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
On the implementation of elliptic curve cryptosystems
CRYPTO '89 Proceedings on Advances in cryptology
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Use of Elliptic Curves in Cryptography
CRYPTO '85 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
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
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
Fast Key Exchange with Elliptic Curve Systems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Counting the number of points on elliptic curves over finite fields: strategies and performances
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
The State of Elliptic Curve Cryptography
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
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
Generating Genus Two Hyperelliptic Curves over Large Characteristic Finite Fields
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
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One of the main difficulties for implementing cryptographic schemes based on elliptic curves defined over finite fields is the necessary computation of the cardinality of these curves. In the case of finite fields F2n, recent theoretical breakthroughs yield a significant speed up of the computations. Once described some of these ideas in the first part of this paper, we show that our current implementation runs from 2 up to 10 times faster than what was done previously. In the second part, we exhibit a slight change of Schoof's algorithm to choose curves with a number of points "nearly" prime and so construct cryptosystems based on random elliptic curves instead of specific curves as it used to be.