Abstract
In 1985, Schoof [136] presented a polynomial time algorithm for computing #E(F q ), the number of Fq-rational points on an elliptic curve E defined over the field F q . The algorithm has a running time of 0(log8 q) bit operations, and is rather cumbersome in practice. Buchmann and Muller [20] combined Schoof’s algorithm with Shanks’ baby-step giant-step algorithm, and were able to compute orders of curves over Fp, where p is a 27-decimal digit prime. The algorithm took 4.5 hours on a SUN-1 SPARC-station.
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© 1993 Springer Science+Business Media New York
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Menezes, A. (1993). Counting Points on Elliptic Curves Over F2m. In: Elliptic Curve Public Key Cryptosystems. The Springer International Series in Engineering and Computer Science, vol 234. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3198-2_7
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DOI: https://doi.org/10.1007/978-1-4615-3198-2_7
Publisher Name: Springer, Boston, MA
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