Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board Member: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Dawson, Ed / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti

4 Issues per year


CiteScore 2016: 0.74

SCImago Journal Rank (SJR) 2016: 0.463
Source Normalized Impact per Paper (SNIP) 2016: 0.778

Mathematical Citation Quotient (MCQ) 2016: 0.16

Online
ISSN
1862-2984
See all formats and pricing
More options …
Volume 9, Issue 2 (Jun 2015)

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

Kim Laine / Kristin Lauter
Published Online: 2015-05-21 | DOI: https://doi.org/10.1515/jmc-2014-0033

Abstract

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

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

MSC: 11Y16; 11T71

About the article

Received: 2014-09-12

Accepted: 2015-04-07

Published Online: 2015-05-21

Published in Print: 2015-06-01


Citation Information: Journal of Mathematical Cryptology, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc-2014-0033.

Export Citation

© 2015 by De Gruyter. Copyright Clearance Center

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Jennifer S. Balakrishnan, Sorina Ionica, Kristin Lauter, and Christelle Vincent
LMS Journal of Computation and Mathematics, 2016, Volume 19, Number A, Page 283

Comments (0)

Please log in or register to comment.
Log in