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-rw-r--r--libraries/spongycastle/core/src/main/java/org/spongycastle/math/ec/ECCurve.java972
1 files changed, 0 insertions, 972 deletions
diff --git a/libraries/spongycastle/core/src/main/java/org/spongycastle/math/ec/ECCurve.java b/libraries/spongycastle/core/src/main/java/org/spongycastle/math/ec/ECCurve.java
deleted file mode 100644
index 137681e3b..000000000
--- a/libraries/spongycastle/core/src/main/java/org/spongycastle/math/ec/ECCurve.java
+++ /dev/null
@@ -1,972 +0,0 @@
-package org.spongycastle.math.ec;
-
-import java.math.BigInteger;
-import java.util.Random;
-
-import org.spongycastle.util.BigIntegers;
-
-/**
- * base class for an elliptic curve
- */
-public abstract class ECCurve
-{
- public static final int COORD_AFFINE = 0;
- public static final int COORD_HOMOGENEOUS = 1;
- public static final int COORD_JACOBIAN = 2;
- public static final int COORD_JACOBIAN_CHUDNOVSKY = 3;
- public static final int COORD_JACOBIAN_MODIFIED = 4;
- public static final int COORD_LAMBDA_AFFINE = 5;
- public static final int COORD_LAMBDA_PROJECTIVE = 6;
- public static final int COORD_SKEWED = 7;
-
- public static int[] getAllCoordinateSystems()
- {
- return new int[]{ COORD_AFFINE, COORD_HOMOGENEOUS, COORD_JACOBIAN, COORD_JACOBIAN_CHUDNOVSKY,
- COORD_JACOBIAN_MODIFIED, COORD_LAMBDA_AFFINE, COORD_LAMBDA_PROJECTIVE, COORD_SKEWED };
- }
-
- public class Config
- {
- protected int coord;
- protected ECMultiplier multiplier;
-
- Config(int coord, ECMultiplier multiplier)
- {
- this.coord = coord;
- this.multiplier = multiplier;
- }
-
- public Config setCoordinateSystem(int coord)
- {
- this.coord = coord;
- return this;
- }
-
- public Config setMultiplier(ECMultiplier multiplier)
- {
- this.multiplier = multiplier;
- return this;
- }
-
- public ECCurve create()
- {
- if (!supportsCoordinateSystem(coord))
- {
- throw new IllegalStateException("unsupported coordinate system");
- }
-
- ECCurve c = cloneCurve();
- if (c == ECCurve.this)
- {
- throw new IllegalStateException("implementation returned current curve");
- }
-
- c.coord = coord;
- c.multiplier = multiplier;
-
- return c;
- }
- }
-
- protected ECFieldElement a, b;
- protected int coord = COORD_AFFINE;
- protected ECMultiplier multiplier = null;
-
- public abstract int getFieldSize();
-
- public abstract ECFieldElement fromBigInteger(BigInteger x);
-
- public Config configure()
- {
- return new Config(this.coord, this.multiplier);
- }
-
- public ECPoint createPoint(BigInteger x, BigInteger y)
- {
- return createPoint(x, y, false);
- }
-
- /**
- * @deprecated per-point compression property will be removed, use {@link #createPoint(BigInteger, BigInteger)}
- * and refer {@link ECPoint#getEncoded(boolean)}
- */
- public ECPoint createPoint(BigInteger x, BigInteger y, boolean withCompression)
- {
- return createRawPoint(fromBigInteger(x), fromBigInteger(y), withCompression);
- }
-
- protected abstract ECCurve cloneCurve();
-
- protected abstract ECPoint createRawPoint(ECFieldElement x, ECFieldElement y, boolean withCompression);
-
- protected ECMultiplier createDefaultMultiplier()
- {
- return new WNafL2RMultiplier();
- }
-
- public boolean supportsCoordinateSystem(int coord)
- {
- return coord == COORD_AFFINE;
- }
-
- public PreCompInfo getPreCompInfo(ECPoint p)
- {
- checkPoint(p);
- return p.preCompInfo;
- }
-
- /**
- * Sets the <code>PreCompInfo</code> for a point on this curve. Used by
- * <code>ECMultiplier</code>s to save the precomputation for this <code>ECPoint</code> for use
- * by subsequent multiplication.
