } else { S2 = t3; SecP160R2Field.Square(Z1.x, S2); U2 = t2; SecP160R2Field.Multiply(S2, X2.x, U2); SecP160R2Field.Multiply(S2, Z1.x, S2); SecP160R2Field.Multiply(S2, Y2.x, S2); } bool Z2IsOne = Z2.IsOne; uint[] U1, S1; if (Z2IsOne) { U1 = X1.x; S1 = Y1.x; } else { S1 = t4; SecP160R2Field.Square(Z2.x, S1); U1 = tt1; SecP160R2Field.Multiply(S1, X1.x, U1); SecP160R2Field.Multiply(S1, Z2.x, S1); SecP160R2Field.Multiply(S1, Y1.x, S1); } uint[] H = Nat160.Create(); SecP160R2Field.Subtract(U1, U2, H); uint[] R = t2; SecP160R2Field.Subtract(S1, S2, R); // Check if b == this or b == -this if (Nat160.IsZero(H)) { if (Nat160.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; SecP160R2Field.Square(H, HSquared); uint[] G = Nat160.Create(); SecP160R2Field.Multiply(HSquared, H, G); uint[] V = t3; SecP160R2Field.Multiply(HSquared, U1, V); SecP160R2Field.Negate(G, G); Nat160.Mul(S1, G, tt1); c = Nat160.AddBothTo(V, V, G); SecP160R2Field.Reduce32(c, G); SecP160R2FieldElement X3 = new SecP160R2FieldElement(t4); SecP160R2Field.Square(R, X3.x); SecP160R2Field.Subtract(X3.x, G, X3.x); SecP160R2FieldElement Y3 = new SecP160R2FieldElement(G); SecP160R2Field.Subtract(V, X3.x, Y3.x); SecP160R2Field.MultiplyAddToExt(Y3.x, R, tt1); SecP160R2Field.Reduce(tt1, Y3.x); SecP160R2FieldElement Z3 = new SecP160R2FieldElement(H); if (!Z1IsOne) { SecP160R2Field.Multiply(Z3.x, Z1.x, Z3.x); } if (!Z2IsOne) { SecP160R2Field.Multiply(Z3.x, Z2.x, Z3.x); } ECFieldElement[] zs = new ECFieldElement[] { Z3 }; return(new SecP160R2Point(curve, X3, Y3, zs, IsCompressed)); }
public override ECFieldElement Add(ECFieldElement b) { uint[] z = Nat160.Create(); SecP160R1Field.Add(x, ((SecP160R1FieldElement)b).x, z); return(new SecP160R1FieldElement(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; SecP160R1FieldElement secP160R1FieldElement = (SecP160R1FieldElement)base.RawXCoord; SecP160R1FieldElement secP160R1FieldElement2 = (SecP160R1FieldElement)base.RawYCoord; SecP160R1FieldElement secP160R1FieldElement3 = (SecP160R1FieldElement)b.RawXCoord; SecP160R1FieldElement secP160R1FieldElement4 = (SecP160R1FieldElement)b.RawYCoord; SecP160R1FieldElement secP160R1FieldElement5 = (SecP160R1FieldElement)base.RawZCoords[0]; SecP160R1FieldElement secP160R1FieldElement6 = (SecP160R1FieldElement)b.RawZCoords[0]; uint[] array = Nat160.CreateExt(); uint[] array2 = Nat160.Create(); uint[] array3 = Nat160.Create(); uint[] array4 = Nat160.Create(); bool isOne = secP160R1FieldElement5.IsOne; uint[] array5; uint[] array6; if (isOne) { array5 = secP160R1FieldElement3.x; array6 = secP160R1FieldElement4.x; } else { array6 = array3; SecP160R1Field.Square(secP160R1FieldElement5.x, array6); array5 = array2; SecP160R1Field.Multiply(array6, secP160R1FieldElement3.x, array5); SecP160R1Field.Multiply(array6, secP160R1FieldElement5.x, array6); SecP160R1Field.Multiply(array6, secP160R1FieldElement4.x, array6); } bool isOne2 = secP160R1FieldElement6.IsOne; uint[] array7; uint[] array8; if (isOne2) { array7 = secP160R1FieldElement.x; array8 = secP160R1FieldElement2.x; } else { array8 = array4; SecP160R1Field.Square(secP160R1FieldElement6.x, array8); array7 = array; SecP160R1Field.Multiply(array8, secP160R1FieldElement.x, array7); SecP160R1Field.Multiply(array8, secP160R1FieldElement6.x, array8); SecP160R1Field.Multiply(array8, secP160R1FieldElement2.x, array8); } uint[] array9 = Nat160.Create(); SecP160R1Field.Subtract(array7, array5, array9); uint[] array10 = array2; SecP160R1Field.Subtract(array8, array6, array10); if (!Nat160.IsZero(array9)) { uint[] array11 = array3; SecP160R1Field.Square(array9, array11); uint[] array12 = Nat160.Create(); SecP160R1Field.Multiply(array11, array9, array12); uint[] array13 = array3; SecP160R1Field.Multiply(array11, array7, array13); SecP160R1Field.Negate(array12, array12); Nat160.Mul(array8, array12, array); uint x = Nat160.AddBothTo(array13, array13, array12); SecP160R1Field.Reduce32(x, array12); SecP160R1FieldElement secP160R1FieldElement7 = new SecP160R1FieldElement(array4); SecP160R1Field.Square(array10, secP160R1FieldElement7.x); SecP160R1Field.Subtract(secP160R1FieldElement7.x, array12, secP160R1FieldElement7.x); SecP160R1FieldElement secP160R1FieldElement8 = new SecP160R1FieldElement(array12); SecP160R1Field.Subtract(array13, secP160R1FieldElement7.x, secP160R1FieldElement8.x); SecP160R1Field.MultiplyAddToExt(secP160R1FieldElement8.x, array10, array); SecP160R1Field.Reduce(array, secP160R1FieldElement8.x); SecP160R1FieldElement secP160R1FieldElement9 = new SecP160R1FieldElement(array9); if (!isOne) { SecP160R1Field.Multiply(secP160R1FieldElement9.x, secP160R1FieldElement5.x, secP160R1FieldElement9.x); } if (!isOne2) { SecP160R1Field.Multiply(secP160R1FieldElement9.x, secP160R1FieldElement6.x, secP160R1FieldElement9.x); } ECFieldElement[] zs = new ECFieldElement[] { secP160R1FieldElement9 }; return(new SecP160R1Point(curve, secP160R1FieldElement7, secP160R1FieldElement8, zs, base.IsCompressed)); } if (Nat160.IsZero(array10)) { return(this.Twice()); } return(curve.Infinity); }
public override ECFieldElement Square() { uint[] z = Nat160.Create(); SecP160R1Field.Square(x, z); return(new SecP160R1FieldElement(z)); }
public static void Multiply(uint[] x, uint[] y, uint[] z) { uint[] tt = Nat160.CreateExt(); Nat160.Mul(x, y, tt); Reduce(tt, z); }
public override ECFieldElement AddOne() { uint[] z = Nat160.Create(); SecP160R2Field.AddOne(x, z); return(new SecP160R2FieldElement(z)); }
public override ECFieldElement Subtract(ECFieldElement b) { uint[] z = Nat160.Create(); SecP160R2Field.Subtract(x, ((SecP160R2FieldElement)b).x, z); return(new SecP160R2FieldElement(z)); }
public static void Square(uint[] x, uint[] z) { uint[] tt = Nat160.CreateExt(); Nat160.Square(x, tt); Reduce(tt, z); }