Almost all primes can be quickly certified
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A pseudo-random bit generator based on elliptic logarithms
Proceedings on Advances in cryptology---CRYPTO '86
The implementation of elliptic curve cryptosystems
AUSCRYPT '90 Proceedings of the international conference on cryptology on Advances in cryptology
Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
On the implementation of elliptic curve cryptosystems
CRYPTO '89 Proceedings on Advances in cryptology
An FFT extension of the elliptic curve method of factorization
An FFT extension of the elliptic curve method of factorization
A new elliptic curve based analogue of RSA
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
New Public-Key Schemes Based on Elliptic Curves over the Ring Zn
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
An Efficient Digital Signature Scheme Based on an Elliptic Curve Over the Ring Zn
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Design of Elliptic Curves with Controllable Lower Boundary of Extension Degree for Reduction Attacks
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
On Ordinary Elliptic Curve Cryptosystems
ASIACRYPT '91 Proceedings of the International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Elliptic Curves over Fp Suitable for Cryptosystems
ASIACRYPT '92 Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Constructing elliptic curves with given group order over large finite fields
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Schoof's algorithm and isogeny cycles
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
The State of Elliptic Curve Cryptography
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Modified Stirling Numbers and p-Divisibility in the Universal Typical pk-Series
Journal of Algebraic Combinatorics: An International Journal
Finding Secure Curves with the Satoh-FGH Algorithm and an Early-Abort Strategy
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Efficient Implementation of Schoof's Algorithm
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Construction of Secure Elliptic Cryptosystems Using CM Tests and Liftings
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Finding good random elliptic curves for cryptosystems defined over IF2n
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Comparing the MOV and FR reductions in elliptic curve cryptography
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
An algorithm for solving the discrete log problem on hyperelliptic curves
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Noisy polynomial interpolation and noisy chinese remaindering
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Algebraic curves and cryptography
Finite Fields and Their Applications
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Cryptographic schemes using elliptic curves over finite fields require the computation of the cardinality of the curves. Dramatic progress have been achieved recently in that field by various authors. The aim of this article is to highlight part of these improvements and to describe an efficient implementation of them in the particular case of the fields GF(2n), for n ≤ 600.