Algorithms and arithmetic operators for computing the ηT pairing in characteristic three

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

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


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 rather slow, the study of hardware architectures became an active research area. In this paper, we discuss several algorithms to compute the ηT pairing in characteristic three and suggest further improvements. These algorithms involve addition, multiplication, cubing, inversion, and sometimes cube root extraction over F3m. We propose a hardware accelerator based on a unified arithmetic operator able to perform the operations required by a given algorithm. We describe the implementation of a compact coprocessor for the field F397) given by F3[x]/(x97 + x12 + 2), which compares favorably with other solutions described in the open literature.

Original languageEnglish
Pages (from-to)1454-1468
Number of pages15
JournalIEEE Transactions on Computers
Issue number11
Publication statusPublished - 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics


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