Method of performing multiplication operation in binary extension finite field

摘要

In a method of performing a multiplication operation in a binary extension finite field, a polynomial defined by; $$ \sum _{n=0}^{W-1}{C}_n·z^n$$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; $$ a\left(z\right)=\sum _{n=0}^{m-1}{a}_n·z^n,b\left(z\right)=\sum _{n=0}^{m-1}{b}_n·z^n,$$and W denotes a number of bits of a word that is an operation processing unit of a processor.