Cryptography Seminar talk
William Stein
David Freeman of UC Berkeley will speak in the number theory / cryptography
seminar on Tuesday, February 26. The title, abstract, time, etc., are below.
Title: Constructing abelian varieties for pairing-based cryptography
Speaker: David Freeman
Date: Tuesday February 26, 2008 at 4pm in Padelford 401
Abstract:
In recent years, the Weil and Tate pairings on abelian varieties over
finite fields have been used to construct a vast number of new and
useful cryptosystems. The abelian varieties used in these systems
must have small embedding degree with respect to a large prime-order
subgroup. Such ``pairing-friendly'' abelian varieties are rare and
thus require specific constructions.
In this talk we describe two of our recent contributions to the
catalogue of pairing-friendly abelian varieties: (1) ordinary
elliptic curves of prime order with embedding degree 10, and (2)
ordinary abelian varieties of arbitrary dimension over $\mathbb{F}_p$
having arbitrary embedding degree with respect to a prime subgroup of
size significantly smaller than $p$. Both results require finding
curves whose Jacobians complex multiplication by a specified CM
field; making this step feasible while maintaining the
pairing-friendly property is the difficult part of such constructions.
The second result is joint work with P. Stevenhagen and M. Streng
(Leiden University).
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org