- *
- * @param point
- * The <code>ECPoint</code> to store precomputations for.
- * @param preCompInfo
- * The values precomputed by the <code>ECMultiplier</code>.
- */
- public void setPreCompInfo(ECPoint point, PreCompInfo preCompInfo)
- {
- checkPoint(point);
- point.preCompInfo = preCompInfo;
- }
-
- public ECPoint importPoint(ECPoint p)
- {
- if (this == p.getCurve())
- {
- return p;
- }
- if (p.isInfinity())
- {
- return getInfinity();
- }
-
- // TODO Default behaviour could be improved if the two curves have the same coordinate system by copying any Z coordinates.
- p = p.normalize();
-
- return createPoint(p.getXCoord().toBigInteger(), p.getYCoord().toBigInteger(), p.withCompression);
- }
-
- /**
- * Normalization ensures that any projective coordinate is 1, and therefore that the x, y
- * coordinates reflect those of the equivalent point in an affine coordinate system. Where more
- * than one point is to be normalized, this method will generally be more efficient than
- * normalizing each point separately.
- *
- * @param points
- * An array of points that will be updated in place with their normalized versions,
- * where necessary
- */
- public void normalizeAll(ECPoint[] points)
- {
- checkPoints(points);
-
- if (this.getCoordinateSystem() == ECCurve.COORD_AFFINE)
- {
- return;
- }
-
- /*
- * Figure out which of the points actually need to be normalized
- */
- ECFieldElement[] zs = new ECFieldElement[points.length];
- int[] indices = new int[points.length];
- int count = 0;
- for (int i = 0; i < points.length; ++i)
- {
- ECPoint p = points[i];
- if (null != p && !p.isNormalized())
- {
- zs[count] = p.getZCoord(0);
- indices[count++] = i;
- }
- }
-
- if (count == 0)
- {
- return;
- }
-
- ECAlgorithms.implMontgomeryTrick(zs, 0, count);
-
- for (int j = 0; j < count; ++j)
- {
- int index = indices[j];
- points[index] = points[index].normalize(zs[j]);
- }
- }
-
- public abstract ECPoint getInfinity();
-
- public ECFieldElement getA()
- {
- return a;
- }
-
- public ECFieldElement getB()
- {
- return b;
- }
-
- public int getCoordinateSystem()
- {
- return coord;
- }
-
- protected abstract ECPoint decompressPoint(int yTilde, BigInteger X1);
-
- /**
- * Sets the default <code>ECMultiplier</code>, unless already set.
- */
- public ECMultiplier getMultiplier()
- {
- if (this.multiplier == null)
- {
- this.multiplier = createDefaultMultiplier();
- }
- return this.multiplier;
- }
-
- /**
- * Decode a point on this curve from its ASN.1 encoding. The different
- * encodings are taken account of, including point compression for
- * <code>F<sub>p</sub></code> (X9.62 s 4.2.1 pg 17).
- * @return The decoded point.
