Basis conversion method and basis conversion device in a finite field

摘要

PROBLEM TO BE SOLVED: To provide a method and an apparatus for basis conversion in a finite field.;SOLUTION: There are provided efficient basis conversion matrices D_sd and D_ds and the basis conversion method in a finite field using the basis conversion matrices wherein a defining polynomial is a pentanomial represented by Xⁿ+X^k(3)+X^K(2)+X^k(1)+1 and wherein exponents n, k(3), K(2) and k(1) satisfy the condition represented by n-K(3)k(3)-k(1). In addition, the apparatus for performing the basis conversion is disclosed. As a pentanomial having a general form in an arbitrary degree is used as the defining polynomial, base conversion can be efficiently performed between a standard representation and a dual representation. Consequently, a dual basis multiplier can be efficiently implemented.;COPYRIGHT: (C)2004,JPO