Abstract : We study an index calculus algorithm to solve the discrete logarithm problem (DLP) in degree~0 class groups of non-hyperelliptic curves of genus~3 over finite fields. We present a heuristic analysis of the algorithm which indicates that the DLP in degree~0 class groups of non-hyperelliptic curves of genus~3 can be solved in an expected time of soft-O(q). This heuristic result relies on one heuristic assumption which is studied experimentally. We also present experimental data which show that a variant of the algorithm is faster than the Rho method even for small group sizes, and we address practical limitations of the algorithm.
https://hal.inria.fr/inria-00107290 Contributor : Emmanuel ThoméConnect in order to contact the contributor Submitted on : Thursday, November 15, 2007 - 11:12:51 AM Last modification on : Friday, February 4, 2022 - 3:34:52 AM Long-term archiving on: : Friday, November 25, 2016 - 6:07:06 PM
Claus Diem, Emmanuel Thomé. Index calculus in class groups of non-hyperelliptic curves of genus three. Journal of Cryptology, Springer Verlag, 2008, 21 (4), pp.593-611. ⟨10.1007/s00145-007-9014-6⟩. ⟨inria-00107290v2⟩