| package org.bouncycastle.math.ec.custom.djb; |
| |
| import org.bouncycastle.math.ec.ECCurve; |
| import org.bouncycastle.math.ec.ECFieldElement; |
| import org.bouncycastle.math.ec.ECPoint; |
| import org.bouncycastle.math.raw.Nat256; |
| |
| public class Curve25519Point extends ECPoint.AbstractFp |
| { |
| /** |
| * Create a point which encodes with point compression. |
| * |
| * @param curve the curve to use |
| * @param x affine x co-ordinate |
| * @param y affine y co-ordinate |
| * |
| * @deprecated Use ECCurve.createPoint to construct points |
| */ |
| public Curve25519Point(ECCurve curve, ECFieldElement x, ECFieldElement y) |
| { |
| this(curve, x, y, false); |
| } |
| |
| /** |
| * Create a point that encodes with or without point compresion. |
| * |
| * @param curve the curve to use |
| * @param x affine x co-ordinate |
| * @param y affine y co-ordinate |
| * @param withCompression if true encode with point compression |
| * |
| * @deprecated per-point compression property will be removed, refer {@link #getEncoded(boolean)} |
| */ |
| public Curve25519Point(ECCurve curve, ECFieldElement x, ECFieldElement y, boolean withCompression) |
| { |
| super(curve, x, y); |
| |
| if ((x == null) != (y == null)) |
| { |
| throw new IllegalArgumentException("Exactly one of the field elements is null"); |
| } |
| |
| this.withCompression = withCompression; |
| } |
| |
| Curve25519Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs, boolean withCompression) |
| { |
| super(curve, x, y, zs); |
| |
| this.withCompression = withCompression; |
| } |
| |
| protected ECPoint detach() |
| { |
| return new Curve25519Point(null, getAffineXCoord(), getAffineYCoord()); |
| } |
| |
| public ECFieldElement getZCoord(int index) |
| { |
| if (index == 1) |
| { |
| return getJacobianModifiedW(); |
| } |
| |
| return super.getZCoord(index); |
| } |
| |
| public ECPoint add(ECPoint b) |
| { |
| if (this.isInfinity()) |
| { |
| return b; |
| } |
| if (b.isInfinity()) |
| { |
| return this; |
| } |
| if (this == b) |
| { |
| return twice(); |
| } |
| |
| ECCurve curve = this.getCurve(); |
| |
| Curve25519FieldElement X1 = (Curve25519FieldElement)this.x, Y1 = (Curve25519FieldElement)this.y, |
| Z1 = (Curve25519FieldElement)this.zs[0]; |
| Curve25519FieldElement X2 = (Curve25519FieldElement)b.getXCoord(), Y2 = (Curve25519FieldElement)b.getYCoord(), |
| Z2 = (Curve25519FieldElement)b.getZCoord(0); |
| |
| int c; |
| int[] tt1 = Nat256.createExt(); |
| int[] t2 = Nat256.create(); |
| int[] t3 = Nat256.create(); |
| int[] t4 = Nat256.create(); |
| |
| boolean Z1IsOne = Z1.isOne(); |
| int[] U2, S2; |
| if (Z1IsOne) |
| { |
| U2 = X2.x; |
| S2 = Y2.x; |
| } |
| else |
| { |
| S2 = t3; |
| Curve25519Field.square(Z1.x, S2); |
| |
| U2 = t2; |
| Curve25519Field.multiply(S2, X2.x, U2); |
| |
| Curve25519Field.multiply(S2, Z1.x, S2); |
| Curve25519Field.multiply(S2, Y2.x, S2); |
| } |
| |
| boolean Z2IsOne = Z2.isOne(); |
| int[] U1, S1; |
| if (Z2IsOne) |
| { |
| U1 = X1.x; |
| S1 = Y1.x; |
| } |
| else |
| { |
| S1 = t4; |
| Curve25519Field.square(Z2.x, S1); |
| |
| U1 = tt1; |
| Curve25519Field.multiply(S1, X1.x, U1); |
| |
| Curve25519Field.multiply(S1, Z2.x, S1); |
| Curve25519Field.multiply(S1, Y1.x, S1); |
| } |
| |
| int[] H = Nat256.create(); |
| Curve25519Field.subtract(U1, U2, H); |
| |
| int[] R = t2; |
| Curve25519Field.subtract(S1, S2, R); |
| |
| // Check if b == this or b == -this |
| if (Nat256.isZero(H)) |
| { |
| if (Nat256.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.getInfinity(); |
| } |
| |
| int[] HSquared = Nat256.create(); |
| Curve25519Field.square(H, HSquared); |
| |
| int[] G = Nat256.create(); |
| Curve25519Field.multiply(HSquared, H, G); |
| |
| int[] V = t3; |
| Curve25519Field.multiply(HSquared, U1, V); |
| |
| Curve25519Field.negate(G, G); |
| Nat256.mul(S1, G, tt1); |
| |
| c = Nat256.addBothTo(V, V, G); |
| Curve25519Field.reduce27(c, G); |
| |
| Curve25519FieldElement X3 = new Curve25519FieldElement(t4); |
| Curve25519Field.square(R, X3.x); |
| Curve25519Field.subtract(X3.x, G, X3.x); |
| |
| Curve25519FieldElement Y3 = new Curve25519FieldElement(G); |
| Curve25519Field.subtract(V, X3.x, Y3.x); |
| Curve25519Field.multiplyAddToExt(Y3.x, R, tt1); |
| Curve25519Field.reduce(tt1, Y3.x); |
| |
| Curve25519FieldElement Z3 = new Curve25519FieldElement(H); |
