Exemplo n.º 1
0
    /**
     * Solves a quadratic equation <code>z<sup>2</sup> + z = beta</code>(X9.62 D.1.6) The other
     * solution is <code>z + 1</code>.
     *
     * @param beta The value to solve the quadratic equation for.
     * @return the solution for <code>z<sup>2</sup> + z = beta</code> or <code>null</code> if no
     *     solution exists.
     */
    private ECFieldElement solveQuadraticEquation(ECFieldElement beta) {
      if (beta.isZero()) {
        return beta;
      }

      ECFieldElement zeroElement = fromBigInteger(ECConstants.ZERO);

      ECFieldElement z = null;
      ECFieldElement gamma = null;

      Random rand = new Random();
      do {
        ECFieldElement t = fromBigInteger(new BigInteger(m, rand));
        z = zeroElement;
        ECFieldElement w = beta;
        for (int i = 1; i <= m - 1; i++) {
          ECFieldElement w2 = w.square();
          z = z.square().add(w2.multiply(t));
          w = w2.add(beta);
        }
        if (!w.isZero()) {
          return null;
        }
        gamma = z.square().add(z);
      } while (gamma.isZero());

      return z;
    }
  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 twice().add(b);
  }
Exemplo n.º 3
0
    public ECPoint createPoint(BigInteger x, BigInteger y, boolean withCompression) {
      ECFieldElement X = fromBigInteger(x), Y = fromBigInteger(y);

      switch (this.getCoordinateSystem()) {
        case COORD_LAMBDA_AFFINE:
        case COORD_LAMBDA_PROJECTIVE:
          {
            if (!X.isZero()) {
              // Y becomes Lambda (X + Y/X) here
              Y = Y.divide(X).add(X);
            }
            break;
          }
        default:
          {
            break;
          }
      }

      return createRawPoint(X, Y, withCompression);
    }
Exemplo n.º 4
0
    /**
     * Decompresses a compressed point P = (xp, yp) (X9.62 s 4.2.2).
     *
     * @param yTilde ~yp, an indication bit for the decompression of yp.
     * @param X1 The field element xp.
     * @return the decompressed point.
     */
    protected ECPoint decompressPoint(int yTilde, BigInteger X1) {
      ECFieldElement xp = fromBigInteger(X1);
      ECFieldElement yp = null;
      if (xp.isZero()) {
        yp = (ECFieldElement.F2m) b;
        for (int i = 0; i < m - 1; i++) {
          yp = yp.square();
        }
      } else {
        ECFieldElement beta = xp.add(a).add(b.multiply(xp.square().invert()));
        ECFieldElement z = solveQuadraticEquation(beta);
        if (z == null) {
          throw new IllegalArgumentException("Invalid point compression");
        }
        if (z.testBitZero() != (yTilde == 1)) {
          z = z.addOne();
        }

        yp = xp.multiply(z);

        switch (this.getCoordinateSystem()) {
          case COORD_LAMBDA_AFFINE:
          case COORD_LAMBDA_PROJECTIVE:
            {
              yp = yp.divide(xp).add(xp);
              break;
            }
          default:
            {
              break;
            }
        }
      }

      return new ECPoint.F2m(this, xp, yp, true);
    }