International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Gaetan Bisson

Publications

Year
Venue
Title
2009
EPRINT
Computing the endomorphism ring of an ordinary elliptic curve over a finite field
Gaetan Bisson Andrew V. Sutherland
We present two algorithms to compute the endomorphism ring of an ordinary elliptic curve E defined over a finite field F_q. Under suitable heuristic assumptions, both have subexponential complexity. We bound the complexity of the first algorithm in terms of log q, while our bound for the second algorithm depends primarily on log |D_E|, where D_E is the discriminant of the order isomorphic to End(E). As a byproduct, our method yields a short certificate that may be used to verify that the endomorphism ring is as claimed.
2008
EPRINT
More Discriminants with the Brezing-Weng Method
Gaetan Bisson Takakazu Satoh
The Brezing-Weng method is a general framework to generate families of pairing-friendly elliptic curves. Here, we introduce an improvement which can be used to generate more curves with larger discriminants. Apart from the number of curves this yields, it provides an easy way to avoid endomorphism rings with small class number.