## Cryptology ePrint Archive: Report 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 $\widetilde{O}(q)$ index calculus algorithm to attack the discrete logarithm problem (DLP) in Jacobians of genus $3$ non-hyperelliptic curves over a finite field $\mathbb{F}_q$. 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 $\widetilde{O}$-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.

Category / Keywords: discrete logarithm problem, index calculus, double large prime, higher genus, genus 3, non-hyperelliptic curve, quartic curve, plane curve, time-memory trade-off

Date: received 16 May 2014, last revised 11 Sep 2014

Contact author: kim laine at gmail com

Available format(s): PDF | BibTeX Citation

Note: Minor typos fixed.

Short URL: ia.cr/2014/346

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