Initial Commit
This commit is contained in:
566
iTechSharp/srcbc/math/ec/ECPoint.cs
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566
iTechSharp/srcbc/math/ec/ECPoint.cs
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using System;
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using System.Collections;
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using System.Diagnostics;
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using Org.BouncyCastle.Asn1.X9;
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using Org.BouncyCastle.Math.EC.Multiplier;
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namespace Org.BouncyCastle.Math.EC
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{
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/**
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* base class for points on elliptic curves.
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*/
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public abstract class ECPoint
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{
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internal readonly ECCurve curve;
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internal readonly ECFieldElement x, y;
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internal readonly bool withCompression;
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internal ECMultiplier multiplier = null;
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internal PreCompInfo preCompInfo = null;
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protected internal ECPoint(
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ECCurve curve,
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ECFieldElement x,
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ECFieldElement y,
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bool withCompression)
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{
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if (curve == null)
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throw new ArgumentNullException("curve");
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this.curve = curve;
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this.x = x;
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this.y = y;
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this.withCompression = withCompression;
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}
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public ECCurve Curve
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{
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get { return curve; }
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}
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public ECFieldElement X
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{
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get { return x; }
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}
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public ECFieldElement Y
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{
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get { return y; }
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}
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public bool IsInfinity
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{
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get { return x == null && y == null; }
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}
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public bool IsCompressed
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{
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get { return withCompression; }
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}
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public override bool Equals(
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object obj)
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{
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if (obj == this)
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return true;
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ECPoint o = obj as ECPoint;
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if (o == null)
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return false;
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if (this.IsInfinity)
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return o.IsInfinity;
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return x.Equals(o.x) && y.Equals(o.y);
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}
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public override int GetHashCode()
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{
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if (this.IsInfinity)
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return 0;
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return x.GetHashCode() ^ y.GetHashCode();
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}
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// /**
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// * Mainly for testing. Explicitly set the <code>ECMultiplier</code>.
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// * @param multiplier The <code>ECMultiplier</code> to be used to multiply
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// * this <code>ECPoint</code>.
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// */
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// internal void SetECMultiplier(
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// ECMultiplier multiplier)
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// {
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// this.multiplier = multiplier;
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// }
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/**
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* Sets the <code>PreCompInfo</code>. Used by <code>ECMultiplier</code>s
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* to save the precomputation for this <code>ECPoint</code> to store the
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* precomputation result for use by subsequent multiplication.
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* @param preCompInfo The values precomputed by the
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* <code>ECMultiplier</code>.
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*/
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internal void SetPreCompInfo(
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PreCompInfo preCompInfo)
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{
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this.preCompInfo = preCompInfo;
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}
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public abstract byte[] GetEncoded();
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public abstract ECPoint Add(ECPoint b);
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public abstract ECPoint Subtract(ECPoint b);
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public abstract ECPoint Negate();
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public abstract ECPoint Twice();
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public abstract ECPoint Multiply(BigInteger b);
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/**
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* Sets the appropriate <code>ECMultiplier</code>, unless already set.
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*/
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internal virtual void AssertECMultiplier()
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{
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if (this.multiplier == null)
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{
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lock (this)
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{
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if (this.multiplier == null)
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{
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this.multiplier = new FpNafMultiplier();
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}
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}
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}
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}
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}
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public abstract class ECPointBase
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: ECPoint
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{
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protected internal ECPointBase(
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ECCurve curve,
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ECFieldElement x,
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ECFieldElement y,
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bool withCompression)
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: base(curve, x, y, withCompression)
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{
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}
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protected internal abstract bool YTilde { get; }
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/**
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* return the field element encoded with point compression. (S 4.3.6)
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*/
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public override byte[] GetEncoded()
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{
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if (this.IsInfinity)
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return new byte[1];
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// Note: some of the tests rely on calculating byte length from the field element
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// (since the test cases use mismatching fields for curve/elements)
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int byteLength = X9IntegerConverter.GetByteLength(x);
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byte[] X = X9IntegerConverter.IntegerToBytes(this.X.ToBigInteger(), byteLength);
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byte[] PO;
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if (withCompression)
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{
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PO = new byte[1 + X.Length];
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PO[0] = (byte)(YTilde ? 0x03 : 0x02);
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}
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else
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{
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byte[] Y = X9IntegerConverter.IntegerToBytes(this.Y.ToBigInteger(), byteLength);
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PO = new byte[1 + X.Length + Y.Length];
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PO[0] = 0x04;
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Y.CopyTo(PO, 1 + X.Length);
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}
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X.CopyTo(PO, 1);
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return PO;
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}
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/**
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* Multiplies this <code>ECPoint</code> by the given number.
