Hardware implementation of the eta pairing in characteristic 2 and 3.

Nicolas Brisebarre (ENS Lyon)

MSI Computational Mathematics Seminar Series

DATE: 2008-03-31
TIME: 11:00:00 - 12:00:00
LOCATION: John Dedman G35
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ABSTRACT:
Pairings were first introduced in cryptology by Menezes, Okamoto & Vanstone and Frey & Rueck for code-breaking purposes. Mitsunari, Sakai & Kasahara and Sakai, Oghishi & Kasahara seem to be the first to have discovered their constructive properties. Since the foundational work of Joux in 2000, an already large and ever increasing number of pairing-based protocols has been found.

The software implementations of these successive algorithmic improvements being rather slow, the need for fine hardware implementations is strong. This is a critical issue to make pairings popular and of common use in cryptography and in particular in view of a successful industrial transfer.

We will start this talk by an introduction to pairings, and finally present recent works that address the problem of getting efficient hardware implementation of the eta and Tate pairings on elliptic curves in characteristic 2 and 3.

This is a joint work with Jean-Luc Beuchat (Univ. Tsukuba, Japan), Jeremie Detrey (B-IT, Bonn), Eiji Okamoto (Univ. Tsukuba), Masaaki Shirase (Future Univ. Hakodate, Japan), Tsuyoshi Takagi (Fut. Univ. Hakodate).
BIO:
http://perso.ens-lyon.fr/nicolas.brisebarre/index.html.en