Time-memory trade-offs for index calculus in genus 3

Journal of mathematical cryptology

article

Kim Laine¹  Kristin Lauter² 

[1] Department of Mathematics;Microsoft Research

关键词: Discrete logarithm problem;    index calculus;    double large prime;    higher genus;    genus 3;    non-hyperelliptic curve;    quartic curve;    plane curve;    time-memory trade-off;   

DOI  :  10.1515/jmc-2014-0033

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, we present a variant of Diem's O˜(q)${\widetilde{O}(q)}$ index calculus algorithm to attack the discrete logarithm problem (DLP) in Jacobians of genus 3 non-hyperelliptic curves over a finite field ? 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 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.

【 授权许可】

CC BY|CC BY-NC-ND