org.cryptimeleon.math.structures.groups.exp

Class ExponentiationAlgorithms

java.lang.Object

org.cryptimeleon.math.structures.groups.exp.ExponentiationAlgorithms

public class ExponentiationAlgorithms
extends java.lang.Object

A class containing multi-exponentiation algorithms.

Field Summary

Fields

Modifier and Type	Field and Description
static double	WNAF_INVERSION_COST_THRESHOLD If number of inversions per group op is at least this, use wNAF instead of the sliding window algorithm.

Constructor Summary

Constructors

Constructor and Description
ExponentiationAlgorithms()

Method Summary

Modifier and Type	Method and Description
static GroupElementImpl	binSquareMultiplyExp(GroupElementImpl base, java.math.BigInteger k) Calculates the result of applying the group operation k times, i.e.
static int	getNLeastSignificantBits(long i, int numberOfLowBits) Retrieves the given number of least significant bits of i.
static GroupElementImpl	interleavingSlidingWindowMultiExp(Multiexponentiation multiexp, int windowSize) Evaluates a multi-exponentiation using the interleaved sliding window algorithm.
static GroupElementImpl	interleavingWnafMultiExp(Multiexponentiation multiexp, int windowSize) Evaluates a multi-exponentiation using an interleaved WNAF-bases algorithm.
static int[]	precomputeExponentDigitsForWnaf(java.math.BigInteger exponent, int windowSize) Prepares WNAF representation (see master thesis by Swante Scholz) of exponent.
static GroupElementImpl	slidingWindowExp(GroupElementImpl base, java.math.BigInteger exponent, SmallExponentPrecomputation precomputation, int windowSize)
static GroupElementImpl	wnafExp(GroupElementImpl base, java.math.BigInteger exponent, SmallExponentPrecomputation precomputation, int windowSize)

Methods inherited from class java.lang.Object

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

Field Detail

WNAF_INVERSION_COST_THRESHOLD

public static final double WNAF_INVERSION_COST_THRESHOLD

If number of inversions per group op is at least this, use wNAF instead of the sliding window algorithm.

See Also:

Constant Field Values

Constructor Detail

ExponentiationAlgorithms

public ExponentiationAlgorithms()

Method Detail

interleavingSlidingWindowMultiExp

public static GroupElementImpl interleavingSlidingWindowMultiExp(Multiexponentiation multiexp,
                                                                 int windowSize)

Evaluates a multi-exponentiation using the interleaved sliding window algorithm.

Powers are computed per basis, instead of for all basis together like for the simultaneous approach. This means that cached powers can be reused in other multi-exponentiations, and, for a large amount of bases, the precomputation is a lot cheaper than in the simultaneous approach. For negative exponents, the base is inverted which does mean the precomputation has to be done anew.

interleavingWnafMultiExp

public static GroupElementImpl interleavingWnafMultiExp(Multiexponentiation multiexp,
                                                        int windowSize)

Evaluates a multi-exponentiation using an interleaved WNAF-bases algorithm.

Useful in groups where inversion is as cheap or cheaper than the group operation itself, such as elliptic curves.

binSquareMultiplyExp

public static GroupElementImpl binSquareMultiplyExp(GroupElementImpl base,
                                                    java.math.BigInteger k)

Calculates the result of applying the group operation k times, i.e. it computes k*this (additive group) or this^k (multiplicative group).

For negative exponents k, computes this.inv().pow(-k).

slidingWindowExp

public static GroupElementImpl slidingWindowExp(GroupElementImpl base,
                                                java.math.BigInteger exponent,
                                                SmallExponentPrecomputation precomputation,
                                                int windowSize)

wnafExp

public static GroupElementImpl wnafExp(GroupElementImpl base,
                                       java.math.BigInteger exponent,
                                       SmallExponentPrecomputation precomputation,
                                       int windowSize)

getNLeastSignificantBits

public static int getNLeastSignificantBits(long i,
                                           int numberOfLowBits)

Retrieves the given number of least significant bits of i.

Works for all n < 32.

Returns:

lowest n bits of i

precomputeExponentDigitsForWnaf

public static int[] precomputeExponentDigitsForWnaf(java.math.BigInteger exponent,
                                                    int windowSize)

Prepares WNAF representation (see master thesis by Swante Scholz) of exponent.

Parameters:

exponent - the exponent to compute WNAF representation for.

windowSize - the window size to use. This determines width of the WNAF representation.

Returns:

array of exponent digits in WNAF form.