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Journal of Cryptology

, Volume 21, Issue 4, pp 593–611 | Cite as

Index Calculus in Class Groups of Non-hyperelliptic Curves of Genus Three

  • Claus Diem
  • Emmanuel Thomé
Article

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 \(\tilde{O}(q)\) . 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.

Keywords

Index calculus Non-hyperelliptic curves Class groups Jacobians 

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Copyright information

© International Association for Cryptologic Research 2007

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität LeipzigLeipzigGermany
  2. 2.INRIA Lorraine, CACAO—bât. AVillers-lès-NancyFrance

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