org.bouncycastle.math.ec
Class ECAlgorithms

java.lang.Object
  org.bouncycastle.math.ec.ECAlgorithms

public class ECAlgorithms

extends java.lang.Object

Constructor Summary

ECAlgorithms()

Method Summary

static ECPoint	cleanPoint(ECCurve c, ECPoint p)
static ECPoint	importPoint(ECCurve c, ECPoint p)
static boolean	isF2mCurve(ECCurve c)
static boolean	isF2mField(FiniteField field)
static boolean	isFpCurve(ECCurve c)
static boolean	isFpField(FiniteField field)
static void	montgomeryTrick(ECFieldElement[] zs, int off, int len)
static void	montgomeryTrick(ECFieldElement[] zs, int off, int len, ECFieldElement scale)
static ECPoint	multiply(ECPoint p, java.math.BigInteger k)
static ECPoint	multiplySecret(ECPoint p, java.math.BigInteger k) Multiply a point by a scalar that must not be leaked - a private key, or any value derived from one - without exposing the scalar through control flow or memory-access pattern.
static ECPoint	multiplySecret(ECPoint p, java.math.BigInteger k, java.math.BigInteger order) As multiplySecret(ECPoint, BigInteger), with the group order supplied rather than taken from the curve.
static ECPoint	referenceMultiply(ECPoint p, java.math.BigInteger k) Simple shift-and-add multiplication.
static ECPoint	shamirsTrick(ECPoint P, java.math.BigInteger k, ECPoint Q, java.math.BigInteger l)
static ECPoint	sumOfMultiplies(ECPoint[] ps, java.math.BigInteger[] ks)
static ECPoint	sumOfTwoMultiplies(ECPoint P, java.math.BigInteger a, ECPoint Q, java.math.BigInteger b)
static ECPoint	sumOfTwoMultipliesSecret(ECPoint P, java.math.BigInteger a, ECPoint Q, java.math.BigInteger b)
static ECPoint	sumOfTwoMultipliesSecret(ECPoint P, java.math.BigInteger a, ECPoint Q, java.math.BigInteger b, java.math.BigInteger order)
static ECPoint	validatePoint(ECPoint p)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ECAlgorithms

public ECAlgorithms()

Method Detail

isF2mCurve

public static boolean isF2mCurve(ECCurve c)

isF2mField

public static boolean isF2mField(FiniteField field)

isFpCurve

public static boolean isFpCurve(ECCurve c)

isFpField

public static boolean isFpField(FiniteField field)

sumOfMultiplies

public static ECPoint sumOfMultiplies(ECPoint[] ps,
                                      java.math.BigInteger[] ks)

sumOfTwoMultiplies

public static ECPoint sumOfTwoMultiplies(ECPoint P,
                                         java.math.BigInteger a,
                                         ECPoint Q,
                                         java.math.BigInteger b)

sumOfTwoMultipliesSecret

public static ECPoint sumOfTwoMultipliesSecret(ECPoint P,
                                               java.math.BigInteger a,
                                               ECPoint Q,
                                               java.math.BigInteger b)

sumOfTwoMultipliesSecret

public static ECPoint sumOfTwoMultipliesSecret(ECPoint P,
                                               java.math.BigInteger a,
                                               ECPoint Q,
                                               java.math.BigInteger b,
                                               java.math.BigInteger order)

shamirsTrick

public static ECPoint shamirsTrick(ECPoint P,
                                   java.math.BigInteger k,
                                   ECPoint Q,
                                   java.math.BigInteger l)

importPoint

public static ECPoint importPoint(ECCurve c,
                                  ECPoint p)

montgomeryTrick

public static void montgomeryTrick(ECFieldElement[] zs,
                                   int off,
                                   int len)

montgomeryTrick

public static void montgomeryTrick(ECFieldElement[] zs,
                                   int off,
                                   int len,
                                   ECFieldElement scale)

referenceMultiply

public static ECPoint referenceMultiply(ECPoint p,
                                        java.math.BigInteger k)

Simple shift-and-add multiplication. Serves as reference implementation to verify (possibly faster) implementations, and for very small scalars. CAUTION: This implementation is NOT constant-time in any way. It is only intended to be used for diagnostics.

Parameters:

p - The point to multiply.

k - The multiplier.

Returns:

The result of the point multiplication kP.

multiply

public static ECPoint multiply(ECPoint p,
                               java.math.BigInteger k)

multiplySecret

public static ECPoint multiplySecret(ECPoint p,
                                     java.math.BigInteger k)

Multiply a point by a scalar that must not be leaked - a private key, or any value derived from one - without exposing the scalar through control flow or memory-access pattern.

ECPoint.multiply(BigInteger) uses the curve's configured multiplier, which for most curves is a windowed-NAF implementation whose timing depends on the scalar; it is the right choice for a public scalar (verification, for instance) but not for a secret one. Use this method wherever the scalar is secret and the point is supplied by a peer.

The result is the same point ECPoint.multiply(BigInteger) would return; only the timing profile differs. See ECConstantTimeMultiplier for what is and is not covered.

Parameters:

p - the point to multiply, typically a peer's public key; must lie in the subgroup whose order is the curve's.

k - the secret scalar; must be less than the curve order.

Returns:

kP.

multiplySecret

public static ECPoint multiplySecret(ECPoint p,
                                     java.math.BigInteger k,
                                     java.math.BigInteger order)

As multiplySecret(ECPoint, BigInteger), with the group order supplied rather than taken from the curve. Prefer this form wherever the order is to hand - domain parameters always carry it, whereas ECCurve.getOrder() is null for a curve built without one.

Parameters:

p - the point to multiply, typically a peer's public key; must lie in the subgroup of order .

k - the secret scalar; must be less than .

order - the group order; must be odd, as every standard EC group order is.

Returns:

kP.

validatePoint

public static ECPoint validatePoint(ECPoint p)

cleanPoint

public static ECPoint cleanPoint(ECCurve c,
                                 ECPoint p)