示例#1
0
 protected BigInteger modInverse(BigInteger x) {
   int bits = getFieldSize();
   int len = (bits + 31) >> 5;
   int[] p = Nat.fromBigInteger(bits, q);
   int[] n = Nat.fromBigInteger(bits, x);
   int[] z = Nat.create(len);
   Mod.invert(p, n, z);
   return Nat.toBigInteger(len, z);
 }
示例#2
0
  public static void squareN(long[] x, int n, long[] z) {
    //        assert n > 0;

    long[] tt = Nat.create64(5);
    implSquare(x, tt);
    reduce(tt, z);

    while (--n > 0) {
      implSquare(z, tt);
      reduce(tt, z);
    }
  }
  public ECPoint add(ECPoint b) {
    if (this.isInfinity()) {
      return b;
    }
    if (b.isInfinity()) {
      return this;
    }
    if (this == b) {
      return twice();
    }

    ECCurve curve = this.getCurve();

    SecP521R1FieldElement X1 = (SecP521R1FieldElement) this.x, Y1 = (SecP521R1FieldElement) this.y;
    SecP521R1FieldElement X2 = (SecP521R1FieldElement) b.getXCoord(),
        Y2 = (SecP521R1FieldElement) b.getYCoord();

    SecP521R1FieldElement Z1 = (SecP521R1FieldElement) this.zs[0];
    SecP521R1FieldElement Z2 = (SecP521R1FieldElement) b.getZCoord(0);

    int[] t1 = Nat.create(17);
    int[] t2 = Nat.create(17);
    int[] t3 = Nat.create(17);
    int[] t4 = Nat.create(17);

    boolean Z1IsOne = Z1.isOne();
    int[] U2, S2;
    if (Z1IsOne) {
      U2 = X2.x;
      S2 = Y2.x;
    } else {
      S2 = t3;
      SecP521R1Field.square(Z1.x, S2);

      U2 = t2;
      SecP521R1Field.multiply(S2, X2.x, U2);

      SecP521R1Field.multiply(S2, Z1.x, S2);
      SecP521R1Field.multiply(S2, Y2.x, S2);
    }

    boolean Z2IsOne = Z2.isOne();
    int[] U1, S1;
    if (Z2IsOne) {
      U1 = X1.x;
      S1 = Y1.x;
    } else {
      S1 = t4;
      SecP521R1Field.square(Z2.x, S1);

      U1 = t1;
      SecP521R1Field.multiply(S1, X1.x, U1);

      SecP521R1Field.multiply(S1, Z2.x, S1);
      SecP521R1Field.multiply(S1, Y1.x, S1);
    }

    int[] H = Nat.create(17);
    SecP521R1Field.subtract(U1, U2, H);

    int[] R = t2;
    SecP521R1Field.subtract(S1, S2, R);

    // Check if b == this or b == -this
    if (Nat.isZero(17, H)) {
      if (Nat.isZero(17, 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 = t3;
    SecP521R1Field.square(H, HSquared);

    int[] G = Nat.create(17);
    SecP521R1Field.multiply(HSquared, H, G);

    int[] V = t3;
    SecP521R1Field.multiply(HSquared, U1, V);

    SecP521R1Field.multiply(S1, G, t1);

    SecP521R1FieldElement X3 = new SecP521R1FieldElement(t4);
    SecP521R1Field.square(R, X3.x);
    SecP521R1Field.add(X3.x, G, X3.x);
    SecP521R1Field.subtract(X3.x, V, X3.x);
    SecP521R1Field.subtract(X3.x, V, X3.x);

    SecP521R1FieldElement Y3 = new SecP521R1FieldElement(G);
    SecP521R1Field.subtract(V, X3.x, Y3.x);
    SecP521R1Field.multiply(Y3.x, R, t2);
    SecP521R1Field.subtract(t2, t1, Y3.x);

    SecP521R1FieldElement Z3 = new SecP521R1FieldElement(H);
    if (!Z1IsOne) {
      SecP521R1Field.multiply(Z3.x, Z1.x, Z3.x);
    }
    if (!Z2IsOne) {
      SecP521R1Field.multiply(Z3.x, Z2.x, Z3.x);
    }

    ECFieldElement[] zs = new ECFieldElement[] {Z3};

    return new SecP521R1Point(curve, X3, Y3, zs, this.withCompression);
  }
  public ECPoint twice() {
    if (this.isInfinity()) {
      return this;
    }

    ECCurve curve = this.getCurve();

    SecP521R1FieldElement Y1 = (SecP521R1FieldElement) this.y;
    if (Y1.isZero()) {
      return curve.getInfinity();
    }

    SecP521R1FieldElement X1 = (SecP521R1FieldElement) this.x,
        Z1 = (SecP521R1FieldElement) this.zs[0];

    int[] t1 = Nat.create(17);
    int[] t2 = Nat.create(17);

    int[] Y1Squared = Nat.create(17);
    SecP521R1Field.square(Y1.x, Y1Squared);

    int[] T = Nat.create(17);
    SecP521R1Field.square(Y1Squared, T);

    boolean Z1IsOne = Z1.isOne();

    int[] Z1Squared = Z1.x;
    if (!Z1IsOne) {
      Z1Squared = t2;
      SecP521R1Field.square(Z1.x, Z1Squared);
    }

    SecP521R1Field.subtract(X1.x, Z1Squared, t1);

    int[] M = t2;
    SecP521R1Field.add(X1.x, Z1Squared, M);
    SecP521R1Field.multiply(M, t1, M);
    Nat.addBothTo(17, M, M, M);
    SecP521R1Field.reduce23(M);

    int[] S = Y1Squared;
    SecP521R1Field.multiply(Y1Squared, X1.x, S);
    Nat.shiftUpBits(17, S, 2, 0);
    SecP521R1Field.reduce23(S);

    Nat.shiftUpBits(17, T, 3, 0, t1);
    SecP521R1Field.reduce23(t1);

    SecP521R1FieldElement X3 = new SecP521R1FieldElement(T);
    SecP521R1Field.square(M, X3.x);
    SecP521R1Field.subtract(X3.x, S, X3.x);
    SecP521R1Field.subtract(X3.x, S, X3.x);

    SecP521R1FieldElement Y3 = new SecP521R1FieldElement(S);
    SecP521R1Field.subtract(S, X3.x, Y3.x);
    SecP521R1Field.multiply(Y3.x, M, Y3.x);
    SecP521R1Field.subtract(Y3.x, t1, Y3.x);

    SecP521R1FieldElement Z3 = new SecP521R1FieldElement(M);
    SecP521R1Field.twice(Y1.x, Z3.x);
    if (!Z1IsOne) {
      SecP521R1Field.multiply(Z3.x, Z1.x, Z3.x);
    }

    return new SecP521R1Point(curve, X3, Y3, new ECFieldElement[] {Z3}, this.withCompression);
  }
示例#5
0
 public static void squareAddToExt(long[] x, long[] zz) {
   long[] tt = Nat.create64(5);
   implSquare(x, tt);
   addExt(zz, tt, zz);
 }
示例#6
0
 public static void square(long[] x, long[] z) {
   long[] tt = Nat.create64(5);
   implSquare(x, tt);
   reduce(tt, z);
 }