Index calculus in class groups of non-hyperelliptic curves of genus three

Claus Diem (1) , Emmanuel Thomé (2)

1 Mathematischen Institut
2 CACAO - Curves, Algebra, Computer Arithmetic, and so On

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.

Domaines: Cryptographie et sécurité [cs.CR]

Claus Diem, Emmanuel Thomé. Index calculus in class groups of non-hyperelliptic curves of genus three. Journal of Cryptology, 2008, 21 (4), pp.593-611. ⟨10.1007/s00145-007-9014-6⟩. ⟨inria-00107290v2⟩