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Proceedings of the third international colloquium on Coding theory and applications
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Fast Elliptic Curve Point Counting Using Gaussian Normal Basis
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Discrete Applied Mathematics - Special issue on the 2000 com2MaC workshop on cryptography
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Foundations of Computational Mathematics
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
Quasi-quadratic elliptic curve point counting using rigid cohomology
Journal of Symbolic Computation
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Computing zeta functions in families of Ca,bcurves using deformation
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Counting points on Cab curves using Monsky--Washnitzer cohomology
Finite Fields and Their Applications
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Finite Fields and Their Applications
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Let p be prime and Z"p"^"n a degree n unramified extension of the ring of p-adic integers Z"p. In this paper we give an overview of some very fast deterministic algorithms for common operations in Z"p"^"n modulo p^N. Combining existing methods with recent work of Kedlaya and Umans about modular composition of polynomials, we achieve quasi-linear time algorithms in the parameters n and N, and quasi-linear or quasi-quadratic time in logp, for most basic operations on these fields, including Galois conjugation, Teichmuller lifting and computing minimal polynomials.