Handbook of theoretical computer science (vol. A)
Construction of Secure Elliptic Cryptosystems Using CM Tests and Liftings
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Generating Class Fields using Shimura Reciprocity
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Computing Hilbert class polynomials
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
The 2-adic CM method for genus 2 curves with application to cryptography
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
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We study the action of modular correspondences in the p- adic neighborhood of CM points. We deduce and prove two stable and efficient p-adic analytic methods for computing singular values of modular functions. On the way we prove a non trivial lower bound for the density of smooth numbers in imaginary quadratic rings and show that the canonical lift of an elliptic curve over Fq can be computed in probabilistic time 驴 exp((log q)1/2+驴) under GRH. We also extend the notion of canonical lift to supersingular elliptic curves and show how to compute it in that case.