using System;
using System.Collections;
using Org.BouncyCastle.Math.EC.Abc;
namespace Org.BouncyCastle.Math.EC{
/// <remarks>Base class for an elliptic curve.</remarks>
public abstract class ECCurve
{
internal ECFieldElement a, b;
public abstract int FieldSize { get; }
public abstract ECFieldElement FromBigInteger(BigInteger x);
public abstract ECPoint CreatePoint(BigInteger x, BigInteger y, bool withCompression);
public abstract ECPoint DecodePoint(byte[] encoded);
public abstract ECPoint Infinity { get; }
public ECFieldElement A
{
get { return a; }
}
public ECFieldElement B
{
get { return b; }
}
public override bool Equals(
object obj)
{
if (obj == this)
return true;
ECCurve other = obj as ECCurve;
if (other == null)
return false;
return Equals(other);
}
protected bool Equals(
ECCurve other)
{
return a.Equals(other.a) && b.Equals(other.b);
}
public override int GetHashCode()
{
return a.GetHashCode() ^ b.GetHashCode();
}
}
public abstract class ECCurveBase : ECCurve
{
protected internal ECCurveBase()
{
}
protected internal abstract ECPoint DecompressPoint(int yTilde, BigInteger X1);
/**
* 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 override ECPoint DecodePoint(
byte[] encoded)
{
ECPoint p = null;
int expectedLength = (FieldSize + 7) / 8;
switch (encoded[0])
{
case 0x00: // infinity
{
if (encoded.Length != 1)
throw new ArgumentException("Incorrect length for infinity encoding", "encoded");
p = Infinity;
break;
}
case 0x02: // compressed
case 0x03: // compressed
{
if (encoded.Length != (expectedLength + 1))
throw new ArgumentException("Incorrect length for compressed encoding", "encoded");
int yTilde = encoded[0] & 1;
BigInteger X1 = new BigInteger(1, encoded, 1, encoded.Length - 1);
p = DecompressPoint(yTilde, X1);
break;
}
case 0x04: // uncompressed
case 0x06: // hybrid
case 0x07: // hybrid
{
if (encoded.Length != (2 * expectedLength + 1))
throw new ArgumentException("Incorrect length for uncompressed/hybrid encoding", "encoded");
BigInteger X1 = new BigInteger(1, encoded, 1, expectedLength);
BigInteger Y1 = new BigInteger(1, encoded, 1 + expectedLength, expectedLength);
p = CreatePoint(X1, Y1, false);
break;
}
default:
throw new FormatException("Invalid point encoding " + encoded[0]);
}
return p;
}
}
/**
* Elliptic curve over Fp
*/
public class FpCurve : ECCurveBase
{
private readonly BigInteger q;
private readonly FpPoint infinity;
public FpCurve(BigInteger q, BigInteger a, BigInteger b)
{
this.q = q;
this.a = FromBigInteger(a);
this.b = FromBigInteger(b);
this.infinity = new FpPoint(this, null, null);
}
public BigInteger Q
{
get { return q; }
}
public override ECPoint Infinity
{
get { return infinity; }
}
public override int FieldSize
{
get { return q.BitLength; }
}
public override ECFieldElement FromBigInteger(BigInteger x)
{
return new FpFieldElement(this.q, x);
}
public override ECPoint CreatePoint(
BigInteger X1,
BigInteger Y1,
bool withCompression)
{
// TODO Validation of X1, Y1?
return new FpPoint(
this,
FromBigInteger(X1),
FromBigInteger(Y1),
withCompression);
}
protected internal override 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 ArithmeticException("Invalid point compression");
BigInteger betaValue = beta.ToBigInteger();
int bit0 = betaValue.TestBit(0) ? 1 : 0;
if (bit0 != yTilde)
{
// Use the other root
beta = FromBigInteger(q.Subtract(betaValue));
}
return new FpPoint(this, x, beta, true);
}
public override bool Equals(
object obj)
{
if (obj == this)
return true;
FpCurve other = obj as FpCurve;
if (other == null)
return false;
return Equals(other);
}
protected bool Equals(
FpCurve other)
{
return base.Equals(other) && q.Equals(other.q);
}
public override int GetHashCode()
{
return base.GetHashCode() ^ q.GetHashCode();
}
}
/**
* 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 class F2mCurve : ECCurveBase
{
/**
* The exponent <code>m</code> of <code>F<sub>2<sup>m</sup></sub></code>.
*/
private readonly int m;
/**
* 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 readonly int k1;
/**
* 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 readonly int k2;
/**
* 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 readonly int k3;
/**
* The order of the base point of the curve.
*/
private readonly BigInteger n;
/**
* The cofactor of the curve.
