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Since 2013 there have been several developments in algorithms for computing discrete logarithms in small-characteristic finite fields, culminating in a quasi-polynomial algorithm. In this paper, we re...
This paper proposes new explicit formulae for the point doubling, tripling and addition on ordinary Weierstrass elliptic curves over finite fields of characteristic three. The cost of basic point oper...
We consider digital expansions of scalars for supersingular Koblitz curves in characteristic three. These are positional representations of integers to the base of $\tau$, where $\tau$ is a zero of th...
This paper is devoted to the design of fast parallel accelerators for the cryptographic Tate pairing in characteristic three over supersingular elliptic curves. We propose here a novel hardware impl...
We present an efficient implementation of T pairing on Intel Core 2 Duo processor. The processing speed of our implementation achieves 92 sec over F97 3 and 553 sec over F193 3 on 2.6GHz processor...
Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. As they rely critically on effi...
Although identity based cryptography o ers a number of functional advantages over conventional public key methods, the computational costs are significantly greater. The dominant part of this cost i...
Given an ordinary elliptic curve on Hesse form over a finite field of characteristic three, we give a sequence of elliptic curves which leads to an effective construction of the canonical lift, and ...
In this paper the benefits of implementation of the Tate pair- ing computation in dedicated hardware are discussed. The main obser- vation lies in the fact that arithmetic architectures in the exten...
n this paper, we propose a modified T pairing algorithm in characteristic three which does not need any cube root extraction. We also discuss its implementation on a low cost platform which hosts a...
Since the introduction of pairings over (hyper)elliptic curves in constructive cryptographic applications, an ever increasing number of protocols based on pairings have appeared in the literature....
In this paper we propose new formulae and algorithms for arithmetic on ordinary elliptic curve with a point of order 3 over finite field of characteristic three, by which the cost of a point multiplic...
We describe further improvements of the T pairing algorithm in characteristic three. Our approach combines the loop unrolling technique introduced by Granger et. al for the Duursma-Lee algorithm, a...
Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being ...

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