rg1/server/Sog/3rd/BouncyCastle/math/ec/custom/djb/Curve25519FieldElement.cs

using System;

using Org.BouncyCastle.Math.Raw;
using Org.BouncyCastle.Utilities;

namespace Org.BouncyCastle.Math.EC.Custom.Djb
{
    internal class Curve25519FieldElement
        : AbstractFpFieldElement
    {
        public static readonly BigInteger Q = Nat256.ToBigInteger(Curve25519Field.P);

        // Calculated as ECConstants.TWO.modPow(Q.shiftRight(2), Q)
        private static readonly uint[] PRECOMP_POW2 = new uint[]{ 0x4a0ea0b0, 0xc4ee1b27, 0xad2fe478, 0x2f431806,
            0x3dfbd7a7, 0x2b4d0099, 0x4fc1df0b, 0x2b832480 };

        protected internal readonly uint[] x;

        public Curve25519FieldElement(BigInteger x)
        {
            if (x == null || x.SignValue < 0 || x.CompareTo(Q) >= 0)
                throw new ArgumentException("value invalid for Curve25519FieldElement", "x");

            this.x = Curve25519Field.FromBigInteger(x);
        }

        public Curve25519FieldElement()
        {
            this.x = Nat256.Create();
        }

        protected internal Curve25519FieldElement(uint[] x)
        {
            this.x = x;
        }

        public override bool IsZero
        {
            get { return Nat256.IsZero(x); }
        }

        public override bool IsOne
        {
            get { return Nat256.IsOne(x); }
        }

        public override bool TestBitZero()
        {
            return Nat256.GetBit(x, 0) == 1;
        }

        public override BigInteger ToBigInteger()
        {
            return Nat256.ToBigInteger(x);
        }

        public override string FieldName
        {
            get { return "Curve25519Field"; }
        }

        public override int FieldSize
        {
            get { return Q.BitLength; }
        }

        public override ECFieldElement Add(ECFieldElement b)
        {
            uint[] z = Nat256.Create();
            Curve25519Field.Add(x, ((Curve25519FieldElement)b).x, z);
            return new Curve25519FieldElement(z);
        }

        public override ECFieldElement AddOne()
        {
            uint[] z = Nat256.Create();
            Curve25519Field.AddOne(x, z);
            return new Curve25519FieldElement(z);
        }

        public override ECFieldElement Subtract(ECFieldElement b)
        {
            uint[] z = Nat256.Create();
            Curve25519Field.Subtract(x, ((Curve25519FieldElement)b).x, z);
            return new Curve25519FieldElement(z);
        }

        public override ECFieldElement Multiply(ECFieldElement b)
        {
            uint[] z = Nat256.Create();
            Curve25519Field.Multiply(x, ((Curve25519FieldElement)b).x, z);
            return new Curve25519FieldElement(z);
        }

        public override ECFieldElement Divide(ECFieldElement b)
        {
            //return Multiply(b.Invert());
            uint[] z = Nat256.Create();
            Curve25519Field.Inv(((Curve25519FieldElement)b).x, z);
            Curve25519Field.Multiply(z, x, z);
            return new Curve25519FieldElement(z);
        }

        public override ECFieldElement Negate()
        {
            uint[] z = Nat256.Create();
            Curve25519Field.Negate(x, z);
            return new Curve25519FieldElement(z);
        }

        public override ECFieldElement Square()
        {
            uint[] z = Nat256.Create();
            Curve25519Field.Square(x, z);
            return new Curve25519FieldElement(z);
        }

        public override ECFieldElement Invert()
        {
            //return new Curve25519FieldElement(ToBigInteger().ModInverse(Q));
            uint[] z = Nat256.Create();
            Curve25519Field.Inv(x, z);
            return new Curve25519FieldElement(z);
        }

        /**
         * 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 2^252 - 2^1 (i.e. m + 1)
             * 
             * Breaking up the exponent's binary representation into "repunits", we get:
             * { 251 1s } { 1 0s }
             * 
             * Therefore we need an addition chain containing 251 (the lengths of the repunits)
             * We use: 1, 2, 3, 4, 7, 11, 15, 30, 60, 120, 131, [251]
             */

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

            uint[] x2 = Nat256.Create();
            Curve25519Field.Square(x1, x2);
            Curve25519Field.Multiply(x2, x1, x2);
            uint[] x3 = x2;
            Curve25519Field.Square(x2, x3);
            Curve25519Field.Multiply(x3, x1, x3);
            uint[] x4 = Nat256.Create();
            Curve25519Field.Square(x3, x4);
            Curve25519Field.Multiply(x4, x1, x4);
            uint[] x7 = Nat256.Create();
            Curve25519Field.SquareN(x4, 3, x7);
            Curve25519Field.Multiply(x7, x3, x7);
            uint[] x11 = x3;
            Curve25519Field.SquareN(x7, 4, x11);
            Curve25519Field.Multiply(x11, x4, x11);
            uint[] x15 = x7;
            Curve25519Field.SquareN(x11, 4, x15);
            Curve25519Field.Multiply(x15, x4, x15);
            uint[] x30 = x4;
            Curve25519Field.SquareN(x15, 15, x30);
            Curve25519Field.Multiply(x30, x15, x30);
            uint[] x60 = x15;
            Curve25519Field.SquareN(x30, 30, x60);
            Curve25519Field.Multiply(x60, x30, x60);
            uint[] x120 = x30;
            Curve25519Field.SquareN(x60, 60, x120);
            Curve25519Field.Multiply(x120, x60, x120);
            uint[] x131 = x60;
            Curve25519Field.SquareN(x120, 11, x131);
            Curve25519Field.Multiply(x131, x11, x131);
            uint[] x251 = x11;
            Curve25519Field.SquareN(x131, 120, x251);
            Curve25519Field.Multiply(x251, x120, x251);

            uint[] t1 = x251;
            Curve25519Field.Square(t1, t1);

            uint[] t2 = x120;
            Curve25519Field.Square(t1, t2);

            if (Nat256.Eq(x1, t2))
            {
                return new Curve25519FieldElement(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
             */
            Curve25519Field.Multiply(t1, PRECOMP_POW2, t1);

            Curve25519Field.Square(t1, t2);

            if (Nat256.Eq(x1, t2))
            {
                return new Curve25519FieldElement(t1);
            }

            return null;
        }

        public override bool Equals(object obj)
        {
            return Equals(obj as Curve25519FieldElement);
        }

        public override bool Equals(ECFieldElement other)
        {
            return Equals(other as Curve25519FieldElement);
        }

        public virtual bool Equals(Curve25519FieldElement other)
        {
            if (this == other)
                return true;
            if (null == other)
                return false;
            return Nat256.Eq(x, other.x);
        }

        public override int GetHashCode()
        {
            return Q.GetHashCode() ^ Arrays.GetHashCode(x, 0, 8);
        }
    }
}