A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Efficient computation of minimal polynomials in algebraic extensions of finite fields
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Modern Computer Algebra
An Extension of Kedlaya's Algorithm to Hyperelliptic Curves in Characteristic 2
Journal of Cryptology
Point Counting in Families of Hyperelliptic Curves
Foundations of Computational Mathematics
New directions in cryptography
IEEE Transactions on Information Theory
Fast computation of canonical lifts of elliptic curves and its application to point counting
Finite Fields and Their Applications
Fast arithmetic in unramified p-adic fields
Finite Fields and Their Applications
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Let E be a nonsupersingular elliptic curve over the finite field with p^n elements. We present a deterministic algorithm that computes the zeta function and hence the number of points of such a curve E in time quasi-quadratic in n. An older algorithm having the same time complexity uses the canonical lift of E, whereas our algorithm uses rigid cohomology combined with a deformation approach. An implementation in small odd characteristic turns out to give very good results.