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

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.

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Correspondence to Claus Diem.

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Communicated by Arjen K. Lenstra

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Diem, C., Thomé, E. Index Calculus in Class Groups of Non-hyperelliptic Curves of Genus Three. J Cryptol 21, 593–611 (2008). https://doi.org/10.1007/s00145-007-9014-6

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Keywords

  • Index calculus
  • Non-hyperelliptic curves
  • Class groups
  • Jacobians