Fast arithmetic for characteristic three finite fields is desirable in pairing-based cryptography
because there is a suitable family of elliptic curves over having embedding degree 6. In this …

In this paper, the authors examine a number of ways of implementing characteristic three
arithmetic for use in cryptosystems based on the Tate pairing. Three alternative …

Abstract In 1999 Silverman [21] introduced a family of binary finite fields which are
composite extensions of F 2 and on which arithmetic operations can be performed more …

A cryptographic pairing evaluates as an element of a finite extension field, and the
evaluation itself involves a considerable amount of extension field arithmetic. It is recognised …

Here we review the state-of-the-art in cryptographic pairing implementation. Starting with a
basic Miller algorithm for the Tate pairing we show how to successively apply a series of …

In the past two years, there have been several dramatic improvements in algorithms for
computing discrete logarithms in small-characteristic finite fields. In this paper, we examine …

We present a software implementation of arithmetic operations in a finite field GF (2 n),
based on an alternative representation of the field elements. An important application is in …

In this paper, we study the discrete logarithm problem in finite fields related to pairing-based
curves. We start with a precise analysis of the state-of-the-art algorithms for computing …

In this paper we describe how to efficiently implement pairing calculation on supersingular
genus 2 curves over prime fields. We find that, contrary to the results reported in [8], pairing …

Abstract In 2013, Joux, and then Barbulescu, Gaudry, Joux and Thomé, presented new
algorithms for computing discrete logarithms in finite fields of small and medium …