Identifying supersingular elliptic curves

Details Identifying supersingular elliptic curves Identifying supersingular elliptic curves

2011-07-06

arxiv.org/abs/1107.1140v2

Mathematics

Number Theory

minor edits, 10 pages

Scientific paper

Given an elliptic curve E over a field of characteristic p, we consider how to efficiently determine whether E is ordinary or supersingular. We analyze the complexity of several existing algorithms and then present a new approach that exploits structural differences between ordinary and supersingular isogeny graphs. This yields a simple algorithm that, given E and a suitable non-residue in F_p^2, determines the supersingularity of E in O(n^3 log^2 n) time and O(n) space, where n=O(log p). Both these complexity bounds are significant improvements over existing methods, as we demonstrate with some practical computations.

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