A coprocessor for the final exponentiation of the ηT pairing in characteristic three

Jean Luc Beuchat, Nicolas Brisebarre, Masaaki Shirase, Tsuyoshi Takagi, Eiji Okamoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)


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. Software implementations being rather slow, the study of hardware architectures became an active research area. Beuchat et al. proposed for instance a coprocessor which computes the characteristic three ηT pairing, from which the Tate pairing can easily be derived, in 33μs on a Cyclone II FPGA. However, a final exponentiation is required to ensure a unique output value and the authors proposed to supplement their ηT pairing accelerator with a coprocessor for exponentiation. Thus, the challenge consists in designing the smallest possible piece of hardware able to perform this task in less than 33 /is on a Cyclone II device. In this paper, we propose a novel arithmetic operator implementing addition, cubing, and multiplication over double-struck F sign397 and show that a coprocessor based on a single such operator meets this timing constraint.

Original languageEnglish
Title of host publicationArithmetic of Finite Fields - First International Workshop, WAIFI 2007, Proceedings
PublisherSpringer Verlag
Number of pages15
ISBN (Print)9783540730736
Publication statusPublished - 2007
Event1st International Workshop on Arithmetic of Finite Fields, WAIFI 2007 - Madrid, Spain
Duration: Jun 21 2007Jun 22 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4547 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other1st International Workshop on Arithmetic of Finite Fields, WAIFI 2007

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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