Section: New Results

Proving the complexity of computing endomorphism rings

Subsequent to the work [6] that has been finally published this year, Gaëtan Bisson has been working on rigorously proving a subexponential running time bound for computing endomorphism rings of ordinary elliptic curves over finite fields. In the end, the proof rests on only one assumption, namely the extended Riemann hypothesis (ERH) [4] .

In his thesis [1] , he has also made substantial advances towards the extension of these algorithms to genus 2 curves.

In studying the above-mentioned algorithms, Gaëtan Bisson, in collaboration with Andrew V. Sutherland, has designed a low-memory, Pollard-rho type algorithm for finding relations in generic groups [5] .