The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

The irreducible polynomials recommended for use by multiple standards documents are in
fact far from optimal on many platforms. Specifically they are suboptimal in terms of …

Fast algorithms for multiplication in finite fields are required for several cryptographic
applications, in particular for implementing elliptic curve operations over binary fields F/sub …

We establish some necessary conditions for the existence of irreducible polynomials of
degree n and weight n over F2. Such polynomials can be used to efficiently implement …

Richard G. Swan proved in 1962 that trinomials x8k+ xm+ 1∈ F2 [x] with 8k> m have an
even number of irreducible factors, and so cannot be irreducible. In fact, he found the parity …

We discuss a family of irreducible polynomials that can be used to speed up square root
extraction in fields of characteristic two. They generalize trinomials discussed by Fong et …

We propose a simple deterministic test for deciding whether or not an element $ a\in\mathbb
{F} _ {2^ n}^{\times} $ or $\mathbb {F} _ {3^ n}^{\times} $ is a zero of the corresponding …

It is well known that the Stickelberger–Swan theorem is very important for determining the
reducibility of polynomials over a binary field. Using this theorem the parity of the number of …

We discuss irreducible polynomials that can be used to speed up square root extraction in
fields of characteristic two. We call such polynomials\textit {square root friendly}. The obvious …

The paper describes the group structure of cyclotomic cosets modula 2n− 1, the group is
cyclic when 2n− 1 is a prime. The integers modula 2n− 1 can be regarded as the exponents …