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

@article{Diem2007IndexCI,
title={Index Calculus in Class Groups of Non-hyperelliptic Curves of Genus Three},
author={Claus Diem and Emmanuel Thom{\'e}},
journal={Journal of Cryptology},
year={2007},
volume={21},
pages={593-611}
}
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… CONTINUE READING
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