Journal of Cryptology
Elliptic curves in cryptography
Elliptic curves in cryptography
Satoh's algorithm in characteristic 2
Mathematics of Computation
A Memory Efficient Version of Satoh's Algorithm
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
An Extension of Kedlaya's Point-Counting Algorithm to Superelliptic Curves
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Computational Aspects of Curves of Genus at Least 2
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Counting Points on Hyperelliptic Curves over Finite Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
An Extension of Kedlaya's Algorithm to Artin-Schreier Curves in Characteristic 2
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Arithmetic on superelliptic curves
Mathematics of Computation
Computing zeta functions of Artin-Schreier curves over finite fields II
Journal of Complexity - Special issue on coding and cryptography
Computing Zeta Functions of Hyperelliptic Curves over Finite Fields of Characteristic 2
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
An Extension of Kedlaya's Algorithm to Artin-Schreier Curves in Characteristic 2
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Computing zeta functions of Artin-Schreier curves over finite fields II
Journal of Complexity - Special issue on coding and cryptography
Decoding by rank-2 bundles over plane quartics
Journal of Symbolic Computation
Abelian varieties and cryptography
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Dickson polynomials, hyperelliptic curves and hyper-bent functions
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
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In this paper we present an extension of Kedlaya's algorithm for computingthe zeta function of an Artin-Schreier curve over a finite field Fq of characteristic 2. The algorithm has running time O(g5+驴 log3+驴 q) and needs O(g3 log3 q) storage space for a genus g curve. Our first implementation in MAGMA shows that one can now generate hyperelliptic curves suitable for cryptography in reasonable time. We also compare our algorithm with an algorithm by Lauder and Wan which has the same time and space complexity. Furthermore, the method introduced in this paper can be used for any hyperelliptic curve over a finite field of characteristic 2.