public bool Equals(IEllipticCurvePoint obj) { if (obj as object == null) { return(false); } if (obj as object == this) { return(true); } EllipticCurvePointC obj1 = obj as EllipticCurvePointC; if (obj1 as object == null) { return(false); } if (m_X == obj1.m_X) { if (m_Y == obj1.m_Y) { if (m_Z == obj1.m_Z) { return(true); } } } return(false); }
/// <summary> /// Adds the this value with another value in elliptic curve /// </summary> /// <param name="value">The value to add with this value</param> /// <returns>The sum of values</returns> public IEllipticCurvePoint Addition(IEllipticCurvePoint value) { EllipticCurvePointC value2 = value as EllipticCurvePointC; if (value2 as object == null) { throw new Exception("Incorrect point type!"); } if (m_a4 != value2.m_a4 || m_a6 != value2.m_a6 || m_Modulo != value2.m_Modulo) { throw new Exception("Incorrect value elliptic curve parameters!"); } if (value2.Infinity) { return(new EllipticCurvePointC(m_X, m_Y, m_Z, this)); } if (Infinity) { return(new EllipticCurvePointC(value2.m_X, value2.m_Y, value2.m_Z, value2)); } if (Equals(value2)) { return(Doubling()); } // Coordinates uint[] a = m_a4.m_Value; uint[] x1 = m_X.m_Value; uint[] y1 = m_Y.m_Value; uint[] z1 = m_Z.m_Value; uint[] x2 = value2.m_X.m_Value; uint[] y2 = value2.m_Y.m_Value; uint[] z2 = value2.m_Z.m_Value; uint[] modulo = m_Modulo.m_Value; int maxModuloBitIndex = BigHelper.MaxNonZeroBitIndex(modulo); int length = modulo.Length; // Get the cache uint[] cache = new uint[length * 2]; uint[] A = new uint[length]; uint[] D = new uint[length]; uint[] B = new uint[length]; uint[] C = new uint[length]; uint[] xr = new uint[length]; uint[] yr = new uint[length]; uint[] zr = new uint[length]; // Z1^2 ModuloOperations.Multiply(z1, z1, modulo, A, cache); // Z1^2 * a ModuloOperations.Multiply(z1, a, modulo, D, cache); // X2 * Z1 ModuloOperations.Multiply(x2, z1, modulo, B, cache); // B = X2 * Z1 + X1 ModuloOperations.Addition(B, x1, modulo); // C = Z1*B ModuloOperations.Multiply(z1, B, modulo, C, cache); // C + Z1^2 * a ModuloOperations.Addition(D, C, modulo); // B * (C + Z1^2 * a) ModuloOperations.Multiply(D, B, modulo, D, cache); // D = B^2 * (C + Z1^2 * a) ModuloOperations.Multiply(D, B, modulo, D, cache); // Y2 * Z1^2 ModuloOperations.Multiply(A, y2, modulo, A, cache); // A = Y2 * Z1^2 + Y1 ModuloOperations.Addition(A, y1, modulo); if (BigHelper.IfZero(B)) { if (BigHelper.IfZero(A)) { return(value2.Doubling()); } else { return(GetInfinity()); } } // Z3 = C^2 ModuloOperations.Multiply(C, C, modulo, zr, cache); // E = A * C ModuloOperations.Multiply(C, A, modulo, C, cache); // A^2 ModuloOperations.Multiply(A, A, modulo, xr, cache); // A^2 + D ModuloOperations.Addition(xr, D, modulo); // X3 = A^2 + D + E ModuloOperations.Addition(xr, C, modulo); // X2 * Z3 ModuloOperations.Multiply(x2, zr, modulo, A, cache); // F = X3 + X2 * Z3 ModuloOperations.Addition(A, xr, modulo); // X2 + Y2 ModuloOperations.Addition(x2, y2, modulo, B); // (X2 + Y2) * Z3 ModuloOperations.Multiply(B, zr, modulo, B, cache); // G = (X2 + Y2) * Z3^2 ModuloOperations.Multiply(B, zr, modulo, B, cache); // E + Z3 ModuloOperations.Addition(C, zr, modulo, yr); // (E + Z3) * F ModuloOperations.Multiply(yr, A, modulo, yr, cache); // (E + Z3) * F + G ModuloOperations.Addition(yr, B, modulo, yr); return(new EllipticCurvePointC(xr, yr, zr, this)); }
