Computing l-Isogenies Using the p-Torsion
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
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 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
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: 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
On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Fast Elliptic Curve Point Counting Using Gaussian Normal Basis
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
A Timing-Resistant Elliptic Curve Backdoor in RSA
Information Security and Cryptology
Fast arithmetic in unramified p-adic fields
Finite Fields and Their Applications
Fast computation of canonical lifts of elliptic curves and its application to point counting
Finite Fields and Their Applications
A p-adic point counting algorithm for elliptic curves on legendre form
Finite Fields and Their Applications
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In this paper we present an algorithm for counting points on elliptic curves over a finite field Fpn of small characteristic, based on Satoh's algorithm. The memory requirement of our algorithm is O(n2), where Satoh's original algorithm needs O(n3) memory. Furthermore, our version has the same run time complexity of O(n3+Ɛ) bit operations, but is faster by a constant factor. We give a detailed description of the algorithm in characteristic 2 and show that the amount of memory needed for the generation of a secure 200-bit elliptic curve is within the range of current smart card technology.