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* @param k The multiplicator.
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* @return <code>k * this</code>.
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*/
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public override ECPoint Multiply(
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BigInteger k)
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{
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if (this.IsInfinity)
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return this;
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if (k.SignValue == 0)
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return this.curve.Infinity;
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AssertECMultiplier();
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return this.multiplier.Multiply(this, k, preCompInfo);
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}
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}
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/**
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* Elliptic curve points over Fp
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*/
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public class FpPoint
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: ECPointBase
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{
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/**
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* Create a point which encodes with point compression.
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*
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* @param curve the curve to use
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* @param x affine x co-ordinate
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* @param y affine y co-ordinate
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*/
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public FpPoint(
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ECCurve curve,
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ECFieldElement x,
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ECFieldElement y)
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: this(curve, x, y, false)
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{
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}
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/**
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* Create a point that encodes with or without point compresion.
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*
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* @param curve the curve to use
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* @param x affine x co-ordinate
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* @param y affine y co-ordinate
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* @param withCompression if true encode with point compression
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*/
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public FpPoint(
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ECCurve curve,
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ECFieldElement x,
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ECFieldElement y,
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bool withCompression)
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: base(curve, x, y, withCompression)
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{
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if ((x != null && y == null) || (x == null && y != null))
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throw new ArgumentException("Exactly one of the field elements is null");
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}
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protected internal override bool YTilde
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{
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get
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{
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return this.Y.ToBigInteger().TestBit(0);
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}
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}
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// B.3 pg 62
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public override ECPoint Add(
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ECPoint b)
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{
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if (this.IsInfinity)
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return b;
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if (b.IsInfinity)
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return this;
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// Check if b = this or b = -this
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if (this.x.Equals(b.x))
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{
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if (this.y.Equals(b.y))
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{
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// this = b, i.e. this must be doubled
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return this.Twice();
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}
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Debug.Assert(this.y.Equals(b.y.Negate()));
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// this = -b, i.e. the result is the point at infinity
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return this.curve.Infinity;
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}
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ECFieldElement gamma = b.y.Subtract(this.y).Divide(b.x.Subtract(this.x));
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ECFieldElement x3 = gamma.Square().Subtract(this.x).Subtract(b.x);
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ECFieldElement y3 = gamma.Multiply(this.x.Subtract(x3)).Subtract(this.y);
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return new FpPoint(curve, x3, y3);
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}
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// B.3 pg 62
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public override ECPoint Twice()
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{
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// Twice identity element (point at infinity) is identity
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if (this.IsInfinity)
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return this;
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// if y1 == 0, then (x1, y1) == (x1, -y1)
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// and hence this = -this and thus 2(x1, y1) == infinity
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if (this.y.ToBigInteger().SignValue == 0)
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return this.curve.Infinity;
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ECFieldElement TWO = this.curve.FromBigInteger(BigInteger.Two);
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ECFieldElement THREE = this.curve.FromBigInteger(BigInteger.Three);
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ECFieldElement gamma = this.x.Square().Multiply(THREE).Add(curve.a).Divide(y.Multiply(TWO));
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ECFieldElement x3 = gamma.Square().Subtract(this.x.Multiply(TWO));
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ECFieldElement y3 = gamma.Multiply(this.x.Subtract(x3)).Subtract(this.y);
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return new FpPoint(curve, x3, y3, this.withCompression);
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}
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// D.3.2 pg 102 (see Note:)
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public override ECPoint Subtract(
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ECPoint b)
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{
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if (b.IsInfinity)
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return this;
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// Add -b
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return Add(b.Negate());
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}
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public override ECPoint Negate()
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{
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return new FpPoint(this.curve, this.x, this.y.Negate(), this.withCompression);
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}
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// TODO Uncomment this to enable WNAF Fp point multiplication
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// /**
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// * Sets the default <code>ECMultiplier</code>, unless already set.
