コード例 #1
0
  public ECPoint twicePlus(ECPoint b) {
    if (this.isInfinity()) {
      return b;
    }
    if (b.isInfinity()) {
      return twice();
    }

    ECCurve curve = this.getCurve();

    ECFieldElement X1 = this.x;
    if (X1.isZero()) {
      // A point with X == 0 is it's own additive inverse
      return b;
    }

    // NOTE: twicePlus() only optimized for lambda-affine argument
    ECFieldElement X2 = b.getRawXCoord(), Z2 = b.getZCoord(0);
    if (X2.isZero() || !Z2.isOne()) {
      return twice().add(b);
    }

    ECFieldElement L1 = this.y, Z1 = this.zs[0];
    ECFieldElement L2 = b.getRawYCoord();

    ECFieldElement X1Sq = X1.square();
    ECFieldElement L1Sq = L1.square();
    ECFieldElement Z1Sq = Z1.square();
    ECFieldElement L1Z1 = L1.multiply(Z1);

    //        ECFieldElement T = curve.getA().multiply(Z1Sq).add(L1Sq).add(L1Z1);
    ECFieldElement T = L1Sq.add(L1Z1);
    ECFieldElement L2plus1 = L2.addOne();
    //        ECFieldElement A =
    // curve.getA().add(L2plus1).multiply(Z1Sq).add(L1Sq).multiplyPlusProduct(T, X1Sq, Z1Sq);
    ECFieldElement A = L2plus1.multiply(Z1Sq).add(L1Sq).multiplyPlusProduct(T, X1Sq, Z1Sq);
    ECFieldElement X2Z1Sq = X2.multiply(Z1Sq);
    ECFieldElement B = X2Z1Sq.add(T).square();

    if (B.isZero()) {
      if (A.isZero()) {
        return b.twice();
      }

      return curve.getInfinity();
    }

    if (A.isZero()) {
      //            return new SecT283K1Point(curve, A, curve.getB().sqrt(), withCompression);
      return new SecT283K1Point(curve, A, curve.getB(), withCompression);
    }

    ECFieldElement X3 = A.square().multiply(X2Z1Sq);
    ECFieldElement Z3 = A.multiply(B).multiply(Z1Sq);
    ECFieldElement L3 = A.add(B).square().multiplyPlusProduct(T, L2plus1, Z3);

    return new SecT283K1Point(curve, X3, L3, new ECFieldElement[] {Z3}, this.withCompression);
  }
コード例 #2
0
  public ECPoint twice() {
    if (this.isInfinity()) {
      return this;
    }

    ECCurve curve = this.getCurve();

    ECFieldElement X1 = this.x;
    if (X1.isZero()) {
      // A point with X == 0 is it's own additive inverse
      return curve.getInfinity();
    }

    ECFieldElement L1 = this.y, Z1 = this.zs[0];

    boolean Z1IsOne = Z1.isOne();
    ECFieldElement Z1Sq = Z1IsOne ? Z1 : Z1.square();
    ECFieldElement T;
    if (Z1IsOne) {
      T = L1.square().add(L1);
    } else {
      T = L1.add(Z1).multiply(L1);
    }

    if (T.isZero()) {
      //            return new SecT283K1Point(curve, T, curve.getB().sqrt(), withCompression);
      return new SecT283K1Point(curve, T, curve.getB(), withCompression);
    }

    ECFieldElement X3 = T.square();
    ECFieldElement Z3 = Z1IsOne ? T : T.multiply(Z1Sq);

    ECFieldElement t1 = L1.add(X1).square();
    ECFieldElement t2 = Z1IsOne ? Z1 : Z1Sq.square();
    ECFieldElement L3 = t1.add(T).add(Z1Sq).multiply(t1).add(t2).add(X3).add(Z3);

    return new SecT283K1Point(curve, X3, L3, new ECFieldElement[] {Z3}, this.withCompression);
  }
コード例 #3
0
  public ECPoint negate() {
    if (this.isInfinity()) {
      return this;
    }

