Paper 2011/606

$GF(2^{n})$ Subquadratic Polynomial Basis Multipliers for Some Irreducible Trinomials

Xi Xiong and Haining Fan

Abstract

The $GF(2^{n})$ multiplication operation in polynomial basis can be represented as a matrix-vector product form, and the matrix is often called the Mastrovito matrix. The Toeplitz matrix-vector product approach has been used to design subquadratic shifted polynomial basis multipliers. In order to apply this approach to subquadratic polynomial basis multipliers, this Mastrovito matrix should be transformed into a Toeplitz matrix. In this paper, two transformation methods are proposed for irreducible trinomial $x^{n}+x^{k}+1$, where $2k+1\leq n$.