- */
- public ECPoint decodePoint(byte[] encoded)
- {
- ECPoint p = null;
- int expectedLength = (getFieldSize() + 7) / 8;
-
- switch (encoded[0])
- {
- case 0x00: // infinity
- {
- if (encoded.length != 1)
- {
- throw new IllegalArgumentException("Incorrect length for infinity encoding");
- }
-
- p = getInfinity();
- break;
- }
- case 0x02: // compressed
- case 0x03: // compressed
- {
- if (encoded.length != (expectedLength + 1))
- {
- throw new IllegalArgumentException("Incorrect length for compressed encoding");
- }
-
- int yTilde = encoded[0] & 1;
- BigInteger X = BigIntegers.fromUnsignedByteArray(encoded, 1, expectedLength);
-
- p = decompressPoint(yTilde, X);
- break;
- }
- case 0x04: // uncompressed
- case 0x06: // hybrid
- case 0x07: // hybrid
- {
- if (encoded.length != (2 * expectedLength + 1))
- {
- throw new IllegalArgumentException("Incorrect length for uncompressed/hybrid encoding");
- }
-
- BigInteger X = BigIntegers.fromUnsignedByteArray(encoded, 1, expectedLength);
- BigInteger Y = BigIntegers.fromUnsignedByteArray(encoded, 1 + expectedLength, expectedLength);
-
- p = createPoint(X, Y);
- break;
- }
- default:
- throw new IllegalArgumentException("Invalid point encoding 0x" + Integer.toString(encoded[0], 16));
- }
-
- return p;
- }
-
- protected void checkPoint(ECPoint point)
- {
- if (null == point || (this != point.getCurve()))
- {
- throw new IllegalArgumentException("'point' must be non-null and on this curve");
- }
- }
-
- protected void checkPoints(ECPoint[] points)
- {
- if (points == null)
- {
- throw new IllegalArgumentException("'points' cannot be null");
- }
-
- for (int i = 0; i < points.length; ++i)
- {
- ECPoint point = points[i];
- if (null != point && this != point.getCurve())
- {
- throw new IllegalArgumentException("'points' entries must be null or on this curve");
- }
- }
- }
-
- /**
- * Elliptic curve over Fp
- */
- public static class Fp extends ECCurve
- {
- private static final int FP_DEFAULT_COORDS = COORD_JACOBIAN_MODIFIED;
-
- BigInteger q, r;
- ECPoint.Fp infinity;
-
- public Fp(BigInteger q, BigInteger a, BigInteger b)
- {
- this.q = q;
- this.r = ECFieldElement.Fp.calculateResidue(q);
- this.infinity = new ECPoint.Fp(this, null, null);
-
- this.a = fromBigInteger(a);
- this.b = fromBigInteger(b);
- this.coord = FP_DEFAULT_COORDS;
- }
-
- protected Fp(BigInteger q, BigInteger r, ECFieldElement a, ECFieldElement b)
- {
- this.q = q;
- this.r = r;
- this.infinity = new ECPoint.Fp(this, null, null);
-
- this.a = a;
- this.b = b;
- this.coord = FP_DEFAULT_COORDS;
- }
-
- protected ECCurve cloneCurve()
- {
- return new Fp(q, r, a, b);
- }
-
- public boolean supportsCoordinateSystem(int coord)
- {
- switch (coord)
- {
- case COORD_AFFINE:
- case COORD_HOMOGENEOUS:
- case COORD_JACOBIAN:
- case COORD_JACOBIAN_MODIFIED:
- return true;
- default:
- return false;
- }
- }
-
- public BigInteger getQ()
- {
- return q;
- }
-
- public int getFieldSize()
- {
- return q.bitLength();
- }
-
- public ECFieldElement fromBigInteger(BigInteger x)
- {
- return new ECFieldElement.Fp(this.q, this.r, x);
- }
-
- protected ECPoint createRawPoint(ECFieldElement x, ECFieldElement y, boolean withCompression)
- {
- return new ECPoint.Fp(this, x, y, withCompression);
- }
-
- public ECPoint importPoint(ECPoint p)
- {
- if (this != p.getCurve() && this.getCoordinateSystem() == COORD_JACOBIAN && !p.isInfinity())
- {
- switch (p.getCurve().getCoordinateSystem())
- {
- case COORD_JACOBIAN:
- case COORD_JACOBIAN_CHUDNOVSKY:
- case COORD_JACOBIAN_MODIFIED:
- return new ECPoint.Fp(this,
- fromBigInteger(p.x.toBigInteger()),
- fromBigInteger(p.y.toBigInteger()),
- new ECFieldElement[]{ fromBigInteger(p.zs[0].toBigInteger()) },
- p.withCompression);
- default:
- break;
- }
- }
-
- return super.importPoint(p);
- }
-
- protected ECPoint decompressPoint(int yTilde, BigInteger X1)
- {
- ECFieldElement x = fromBigInteger(X1);
- ECFieldElement alpha = x.multiply(x.square().add(a)).add(b);
- ECFieldElement beta = alpha.sqrt();
-
- //
- // if we can't find a sqrt we haven't got a point on the
- // curve - run!