    ECFieldElement X = this.x;
    if (X.isZero()) {
      return this;
    }

    // L is actually Lambda (X + Y/X) here
    ECFieldElement L = this.y, Z = this.zs[0];
    return new SecT283K1Point(curve, X, L.add(Z), new ECFieldElement[] {Z}, this.withCompression);
  }
コード例 #4
0
  public ECFieldElement getYCoord() {
    ECFieldElement X = x, L = y;

    if (this.isInfinity() || X.isZero()) {
      return L;
    }

    // Y is actually Lambda (X + Y/X) here; convert to affine value on the fly
    ECFieldElement Y = L.add(X).multiply(X);

    ECFieldElement Z = zs[0];
    if (!Z.isOne()) {
      Y = Y.divide(Z);
    }

    return Y;
  }
コード例 #5
0
  public ECPoint add(ECPoint b) {
    if (this.isInfinity()) {
      return b;
    }
    if (b.isInfinity()) {
      return this;
    }

    ECCurve curve = this.getCurve();

    ECFieldElement X1 = this.x;
    ECFieldElement X2 = b.getRawXCoord();

    if (X1.isZero()) {
      if (X2.isZero()) {
        return curve.getInfinity();
      }

      return b.add(this);
    }

    ECFieldElement L1 = this.y, Z1 = this.zs[0];
    ECFieldElement L2 = b.getRawYCoord(), Z2 = b.getZCoord(0);

    boolean Z1IsOne = Z1.isOne();
    ECFieldElement U2 = X2, S2 = L2;
    if (!Z1IsOne) {
      U2 = U2.multiply(Z1);
      S2 = S2.multiply(Z1);
    }

    boolean Z2IsOne = Z2.isOne();
    ECFieldElement U1 = X1, S1 = L1;
    if (!Z2IsOne) {
      U1 = U1.multiply(Z2);
      S1 = S1.multiply(Z2);
    }

    ECFieldElement A = S1.add(S2);
    ECFieldElement B = U1.add(U2);

    if (B.isZero()) {
      if (A.isZero()) {
        return twice();
      }

      return curve.getInfinity();
    }

    ECFieldElement X3, L3, Z3;
    if (X2.isZero()) {
      // TODO This can probably be optimized quite a bit
      ECPoint p = this.normalize();
      X1 = p.getXCoord();
      ECFieldElement Y1 = p.getYCoord();

      ECFieldElement Y2 = L2;
      ECFieldElement L = Y1.add(Y2).divide(X1);

      //            X3 = L.square().add(L).add(X1).add(curve.getA());
      X3 = L.square().add(L).add(X1);
      if (X3.isZero()) {
        //                return new SecT283K1Point(curve, X3, curve.getB().sqrt(),
        // this.withCompression);
        return new SecT283K1Point(curve, X3, curve.getB(), this.withCompression);
      }

      ECFieldElement Y3 = L.multiply(X1.add(X3)).add(X3).add(Y1);
      L3 = Y3.divide(X3).add(X3);
      Z3 = curve.fromBigInteger(ECConstants.ONE);
    } else {
      B = B.square();

      ECFieldElement AU1 = A.multiply(U1);
      ECFieldElement AU2 = A.multiply(U2);

      X3 = AU1.multiply(AU2);
      if (X3.isZero()) {
        //                return new SecT283K1Point(curve, X3, curve.getB().sqrt(),
        // this.withCompression);
        return new SecT283K1Point(curve, X3, curve.getB(), this.withCompression);
      }

      ECFieldElement ABZ2 = A.multiply(B);
      if (!Z2IsOne) {
        ABZ2 = ABZ2.multiply(Z2);
      }

      L3 = AU2.add(B).squarePlusProduct(ABZ2, L1.add(Z1));

      Z3 = ABZ2;
      if (!Z1IsOne) {
        Z3 = Z3.multiply(Z1);
      }
    }

    return new SecT283K1Point(curve, X3, L3, new ECFieldElement[] {Z3}, this.withCompression);
  }