Algorithmica
Almost all primes can be quickly certified
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The implementation of elliptic curve cryptosystems
AUSCRYPT '90 Proceedings of the international conference on cryptology on Advances in cryptology
Handbook of theoretical computer science (vol. A)
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
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
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
A new method of building more non-supersingular elliptic curves
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part II
Constructing pairing-friendly elliptic curves with embedding degree 10
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
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Elliptic curves play an important rôle in many areas of modern cryptology such as integer factorization and primality proving. Moreover, they can be used in cryptosystems based on discrete logarithms for building one-way permutations. For the latter purpose, it is required to have cyclic elliptic curves over finite fields. The aim of this note is to explain how to construct such curves over a finite field of large prime cardinality, using the ECPP primality proving test of Atkin and Morain.