Reynald Lercier

R. Lercier. Finding Good Random Elliptic Curves for Cryptosystems Defined Over GF(2ⁿ). In W. Fumy, editor, Advances in Cryptology - EUROCRYPT '97: International Conference on the Theory and Application of Cryptographic Techniques, Konstanz, Germany, May 1997. Proceedings, volume 1233 of Lecture Notes in Computer Science, pages 379-392. Springer Berlin / Heidelberg, May 1997.

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 GF(2ⁿ), 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.

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