/// <summary> /// Сложить две точки на кривой /// </summary> /// <param name="value1"></param> /// <param name="value2"></param> /// <returns></returns> public IEllipticCurvePoint Addition(IEllipticCurvePoint value) { EllipticCurvePointB value2 = value as EllipticCurvePointB; if (value2 as object == null) { throw new Exception("Incorrect point type!"); } if (m_a4 != value2.m_a4 || m_a6 != value2.m_a6 || m_Modulo != value2.m_Modulo) { throw new Exception("Incorrect value elliptic curve parameters!"); } if (Equals(value2)) { return(Doubling()); } // Исходные координаты uint[] a = m_a4.m_Value; uint[] x1 = m_X.m_Value; uint[] y1 = m_Y.m_Value; uint[] z1 = m_Z.m_Value; uint[] x2 = value2.m_X.m_Value; uint[] y2 = value2.m_Y.m_Value; uint[] z2 = value2.m_Z.m_Value; uint[] modulo = m_Modulo.m_Value; int maxModuloBitIndex = BigHelper.MaxNonZeroBitIndex(modulo); int length = modulo.Length; // Выделим кэш операций умножения uint[] cache = new uint[length * 2]; // Временные переменные uint[] u1 = new uint[length]; uint[] u2 = new uint[length]; uint[] s1 = new uint[length]; uint[] s2 = new uint[length]; uint[] xr = new uint[length]; uint[] yr = new uint[length]; uint[] zr = new uint[length]; // Вычислить U1, U2, S1, S2 ModuloOperations.Multiply(z2, z2, modulo, u1, cache); ModuloOperations.Multiply(z1, z1, modulo, u2, cache); ModuloOperations.Multiply(u1, z2, modulo, s1, cache); ModuloOperations.Multiply(u2, z1, modulo, s2, cache); ModuloOperations.Multiply(u1, x1, modulo, u1, cache); ModuloOperations.Multiply(u2, x2, modulo, u2, cache); ModuloOperations.Multiply(s1, y1, modulo, s1, cache); ModuloOperations.Multiply(s2, y2, modulo, s2, cache); // Проверим, может расчет if (Eguals(u1, u2)) { if (Eguals(s1, s2)) { return(Doubling()); } else { return(GetInfinity()); } } ModuloOperations.Substraction(u2, u1, modulo); ModuloOperations.Substraction(s2, s1, modulo); //H^2 ModuloOperations.Multiply(u2, u2, modulo, yr, cache); //H^3 ModuloOperations.Multiply(yr, u2, modulo, zr, cache); //R^2 ModuloOperations.Multiply(s2, s2, modulo, xr, cache); //R^2 - H^3 ModuloOperations.Substraction(xr, zr, modulo); //U1*H^2 ModuloOperations.Multiply(u1, yr, modulo, yr, cache); //2*U1*H^2 ModuloOperations.Multiply(yr, 2, modulo, u1, cache); //X3 = R^2 - H^3 - 2*U1*H^2 ModuloOperations.Substraction(xr, u1, modulo); //U1*H^2 - X3 ModuloOperations.Substraction(yr, xr, modulo); //R*(U1*H^2 - X3) ModuloOperations.Multiply(yr, s2, modulo, yr, cache); //S1*H^3 ModuloOperations.Multiply(s1, zr, modulo, zr, cache); //R*(U1*H^2 - X3) - S1*H^3 ModuloOperations.Substraction(yr, zr, modulo); //Z1*Z2 ModuloOperations.Multiply(z1, z2, modulo, zr, cache); //Z3 = H*Z1*Z2 ModuloOperations.Multiply(zr, u2, modulo, zr, cache); return(new EllipticCurvePointB(xr, yr, zr, this)); }
internal EllipticCurvePoint(uint x, uint y, uint z, IEllipticCurvePoint resolver) { m_Resolver = new EllipticCurvePointB(x, y, z, resolver as EllipticCurvePointB); }
internal EllipticCurvePoint(IntBig x, IntBig y, IntBig z, IEllipticCurvePoint resolver) { m_Resolver = new EllipticCurvePointB(x, y, z, resolver as EllipticCurvePointB); }
internal EllipticCurvePoint(IEllipticCurvePoint resolver) { m_Resolver = resolver; }