Package cc.redberry.rings.poly.univar

Class ModularComposition

java.lang.Object

cc.redberry.rings.poly.univar.ModularComposition

public final class ModularComposition
extends Object

Univariate polynomial modular composition.

Since:

1.0

Method Summary

Modifier and Type	Method	Description
static <T extends IUnivariatePolynomial<T>> T	composition(T poly, T point, T polyModulus)	Returns modular composition poly(point) mod polyModulus.
static <T extends IUnivariatePolynomial<T>> T	composition(T poly, T point, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod)	Returns modular composition poly(point) mod polyModulus.
static <T extends IUnivariatePolynomial<T>> T	compositionBrentKung(T poly, ArrayList<T> pointPowers, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, int tBrentKung)	Returns modular composition poly(point) mod polyModulus calculated using Brent & Kung algorithm for modular composition.
static <T extends IUnivariatePolynomial<T>> T	compositionBrentKung(T poly, T point, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod)	Returns modular composition poly(point) mod polyModulus calculated using Brent & Kung algorithm for modular composition.
static UnivariatePolynomialZp64	compositionHorner(UnivariatePolynomialZp64 poly, UnivariatePolynomialZp64 point, UnivariatePolynomialZp64 polyModulus, UnivariateDivision.InverseModMonomial<UnivariatePolynomialZp64> invMod)	Returns modular composition poly(point) mod polyModulus calculated with plain Horner scheme.
static <T extends IUnivariatePolynomial<T>> ArrayList<T>	polyPowers(T poly, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, int nIterations)	Returns poly^{i} mod polyModulus for i in [0...nIterations]
static <E> UnivariatePolynomial<E>	powModulusMod(UnivariatePolynomial<E> poly, UnivariatePolynomial<E> polyModulus, UnivariateDivision.InverseModMonomial<UnivariatePolynomial<E>> invMod, ArrayList<UnivariatePolynomial<E>> xPowers)	Returns poly^modulus mod polyModulus using precomputed monomial powers x^{i*modulus} mod polyModulus for i in [0...degree(poly)]
static UnivariatePolynomialZp64	powModulusMod(UnivariatePolynomialZp64 poly, UnivariatePolynomialZp64 polyModulus, UnivariateDivision.InverseModMonomial<UnivariatePolynomialZp64> invMod, ArrayList<UnivariatePolynomialZp64> xPowers)	Returns poly^modulus mod polyModulus using precomputed monomial powers x^{i*modulus} mod polyModulus for i in [0...degree(poly)]
static <T extends IUnivariatePolynomial<T>> T	powModulusMod(T poly, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, ArrayList<T> xPowers)	Returns poly^modulus mod polyModulus using precomputed monomial powers x^{i*modulus} mod polyModulus for i in [0...degree(poly)]
static <T extends IUnivariatePolynomial<T>> ArrayList<T>	xPowers(T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod)	Returns x^{i*modulus} mod polyModulus for i in [0...degree], where degree is polyModulus degree.

Methods inherited from class java.lang.Object

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

Method Detail

xPowers

public static <T extends IUnivariatePolynomial<T>> ArrayList<T> xPowers(T polyModulus,
                                                                        UnivariateDivision.InverseModMonomial<T> invMod)

Returns x^{i*modulus} mod polyModulus for i in [0...degree], where degree is polyModulus degree.

Parameters:

polyModulus - the monic modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

Returns:

x^{i*modulus} mod polyModulus for i in [0...degree], where degree is polyModulus degree

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

polyPowers

public static <T extends IUnivariatePolynomial<T>> ArrayList<T> polyPowers(T poly,
                                                                           T polyModulus,
                                                                           UnivariateDivision.InverseModMonomial<T> invMod,
                                                                           int nIterations)

Returns poly^{i} mod polyModulus for i in [0...nIterations]

Parameters:

poly - the polynomial

polyModulus - the monic polynomial modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

Returns:

poly^{i} mod polyModulus for i in [0...nIterations]

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

powModulusMod

public static UnivariatePolynomialZp64 powModulusMod(UnivariatePolynomialZp64 poly,
                                                     UnivariatePolynomialZp64 polyModulus,
                                                     UnivariateDivision.InverseModMonomial<UnivariatePolynomialZp64> invMod,
                                                     ArrayList<UnivariatePolynomialZp64> xPowers)

Returns poly^modulus mod polyModulus using precomputed monomial powers x^{i*modulus} mod polyModulus for i in [0...degree(poly)]

Parameters:

poly - the polynomial

polyModulus - the monic polynomial modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

xPowers - precomputed monomial powers x^{i*modulus} mod polyModulus for i in [0...degree(poly)]

Returns:

poly^modulus mod polyModulus

See Also:

xPowers(IUnivariatePolynomial, UnivariateDivision.InverseModMonomial), UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

powModulusMod

public static <E> UnivariatePolynomial<E> powModulusMod(UnivariatePolynomial<E> poly,
                                                        UnivariatePolynomial<E> polyModulus,
                                                        UnivariateDivision.InverseModMonomial<UnivariatePolynomial<E>> invMod,
                                                        ArrayList<UnivariatePolynomial<E>> xPowers)

