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
Time-memory trade-offs for index calculus in genus 3
In this paper, we present a variant of Diem's 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.
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