- //
- if (beta == null)
- {
- throw new RuntimeException("Invalid point compression");
- }
-
- BigInteger betaValue = beta.toBigInteger();
- if (betaValue.testBit(0) != (yTilde == 1))
- {
- // Use the other root
- beta = fromBigInteger(q.subtract(betaValue));
- }
-
- return new ECPoint.Fp(this, x, beta, true);
- }
-
- public ECPoint getInfinity()
- {
- return infinity;
- }
-
- public boolean equals(
- Object anObject)
- {
- if (anObject == this)
- {
- return true;
- }
-
- if (!(anObject instanceof ECCurve.Fp))
- {
- return false;
- }
-
- ECCurve.Fp other = (ECCurve.Fp) anObject;
-
- return this.q.equals(other.q)
- && a.equals(other.a) && b.equals(other.b);
- }
-
- public int hashCode()
- {
- return a.hashCode() ^ b.hashCode() ^ q.hashCode();
- }
- }
-
- /**
- * Elliptic curves over F2m. The Weierstrass equation is given by
- * <code>y<sup>2</sup> + xy = x<sup>3</sup> + ax<sup>2</sup> + b</code>.
- */
- public static class F2m extends ECCurve
- {
- private static final int F2M_DEFAULT_COORDS = COORD_AFFINE;
-
- /**
- * The exponent <code>m</code> of <code>F<sub>2<sup>m</sup></sub></code>.
- */
- private int m; // can't be final - JDK 1.1
-
- /**
- * TPB: The integer <code>k</code> where <code>x<sup>m</sup> +
- * x<sup>k</sup> + 1</code> represents the reduction polynomial
- * <code>f(z)</code>.<br>
- * PPB: The integer <code>k1</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.<br>
- */
- private int k1; // can't be final - JDK 1.1
-
- /**
- * TPB: Always set to <code>0</code><br>
- * PPB: The integer <code>k2</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.<br>
- */
- private int k2; // can't be final - JDK 1.1
-
- /**
- * TPB: Always set to <code>0</code><br>
- * PPB: The integer <code>k3</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.<br>
- */
- private int k3; // can't be final - JDK 1.1
-
- /**
- * The order of the base point of the curve.
- */
- private BigInteger n; // can't be final - JDK 1.1
-
- /**
- * The cofactor of the curve.
- */
- private BigInteger h; // can't be final - JDK 1.1
-
- /**
- * The point at infinity on this curve.
- */
- private ECPoint.F2m infinity; // can't be final - JDK 1.1
-
- /**
- * The parameter <code>&mu;</code> of the elliptic curve if this is
- * a Koblitz curve.
- */
- private byte mu = 0;
-
- /**
- * The auxiliary values <code>s<sub>0</sub></code> and
- * <code>s<sub>1</sub></code> used for partial modular reduction for
- * Koblitz curves.
- */
- private BigInteger[] si = null;
-
- /**
- * Constructor for Trinomial Polynomial Basis (TPB).
- * @param m The exponent <code>m</code> of
- * <code>F<sub>2<sup>m</sup></sub></code>.
- * @param k The integer <code>k</code> where <code>x<sup>m</sup> +
- * x<sup>k</sup> + 1</code> represents the reduction
- * polynomial <code>f(z)</code>.
- * @param a The coefficient <code>a</code> in the Weierstrass equation
- * for non-supersingular elliptic curves over
- * <code>F<sub>2<sup>m</sup></sub></code>.
- * @param b The coefficient <code>b</code> in the Weierstrass equation
- * for non-supersingular elliptic curves over
- * <code>F<sub>2<sup>m</sup></sub></code>.
- */
- public F2m(
- int m,
- int k,
- BigInteger a,
- BigInteger b)
- {
- this(m, k, 0, 0, a, b, null, null);
- }
-
- /**
- * Constructor for Trinomial Polynomial Basis (TPB).