Returns poly^modulus mod polyModulus using precomputed monomial powers x^{i*modulus} mod polyModulus for i in [0...degree(poly)]

Parameters:

poly - the polynomial

polyModulus - the monic polynomial modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

xPowers - precomputed monomial powers x^{i*modulus} mod polyModulus for i in [0...degree(poly)]

Returns:

poly^modulus mod polyModulus

See Also:

xPowers(IUnivariatePolynomial, UnivariateDivision.InverseModMonomial), UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

powModulusMod

public static <T extends IUnivariatePolynomial<T>> T powModulusMod(T poly,
                                                                   T polyModulus,
                                                                   UnivariateDivision.InverseModMonomial<T> invMod,
                                                                   ArrayList<T> xPowers)

Returns poly^modulus mod polyModulus using precomputed monomial powers x^{i*modulus} mod polyModulus for i in [0...degree(poly)]

Parameters:

poly - the polynomial

polyModulus - the monic polynomial modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

xPowers - precomputed monomial powers x^{i*modulus} mod polyModulus for i in [0...degree(poly)]

Returns:

poly^modulus mod polyModulus

See Also:

xPowers(IUnivariatePolynomial, UnivariateDivision.InverseModMonomial), UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

compositionBrentKung

public static <T extends IUnivariatePolynomial<T>> T compositionBrentKung(T poly,
                                                                          ArrayList<T> pointPowers,
                                                                          T polyModulus,
                                                                          UnivariateDivision.InverseModMonomial<T> invMod,
                                                                          int tBrentKung)

Returns modular composition poly(point) mod polyModulus calculated using Brent & Kung algorithm for modular composition.

Parameters:

poly - the polynomial

pointPowers - precomputed powers of evaluation point point^{i} mod polyModulus

polyModulus - the monic polynomial modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

tBrentKung - Brent-Kung splitting parameter (optimal choice is ~sqrt(main.degree))

Returns:

modular composition poly(point) mod polyModulus

See Also:

polyPowers(IUnivariatePolynomial, IUnivariatePolynomial, UnivariateDivision.InverseModMonomial, int), UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

compositionBrentKung

public static <T extends IUnivariatePolynomial<T>> T compositionBrentKung(T poly,
                                                                          T point,
                                                                          T polyModulus,
                                                                          UnivariateDivision.InverseModMonomial<T> invMod)

Returns modular composition poly(point) mod polyModulus calculated using Brent & Kung algorithm for modular composition.

Parameters:

poly - the polynomial

point - the evaluation point

polyModulus - the monic polynomial modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial) )})

Returns:

modular composition poly(point) mod polyModulus

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

compositionHorner

public static UnivariatePolynomialZp64 compositionHorner(UnivariatePolynomialZp64 poly,
                                                         UnivariatePolynomialZp64 point,
                                                         UnivariatePolynomialZp64 polyModulus,
                                                         UnivariateDivision.InverseModMonomial<UnivariatePolynomialZp64> invMod)

Returns modular composition poly(point) mod polyModulus calculated with plain Horner scheme.

Parameters:

poly - the polynomial

point - the evaluation point

polyModulus - the monic polynomial modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial) )})

Returns:

modular composition poly(point) mod polyModulus

See Also:

UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

composition

public static <T extends IUnivariatePolynomial<T>> T composition(T poly,
                                                                 T point,
                                                                 T polyModulus,
                                                                 UnivariateDivision.InverseModMonomial<T> invMod)

Returns modular composition poly(point) mod polyModulus. Brent & Kung algorithm used (compositionBrentKung(IUnivariatePolynomial, ArrayList, IUnivariatePolynomial, UnivariateDivision.InverseModMonomial, int)

Parameters:

poly - the polynomial

point - the evaluation point

polyModulus - the monic polynomial modulus

invMod - pre-conditioned modulus (UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial))

Returns:

modular composition poly(point) mod polyModulus

See Also:

polyPowers(IUnivariatePolynomial, IUnivariatePolynomial, UnivariateDivision.InverseModMonomial, int), UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)

composition

public static <T extends IUnivariatePolynomial<T>> T composition(T poly,
                                                                 T point,
                                                                 T polyModulus)

Returns modular composition poly(point) mod polyModulus. Brent & Kung algorithm used (compositionBrentKung(IUnivariatePolynomial, ArrayList, IUnivariatePolynomial, UnivariateDivision.InverseModMonomial, int)

Parameters:

poly - the polynomial

point - the evaluation point

polyModulus - the monic polynomial modulus

Returns:

modular composition poly(point) mod polyModulus

See Also:

polyPowers(IUnivariatePolynomial, IUnivariatePolynomial, UnivariateDivision.InverseModMonomial, int), UnivariateDivision.fastDivisionPreConditioning(IUnivariatePolynomial)