*/
private readonly BigInteger h;
/**
* The point at infinity on this curve.
*/
private readonly F2mPoint infinity;
/**
* The parameter <code>μ</code> of the elliptic curve if this is
* a Koblitz curve.
*/
private sbyte 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 F2mCurve(
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 F2mCurve(
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 F2mCurve(
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 F2mCurve(
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;
this.infinity = new F2mPoint(this, null, null);
if (k1 == 0)
throw new ArgumentException("k1 must be > 0");
if (k2 == 0)
{
if (k3 != 0)
throw new ArgumentException("k3 must be 0 if k2 == 0");
}
else
{
if (k2 <= k1)
throw new ArgumentException("k2 must be > k1");
if (k3 <= k2)
throw new ArgumentException("k3 must be > k2");
}
this.a = FromBigInteger(a);
this.b = FromBigInteger(b);
}
public override ECPoint Infinity
{
get { return infinity; }
}
public override int FieldSize
{
get { return m; }
}
public override ECFieldElement FromBigInteger(BigInteger x)
{
return new F2mFieldElement(this.m, this.k1, this.k2, this.k3, x);
}
/**
* Returns true if this is a Koblitz curve (ABC curve).
* @return true if this is a Koblitz curve (ABC curve), false otherwise
*/
public bool IsKoblitz
{
get
{
return n != null && h != null
&& (a.ToBigInteger().Equals(BigInteger.Zero)
|| a.ToBigInteger().Equals(BigInteger.One))
&& b.ToBigInteger().Equals(BigInteger.One);
}
}
/**
* Returns the parameter <code>μ</code> of the elliptic curve.
* @return <code>μ</code> of the elliptic curve.
* @throws ArgumentException if the given ECCurve is not a
* Koblitz curve.
*/
internal sbyte GetMu()
{
if (mu == 0)
{
lock (this)
{
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.
*/
internal BigInteger[] GetSi()
{
if (si == null)
{
lock (this)
{
if (si == null)
{
si = Tnaf.GetSi(this);
}
}
}
return si;
}
public override ECPoint CreatePoint(
BigInteger X1,
BigInteger Y1,
bool withCompression)
{
// TODO Validation of X1, Y1?
return new F2mPoint(
this,
FromBigInteger(X1),
FromBigInteger(Y1),
withCompression);
}
protected internal override ECPoint DecompressPoint(
int yTilde,
BigInteger X1)
{
ECFieldElement xp = FromBigInteger(X1);
ECFieldElement yp = null;
if (xp.ToBigInteger().SignValue == 0)
{
yp = (F2mFieldElement)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 = solveQuadradicEquation(beta);
if (z == null)
throw new ArithmeticException("Invalid point compression");
int zBit = z.ToBigInteger().TestBit(0) ? 1 : 0;
if (zBit != yTilde)
{
z = z.Add(FromBigInteger(BigInteger.One));
}
yp = xp.Multiply(z);
}
return new F2mPoint(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 qradratic equation for.
* @return the solution for <code>z<sup>2</sup> + z = beta</code> or
* <code>null</code> if no solution exists.
*/
private ECFieldElement solveQuadradicEquation(ECFieldElement beta)
{
if (beta.ToBigInteger().SignValue == 0)
{
return FromBigInteger(BigInteger.Zero);
}
ECFieldElement z = null;
ECFieldElement gamma = FromBigInteger(BigInteger.Zero);
while (gamma.ToBigInteger().SignValue == 0)
{
ECFieldElement t = FromBigInteger(new BigInteger(m, new Random()));
z = FromBigInteger(BigInteger.Zero);
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.ToBigInteger().SignValue != 0)
{
return null;
}
gamma = z.Square().Add(z);
}
return z;
}
public override bool Equals(
object obj)
{
if (obj == this)
return true;
F2mCurve other = obj as F2mCurve;
if (other == null)
return false;
return Equals(other);
}
protected bool Equals(
F2mCurve other)
{
return m == other.m
&& k1 == other.k1
&& k2 == other.k2
&& k3 == other.k3
&& base.Equals(other);
}
public override int GetHashCode()
{
return base.GetHashCode() ^ m ^ k1 ^ k2 ^ k3;
}
public int M
{
get { return m; }
}
/**
* Return true if curve uses a Trinomial basis.
*
* @return true if curve Trinomial, false otherwise.
*/
public bool IsTrinomial()
{
return k2 == 0 && k3 == 0;
}
public int K1
{
get { return k1; }
}
public int K2
{
get { return k2; }
}
public int K3
{
get { return k3; }
}
public BigInteger N
{
get { return n; }
}
public BigInteger H
{
get { return h; }
}
}
}
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