Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On fast multiplication of polynomials over arbitrary algebras
Acta Informatica
A course in computational algebraic number theory
A course in computational algebraic number theory
Elliptic curves and their applications to cryptography: an introduction
Elliptic curves and their applications to cryptography: an introduction
Elliptic curves in cryptography
Elliptic curves in cryptography
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Satoh's algorithm in characteristic 2
Mathematics of Computation
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
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
Schoof's algorithm and isogeny cycles
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Computational Aspects of Curves of Genus at Least 2
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Computing l-Isogenies Using the p-Torsion
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
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
Fast Elliptic Curve Point Counting Using Gaussian Normal Basis
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
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
Fast computation of canonical lifts of elliptic curves and its application to point counting
Finite Fields and Their Applications
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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
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
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
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Let p be a prime and let q := pN. Let E be an elliptic curve over Fq. We are interested in efficient algorithms to compute the order of the group E(Fq) of Fq-rational points of E. An l-adic algorithm, known as the SEA algorithm, computes #E(Fq) with O((log q)4+驴) bit operations (with fast arithmetic) and O((log q)2) memory. In this article, we survey recent advances in p-adic algorithms. For a fixed small p, the computational complexity of the known fastest p-adic point counting algorithm is O(N3+驴) in time and O(N2) in space. If we accept some precomputation depending only on p and N or a certain restriction on N, the time complexity is reduced to O(N2.5+驴) still with O(N2) space requirement.