- * @param m The exponent <code>m</code> of
- * <code>F<sub>2<sup>m</sup></sub></code>.
- * @param k The integer <code>k</code> where <code>x<sup>m</sup> +
- * x<sup>k</sup> + 1</code> represents the reduction
- * polynomial <code>f(z)</code>.
- * @param a The coefficient <code>a</code> in the Weierstrass equation
- * for non-supersingular elliptic curves over
- * <code>F<sub>2<sup>m</sup></sub></code>.
- * @param b The coefficient <code>b</code> in the Weierstrass equation
- * for non-supersingular elliptic curves over
- * <code>F<sub>2<sup>m</sup></sub></code>.
- * @param n The order of the main subgroup of the elliptic curve.
- * @param h The cofactor of the elliptic curve, i.e.
- * <code>#E<sub>a</sub>(F<sub>2<sup>m</sup></sub>) = h * n</code>.
- */
- public F2m(
- int m,
- int k,
- BigInteger a,
- BigInteger b,
- BigInteger n,
- BigInteger h)
- {
- this(m, k, 0, 0, a, b, n, h);
- }
-
- /**
- * Constructor for Pentanomial Polynomial Basis (PPB).
- * @param m The exponent <code>m</code> of
- * <code>F<sub>2<sup>m</sup></sub></code>.
- * @param k1 The integer <code>k1</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.
- * @param k2 The integer <code>k2</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.
- * @param k3 The integer <code>k3</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.
- * @param a The coefficient <code>a</code> in the Weierstrass equation
- * for non-supersingular elliptic curves over
- * <code>F<sub>2<sup>m</sup></sub></code>.
- * @param b The coefficient <code>b</code> in the Weierstrass equation
- * for non-supersingular elliptic curves over
- * <code>F<sub>2<sup>m</sup></sub></code>.
- */
- public F2m(
- int m,
- int k1,
- int k2,
- int k3,
- BigInteger a,
- BigInteger b)
- {
- this(m, k1, k2, k3, a, b, null, null);
- }
-
- /**
- * Constructor for Pentanomial Polynomial Basis (PPB).
- * @param m The exponent <code>m</code> of
- * <code>F<sub>2<sup>m</sup></sub></code>.
- * @param k1 The integer <code>k1</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.
- * @param k2 The integer <code>k2</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.
- * @param k3 The integer <code>k3</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.
- * @param a The coefficient <code>a</code> in the Weierstrass equation
- * for non-supersingular elliptic curves over
- * <code>F<sub>2<sup>m</sup></sub></code>.
- * @param b The coefficient <code>b</code> in the Weierstrass equation
- * for non-supersingular elliptic curves over
- * <code>F<sub>2<sup>m</sup></sub></code>.
- * @param n The order of the main subgroup of the elliptic curve.
- * @param h The cofactor of the elliptic curve, i.e.
- * <code>#E<sub>a</sub>(F<sub>2<sup>m</sup></sub>) = h * n</code>.
