Contents

GFpxInit

Initializes the context of a GF(pd) field.

Syntax

IppStatus ippsGFpxInit(const IppsGFpState* pParentGF, int extDeg, const IppsGfpElement* const ppGroundElm[], int polyTerms, const IppsGFpMethod* method, IppsGFpState* pGFpx);

Include Files

ippcp.h

Parameters

pParentGF

Pointer to the context of the finite field GF(p) being extended.

extDeg

Degree of the extension.

ppGroundElm[]

Double pointer to the array of IppsGFpElement contexts representing coefficients of the field polynomial.

polyTerms

Number of the field polynomial coefficients.

method

Pointer to the implementation of a basic arithmetic (methods) over the extended GF(p) finite field.

pGFpx

Pointer to the context of the GF(pd) field being initialized.

Description

The function initializes the memory buffer pGFpx associated with the IppsGFpState context and sets up the specific irreducible polynomial. The initialized context is used in the functions that create contexts of elements of the GF(pd) field and perform operations with the field elements. The function assumes the use of a general field polynomial g(x) = xd + x:sup:`d - 1`a:sub:`d - 1` + x:sup:`d - 2`a:sub:`d - 2` + ⋯ + x1a1 + a0 over GF(p).

Note

  • The function does not check the polynomial’s irreducibility.

  • In general, the GF(pd) extension requires a field polynomial g(x) of degree d. However, because g(x) is considered a monic polynomial (the coefficient of xd is always assumed equal to 1), the leading coefficient is not required: polyTerms <= (extDeg - 1).

Note

Important

  • When calling the functions over the GF(pd) field, a properly initialized pParentGF context of the finite field GF(p) is required.

  • Do not release the pParentGF context of the parent field as long as application deals with either the parent or the extended finite field pointed to by pGFpx.

Return Values

ippStsNoErr

Indicates no error. Any other value indicates an error or warning.

ippStsNullPtrErr

Indicates an error condition if any of the specified pointers is NULL.

ippStsContextMatchErr

Indicates an error condition if any of the context parameters referenced by elements of ppGroundElm[] or pParentGF does not match the operation.

ippStsBadArgErr

Indicates an error condition in the following cases:

  • extDeg > 8 or extDeg < 2.

  • polyTerms > (extDeg - 1) or polyTerms < 1.

  • method is not an output of a GFpxMethod function.

  • method is not compatible with the value of extDeg.

ippStsOutOfRangeErr

Indicates an error condition if the length of any of the values defined by ppGroundElm[] is not equal to the length of an element of the parent finite field pParentGF.

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GFpxMethod