Arithmetic Functions for Polynomials over GF(2^m)

This section considers polynomials over GF(2^m), which means that coefficients of polynomials belong to GF(2 ^m). The arithmetic functions for the polynomials have the same limitation as the GF(2^m) arithmetic functions: 1<m<=8. The operations that these functions implement form the next functionality level of Intel IPP for data integrity.

The table below lists the Intel IPP arithmetic functions for polynomials over GF(2 ^m).

Intel IPP Arithmetic Functions for Polynomials over GF(2^m)
Function Base Name	Operation
PolyGFGetSize	Gets the size of the ippsPolyGF_8u context in bytes.
PolyGFInit	Initializes user-supplied memory as the IppsPolyGF_8u context for future use.
PolyGFSetCoeffs	Defines the polynomial.
PolyGFSetDegree	Sets up the polynomial degree.
PolyGFCopy	Copies one polynomial to another.
PolyGFGetRef	Gets references to the polynomial characteristics: degree, coefficients, and the base finite field.
PolyGFAdd	Adds polynomials.
PolyGFSub	Subtracts one polynomial from another.
PolyGFMul	Multiplies polynomials.
PolyGFMod	Reduces a polynomial modulo another polynomial.
PolyGFDiv	Divides polynomials.
PolyGFShlC	Shifts a polynomial left.
PolyGFShrC	Shifts a polynomial right.
PolyGFIrreducible	Tests a given polynomial for being irreducible.
PolyGFPrimitive	Tests a given polynomial for being primitive.
PolyGFValue	Computes the value of a polynomial for a given argument.
PolyGFDerive	Computes the derivate of a given polynomial.
PolyGFRoots	Computes roots of a given polynomial.
PolyGFGCD	Computes the greatest common divisor of two polynomials.

A context of the IppsPolyGF_8u type represents each polynomial that the functions described in this section operate on. The context carries not only characteristics of the polynomial but also the definition of the base field GF(2^m), the maximum possible degree of a polynomial, and a working buffer sufficient for the polynomial arithmetic operations.