Order counting of elliptic curves defined over finite fields of characteristic 2

Algorithms for counting the order of the rational points group are indispensable for the random selection of secure elliptic curves used in cryptosystems. In the case of curves over fields having large characteristics, it is possible to use the SEA (Schoof-Elkies-Atkin) algorithm [3, 5, 16], but in the case of elliptic curves defined over finite fields of characteristic 2, the SEA algorithm can be applied only in a modified form. In the case of characteristic 2, the authors implemented the Lercier [10] and Couveignes [2] algorithms, and combined them with an improved Intelligent Choice System [7, 8] proposed by the authors earlier. It was confirmed that in the case of characteristic 2 the combination of these methods allows for a fast generation of secure curves. (C) 2001 Scripta. Technica.