International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Andreas Enge

Affiliation: INRIA Bordeaux-Sud-Ouest

Publications

Year
Venue
Title
2011
JOFC
2010
EPRINT
Class Invariants by the CRT Method
Andreas Enge Andrew V. Sutherland
We adapt the CRT approach to computing Hilbert class polynomials to handle a wide range of class invariants. For suitable discriminants D, this improves its performance by a large constant factor, more than 200 in the most favourable circumstances. This has enabled record-breaking constructions of elliptic curves via the CM method, including examples with |D| > 10^{15}.
2008
EPRINT
Computing Hilbert Class Polynomials
We present and analyze two algorithms for computing the Hilbert class polynomial H_D(X). The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing H_D(X), and we show that all methods have comparable run times.
2007
EUROCRYPT
2005
JOFC
2002
EPRINT
Building curves with arbitrary small MOV degree over finite prime fields
We investigate the possibility of building elliptic curves over finite prime fields having given small MOV-degrees. Using complex multiplication, we give many examples of such curves.
2002
EPRINT
Practical Non-Interactive Key Distribution Based on Pairings
Régis Dupont Andreas Enge
We propose a practical non-interactive key distribution protocol based on pairings and define a notion of security for such a scheme. We prove the security of the system in this setting under the GDBH assumption, and present some possible realisations using Weil or Tate pairings on supersingular and ordinary elliptic curves.