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// */
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// internal override void AssertECMultiplier()
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// {
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// if (this.multiplier == null)
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// {
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// lock (this)
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// {
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// if (this.multiplier == null)
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// {
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// this.multiplier = new WNafMultiplier();
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// }
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// }
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// }
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// }
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}
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/**
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* Elliptic curve points over F2m
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*/
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public class F2mPoint
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: ECPointBase
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{
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/**
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* @param curve base curve
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* @param x x point
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* @param y y point
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*/
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public F2mPoint(
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ECCurve curve,
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ECFieldElement x,
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ECFieldElement y)
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: this(curve, x, y, false)
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{
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}
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/**
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* @param curve base curve
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* @param x x point
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* @param y y point
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* @param withCompression true if encode with point compression.
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*/
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public F2mPoint(
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ECCurve curve,
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ECFieldElement x,
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ECFieldElement y,
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bool withCompression)
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: base(curve, x, y, withCompression)
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{
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if ((x != null && y == null) || (x == null && y != null))
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{
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throw new ArgumentException("Exactly one of the field elements is null");
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}
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if (x != null)
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{
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// Check if x and y are elements of the same field
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F2mFieldElement.CheckFieldElements(this.x, this.y);
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// Check if x and a are elements of the same field
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F2mFieldElement.CheckFieldElements(this.x, this.curve.A);
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}
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}
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/**
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* Constructor for point at infinity
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*/
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[Obsolete("Use ECCurve.Infinity property")]
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public F2mPoint(
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ECCurve curve)
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: this(curve, null, null)
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{
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}
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protected internal override bool YTilde
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{
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get
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{
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// X9.62 4.2.2 and 4.3.6:
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// if x = 0 then ypTilde := 0, else ypTilde is the rightmost
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// bit of y * x^(-1)
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return this.X.ToBigInteger().SignValue != 0
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&& this.Y.Multiply(this.X.Invert()).ToBigInteger().TestBit(0);
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}
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}
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/**
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* Check, if two <code>ECPoint</code>s can be added or subtracted.
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* @param a The first <code>ECPoint</code> to check.
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* @param b The second <code>ECPoint</code> to check.
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* @throws IllegalArgumentException if <code>a</code> and <code>b</code>
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* cannot be added.
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*/
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private static void CheckPoints(
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ECPoint a,
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ECPoint b)
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{
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// Check, if points are on the same curve
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if (!a.curve.Equals(b.curve))
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throw new ArgumentException("Only points on the same curve can be added or subtracted");
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// F2mFieldElement.CheckFieldElements(a.x, b.x);
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}
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/* (non-Javadoc)
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* @see org.bouncycastle.math.ec.ECPoint#add(org.bouncycastle.math.ec.ECPoint)
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*/
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public override ECPoint Add(ECPoint b)
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{
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CheckPoints(this, b);
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return AddSimple((F2mPoint) b);
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}
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/**
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* Adds another <code>ECPoints.F2m</code> to <code>this</code> without
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* checking if both points are on the same curve. Used by multiplication
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* algorithms, because there all points are a multiple of the same point
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* and hence the checks can be omitted.
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* @param b The other <code>ECPoints.F2m</code> to add to
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* <code>this</code>.