| if (!Z1IsOne) |
| { |
| Curve25519Field.multiply(Z3.x, Z1.x, Z3.x); |
| } |
| if (!Z2IsOne) |
| { |
| Curve25519Field.multiply(Z3.x, Z2.x, Z3.x); |
| } |
| |
| int[] Z3Squared = (Z1IsOne && Z2IsOne) ? HSquared : null; |
| |
| // TODO If the result will only be used in a subsequent addition, we don't need W3 |
| Curve25519FieldElement W3 = calculateJacobianModifiedW((Curve25519FieldElement)Z3, Z3Squared); |
| |
| ECFieldElement[] zs = new ECFieldElement[]{ Z3, W3 }; |
| |
| return new Curve25519Point(curve, X3, Y3, zs, this.withCompression); |
| } |
| |
| public ECPoint twice() |
| { |
| if (this.isInfinity()) |
| { |
| return this; |
| } |
| |
| ECCurve curve = this.getCurve(); |
| |
| ECFieldElement Y1 = this.y; |
| if (Y1.isZero()) |
| { |
| return curve.getInfinity(); |
| } |
| |
| return twiceJacobianModified(true); |
| } |
| |
| public ECPoint twicePlus(ECPoint b) |
| { |
| if (this == b) |
| { |
| return threeTimes(); |
| } |
| if (this.isInfinity()) |
| { |
| return b; |
| } |
| if (b.isInfinity()) |
| { |
| return twice(); |
| } |
| |
| ECFieldElement Y1 = this.y; |
| if (Y1.isZero()) |
| { |
| return b; |
| } |
| |
| return twiceJacobianModified(false).add(b); |
| } |
| |
| public ECPoint threeTimes() |
| { |
| if (this.isInfinity()) |
| { |
| return this; |
| } |
| |
| ECFieldElement Y1 = this.y; |
| if (Y1.isZero()) |
| { |
| return this; |
| } |
| |
| return twiceJacobianModified(false).add(this); |
| } |
| |
| public ECPoint negate() |
| { |
| if (this.isInfinity()) |
| { |
| return this; |
| } |
| |
| return new Curve25519Point(this.getCurve(), this.x, this.y.negate(), this.zs, this.withCompression); |
| } |
| |
| protected Curve25519FieldElement calculateJacobianModifiedW(Curve25519FieldElement Z, int[] ZSquared) |
| { |
| Curve25519FieldElement a4 = (Curve25519FieldElement)this.getCurve().getA(); |
| if (Z.isOne()) |
| { |
| return a4; |
| } |
| |
| Curve25519FieldElement W = new Curve25519FieldElement(); |
| if (ZSquared == null) |
| { |
| ZSquared = W.x; |
| Curve25519Field.square(Z.x, ZSquared); |
| } |
| Curve25519Field.square(ZSquared, W.x); |
| Curve25519Field.multiply(W.x, a4.x, W.x); |
| return W; |
| } |
| |
| protected Curve25519FieldElement getJacobianModifiedW() |
| { |
| Curve25519FieldElement W = (Curve25519FieldElement)this.zs[1]; |
| if (W == null) |
| { |
| // NOTE: Rarely, twicePlus will result in the need for a lazy W1 calculation here |
| this.zs[1] = W = calculateJacobianModifiedW((Curve25519FieldElement)this.zs[0], null); |
| } |
| return W; |
| } |
| |
| protected Curve25519Point twiceJacobianModified(boolean calculateW) |
| { |
| Curve25519FieldElement X1 = (Curve25519FieldElement)this.x, Y1 = (Curve25519FieldElement)this.y, |
| Z1 = (Curve25519FieldElement)this.zs[0], W1 = getJacobianModifiedW(); |
| |
| int c; |
| |
| int[] M = Nat256.create(); |
| Curve25519Field.square(X1.x, M); |
| c = Nat256.addBothTo(M, M, M); |
| c += Nat256.addTo(W1.x, M); |
| Curve25519Field.reduce27(c, M); |
| |
| int[] _2Y1 = Nat256.create(); |
| Curve25519Field.twice(Y1.x, _2Y1); |
| |
| int[] _2Y1Squared = Nat256.create(); |
| Curve25519Field.multiply(_2Y1, Y1.x, _2Y1Squared); |
| |
| int[] S = Nat256.create(); |
| Curve25519Field.multiply(_2Y1Squared, X1.x, S); |
| Curve25519Field.twice(S, S); |
| |
| int[] _8T = Nat256.create(); |
| Curve25519Field.square(_2Y1Squared, _8T); |
| Curve25519Field.twice(_8T, _8T); |
| |
| Curve25519FieldElement X3 = new Curve25519FieldElement(_2Y1Squared); |
| Curve25519Field.square(M, X3.x); |
| Curve25519Field.subtract(X3.x, S, X3.x); |
| Curve25519Field.subtract(X3.x, S, X3.x); |
| |
| Curve25519FieldElement Y3 = new Curve25519FieldElement(S); |
| Curve25519Field.subtract(S, X3.x, Y3.x); |
| Curve25519Field.multiply(Y3.x, M, Y3.x); |
| Curve25519Field.subtract(Y3.x, _8T, Y3.x); |
| |
| Curve25519FieldElement Z3 = new Curve25519FieldElement(_2Y1); |
| if (!Nat256.isOne(Z1.x)) |
| { |
| Curve25519Field.multiply(Z3.x, Z1.x, Z3.x); |
| } |
| |
| Curve25519FieldElement W3 = null; |
| if (calculateW) |
| { |
| W3 = new Curve25519FieldElement(_8T); |
| Curve25519Field.multiply(W3.x, W1.x, W3.x); |
| Curve25519Field.twice(W3.x, W3.x); |
| } |
| |
| return new Curve25519Point(this.getCurve(), X3, Y3, new ECFieldElement[]{ Z3, W3 }, this.withCompression); |
| } |
| } |