Counting the number of points on elliptic curves over finite fields: strategies and performances. (English) Zbl 0903.11029

Lercier, Reynald; Morain, François

Guillou, Louis C. (ed.) et al., Advances in cryptology - EUROCRYPT ’95. International conference on the theory and application of cryptographic techniques, Saint-Malo, France, May 21-25, 1995. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 921, 79-94 (1995).

Summary: 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 \(\text{GF}(2^n)\), for \(n\leq 600\).
For the entire collection see [Zbl 0866.00067].

MSC:

11Y16	Number-theoretic algorithms; complexity
94A60	Cryptography
14H52	Elliptic curves
68W30	Symbolic computation and algebraic computation

Keywords:

key exchange algorithms; non-supersingular curves; cardinality; elliptic curves over finite fields

Citations:

Zbl 0866.00067