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* @return <code>this + b</code>
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*/
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internal F2mPoint AddSimple(F2mPoint b)
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{
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if (this.IsInfinity)
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return b;
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if (b.IsInfinity)
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return this;
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F2mFieldElement x2 = (F2mFieldElement) b.X;
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F2mFieldElement y2 = (F2mFieldElement) b.Y;
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// Check if b == this or b == -this
|
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if (this.x.Equals(x2))
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{
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// this == b, i.e. this must be doubled
|
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if (this.y.Equals(y2))
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return (F2mPoint) this.Twice();
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// this = -other, i.e. the result is the point at infinity
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return (F2mPoint) this.curve.Infinity;
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}
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ECFieldElement xSum = this.x.Add(x2);
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F2mFieldElement lambda
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= (F2mFieldElement)(this.y.Add(y2)).Divide(xSum);
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F2mFieldElement x3
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= (F2mFieldElement)lambda.Square().Add(lambda).Add(xSum).Add(this.curve.A);
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F2mFieldElement y3
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= (F2mFieldElement)lambda.Multiply(this.x.Add(x3)).Add(x3).Add(this.y);
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return new F2mPoint(curve, x3, y3, withCompression);
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}
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/* (non-Javadoc)
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* @see org.bouncycastle.math.ec.ECPoint#subtract(org.bouncycastle.math.ec.ECPoint)
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*/
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public override ECPoint Subtract(
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ECPoint b)
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{
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CheckPoints(this, b);
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return SubtractSimple((F2mPoint) b);
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}
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|
||||
/**
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* Subtracts another <code>ECPoints.F2m</code> from <code>this</code>
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* without checking if both points are on the same curve. Used by
|
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* multiplication algorithms, because there all points are a multiple
|
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* of the same point and hence the checks can be omitted.
|
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* @param b The other <code>ECPoints.F2m</code> to subtract from
|
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* <code>this</code>.
|
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* @return <code>this - b</code>
|
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*/
|
||||
internal F2mPoint SubtractSimple(
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F2mPoint b)
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{
|
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if (b.IsInfinity)
|
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return this;
|
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|
||||
// Add -b
|
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return AddSimple((F2mPoint) b.Negate());
|
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}
|
||||
|
||||
/* (non-Javadoc)
|
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* @see Org.BouncyCastle.Math.EC.ECPoint#twice()
|
||||
*/
|
||||
public override ECPoint Twice()
|
||||
{
|
||||
// Twice identity element (point at infinity) is identity
|
||||
if (this.IsInfinity)
|
||||
return this;
|
||||
|
||||
// if x1 == 0, then (x1, y1) == (x1, x1 + y1)
|
||||
// and hence this = -this and thus 2(x1, y1) == infinity
|
||||
if (this.x.ToBigInteger().SignValue == 0)
|
||||
return this.curve.Infinity;
|
||||
|
||||
F2mFieldElement lambda = (F2mFieldElement) this.x.Add(this.y.Divide(this.x));
|
||||
F2mFieldElement x2 = (F2mFieldElement)lambda.Square().Add(lambda).Add(this.curve.A);
|
||||
ECFieldElement ONE = this.curve.FromBigInteger(BigInteger.One);
|
||||
F2mFieldElement y2 = (F2mFieldElement)this.x.Square().Add(
|
||||
x2.Multiply(lambda.Add(ONE)));
|
||||
|
||||
return new F2mPoint(this.curve, x2, y2, withCompression);
|
||||
}
|
||||
|
||||
public override ECPoint Negate()
|
||||
{
|
||||
return new F2mPoint(curve, this.x, this.x.Add(this.y), withCompression);
|
||||
}
|
||||
|
||||
// TODO Uncomment this to enable WNAF/WTNAF F2m point multiplication
|
||||
// /**
|
||||
// * Sets the appropriate <code>ECMultiplier</code>, unless already set.
|
||||
// */
|
||||
// internal override void AssertECMultiplier()
|
||||
// {
|
||||
// if (this.multiplier == null)
|
||||
// {
|
||||
// lock (this)
|
||||
// {
|
||||
// if (this.multiplier == null)
|
||||
// {
|
||||
// if (((F2mCurve) this.curve).IsKoblitz)
|
||||
// {
|
||||
// this.multiplier = new WTauNafMultiplier();
|
||||
// }
|
||||
// else
|
||||
// {
|
||||
// this.multiplier = new WNafMultiplier();
|
||||
// }
|
||||
// }
|
||||
// }
|
||||
// }
|
||||
// }
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user