Method and apparatus for basis conversion in finite field

摘要

There are provided efficient basis conversion matrices D_sd and D_ds and a basis conversion method in a finite field GF(2ⁿ) using the basis conversion matrices for a case where a defining polynomial is a pentanomial, xⁿ+x^k(3)+x^k(2)+x^k(1)+1, and the exponents n, k(3), k(2), and (k1) satisfy the condition, n−k(3)k(3)−k(1). In addition, an apparatus for the basis conversion in the finite field GF(2ⁿ) is provided. Since a pentanomial having a general form in an arbitrary degree is used as the defining polynomial, basis conversion between a standard representation and a dual representation is efficiently performed. Consequently, a dual basis multiplier can be efficiently implemented.