Bit-Parallel Polynomial Basis Multiplier for New Classes of Finite Fields

Bit-parallel finite field multiplication using polynomial basis can be realized in two steps: polynomial multiplication and reduction modulo the irreducible polynomial. In this article, we present an upper complexity bound for the modular polynomial ...

Montgomery multiplication in {\rm GF}(2^m) is defined by a(x)b(x)r^{-1}(x)\bmod{f(x)}, where the field is generated by a root of the irreducible polynomial f(x), a(x) and b(x) are two field elements in {\rm GF}(2^m), and r(x) is a fixed field element in ...

We present a bit-parallel polynomial basis multiplier based on a new divide-and-conquer approach using squaring. In particular, we apply the proposed approach to special types of irreducible pentanomials called as types I and II pentanomials, and induce ...