Time-Memory Trade-offs for Index Calculus in Genus 3

Kim Laine; Kristin Lauter

Paper 2014/346

Time-Memory Trade-offs for Index Calculus in Genus 3

Kim Laine and Kristin Lauter

Abstract

In this paper, we present a variant of Diem's $\tilde{O} (q)$ index calculus algorithm to attack the discrete logarithm problem (DLP) in Jacobians of genus $3$ non-hyperelliptic curves over a finite field $F_{q}$ . We implement this new variant in C++ and study the complexity in both theory and practice, making the logarithmic factors and constants hidden in the $\tilde{O}$ -notation precise. Our variant improves the computational complexity at the cost of a moderate increase in memory consumption, but we also improve the computational complexity even when we limit the memory usage to that of Diem's original algorithm. Finally, we examine how parallelization can help to reduce both the memory cost per computer and the running time for our algorithms.

Note: Minor typos fixed.

Metadata

Available format(s): PDF
Publication info: Preprint. MINOR revision.
Keywords: discrete logarithm problem index calculus double large prime higher genus genus 3 non-hyperelliptic curve quartic curve plane curve time-memory trade-off
Contact author(s): kim laine @ gmail com
History: 2014-09-12: last of 2 revisions; 2014-05-19: received; See all versions
Short URL: https://ia.cr/2014/346
License: CC BY

BibTeX

@misc{cryptoeprint:2014/346,
      author = {Kim Laine and Kristin Lauter},
      title = {Time-Memory Trade-offs for Index Calculus in Genus 3},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/346},
      year = {2014},
      url = {https://eprint.iacr.org/2014/346}
}