Method of performing multiplication operation in binary extension finite field

摘要

Disclosed herein is a method of performing a multiplication operation in a binary extension finite field. In the method, a polynomial defined by ∑n=0W-1Cn⋅zn is produced by expanding polynomial basis multiplication for multiplication of two polynomials a(z) and b(z) in a binary extension finite field. A mapping table is generated in which bit values having pieces of information about respective terms of the produced polynomial are mapped to respective rows. A code for calculating the polynomial, produced by expanding the polynomial basis multiplication for the multiplication of the two polynomials, with reference to the mapping table is generated. A multiplication operation of the two polynomials a(z) and b(z) in the binary extension finite field is performed by executing the code for calculating the polynomial wherein az=∑n=0m-1an⋅zn,bz=∑n=0m-1bn⋅zn, and W denotes a number of bits of a word that is an operation processing unit of a processor.