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 …

Настоящая книга посвящена перспективному направлению в области защиты
информации, математическую основу которого составляет теория эллиптических …

This paper surveys bit-parallel multipliers for finite field GF (2 n) according to i) quadratic and
subquadratic arithmetic complexities of the underlying algorithms, ii) various bases used for …

COMPLEXITY OF COMPUTATION IN FINITE FIELDS SB Gashkov and IS Sergeev UDC
512.624 Page 1 Journal of Mathematical Sciences, Vol. 191, No. 5, June, 2013 COMPLEXITY …

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 …

A polynomial f (x) over a field K is called stable if all of its iterates are irreducible over K. In
this paper, we study the stability of trinomials over finite fields. We show that if f (x) is a …

In the recent past, subquadratic space complexity multipliers have been proposed for binary
fields defined by irreducible trinomials and some specific pentanomials. For such multipliers …

Hardware implementation of multiplication in finite field GF (2m) based on sparse
polynomials is found to be advantageous in terms of space-complexity as well as the time …

We present low complexity formulae for the computation of cubing and cube root over IF 3 m
constructed using special classes of irreducible trinomials, tetranomials and pentanomials …

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 …