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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 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.
Cited literature [25 references]
https://hal.inria.fr/inria-00107290
Contributor : Emmanuel Thomé <>
Submitted on : Thursday, November 15, 2007 - 11:12:51 AM
Last modification on : Wednesday, October 14, 2020 - 3:54:03 PM
Long-term archiving on: : Friday, November 25, 2016 - 6:07:06 PM
Contributor : Emmanuel Thomé <>
Submitted on : Thursday, November 15, 2007 - 11:12:51 AM
Last modification on : Wednesday, October 14, 2020 - 3:54:03 PM
Long-term archiving on: : Friday, November 25, 2016 - 6:07:06 PM
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non-he-genus3.pdf
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