- */
- public F2m(
- int m,
- int k1,
- int k2,
- int k3,
- BigInteger a,
- BigInteger b,
- BigInteger n,
- BigInteger h)
- {
- this.m = m;
- this.k1 = k1;
- this.k2 = k2;
- this.k3 = k3;
- this.n = n;
- this.h = h;
-
- if (k1 == 0)
- {
- throw new IllegalArgumentException("k1 must be > 0");
- }
-
- if (k2 == 0)
- {
- if (k3 != 0)
- {
- throw new IllegalArgumentException("k3 must be 0 if k2 == 0");
- }
- }
- else
- {
- if (k2 <= k1)
- {
- throw new IllegalArgumentException("k2 must be > k1");
- }
-
- if (k3 <= k2)
- {
- throw new IllegalArgumentException("k3 must be > k2");
- }
- }
-
- this.infinity = new ECPoint.F2m(this, null, null);
- this.a = fromBigInteger(a);
- this.b = fromBigInteger(b);
- this.coord = F2M_DEFAULT_COORDS;
- }
-
- protected F2m(int m, int k1, int k2, int k3, ECFieldElement a, ECFieldElement b, BigInteger n, BigInteger h)
- {
- this.m = m;
- this.k1 = k1;
- this.k2 = k2;
- this.k3 = k3;
- this.n = n;
- this.h = h;
-
- this.infinity = new ECPoint.F2m(this, null, null);
- this.a = a;
- this.b = b;
- this.coord = F2M_DEFAULT_COORDS;
- }
-
- protected ECCurve cloneCurve()
- {
- return new F2m(m, k1, k2, k3, a, b, n, h);
- }
-
- public boolean supportsCoordinateSystem(int coord)
- {
- switch (coord)
- {
- case COORD_AFFINE:
- case COORD_HOMOGENEOUS:
- case COORD_LAMBDA_PROJECTIVE:
- return true;
- default:
- return false;
- }
- }
-
- protected ECMultiplier createDefaultMultiplier()
- {
- if (isKoblitz())
- {
- return new WTauNafMultiplier();
- }
-
- return super.createDefaultMultiplier();
- }
-
- public int getFieldSize()
- {
- return m;
- }
-
- public ECFieldElement fromBigInteger(BigInteger x)
- {
- return new ECFieldElement.F2m(this.m, this.k1, this.k2, this.k3, x);
- }
-
- 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);
- }
-
- protected ECPoint createRawPoint(ECFieldElement x, ECFieldElement y, boolean withCompression)
- {
- return new ECPoint.F2m(this, x, y, withCompression);
- }
-
- public ECPoint getInfinity()
- {
- return infinity;
- }
-
- /**
- * Returns true if this is a Koblitz curve (ABC curve).
- * @return true if this is a Koblitz curve (ABC curve), false otherwise
- */
- public boolean isKoblitz()
- {
- return n != null && h != null && a.bitLength() <= 1 && b.bitLength() == 1;
- }
-
- /**
- * Returns the parameter <code>&mu;</code> of the elliptic curve.
- * @return <code>&mu;</code> of the elliptic curve.
- * @throws IllegalArgumentException if the given ECCurve is not a
- * Koblitz curve.
- */
- synchronized byte getMu()
- {
- if (mu == 0)
- {
- mu = Tnaf.getMu(this);
- }
- return mu;
- }
-
- /**
- * @return the auxiliary values <code>s<sub>0</sub></code> and
- * <code>s<sub>1</sub></code> used for partial modular reduction for
- * Koblitz curves.
- */
- synchronized BigInteger[] getSi()
- {
- if (si == null)
- {
- si = Tnaf.getSi(this);
- }
- return si;
- }
-
- /**
- * 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);
- }
-
- /**
- * 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 boolean equals(
- Object anObject)
- {
- if (anObject == this)
- {
- return true;
- }
-
- if (!(anObject instanceof ECCurve.F2m))
- {
- return false;
- }
-
- ECCurve.F2m other = (ECCurve.F2m)anObject;
-
- return (this.m == other.m) && (this.k1 == other.k1)
- && (this.k2 == other.k2) && (this.k3 == other.k3)
- && a.equals(other.a) && b.equals(other.b);
- }
-
- public int hashCode()
- {
- return this.a.hashCode() ^ this.b.hashCode() ^ m ^ k1 ^ k2 ^ k3;
- }
-
- public int getM()
- {
- return m;
- }
-
- /**
- * Return true if curve uses a Trinomial basis.
- *
- * @return true if curve Trinomial, false otherwise.
- */
- public boolean isTrinomial()
- {
- return k2 == 0 && k3 == 0;
- }
-
- public int getK1()
- {
- return k1;
- }
-
- public int getK2()
- {
- return k2;
- }
-
- public int getK3()
- {
- return k3;
- }
-
- public BigInteger getN()
- {
- return n;
- }
-
- public BigInteger getH()
- {
- return h;
- }
- }
-}
generated by cgit v1.2.3 (git 2.25.1) at 2024-06-10 20:19:45 +0000