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Journal of Mathematical Cryptology

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

Editorial Board: 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 2017: 1.43

SCImago Journal Rank (SJR) 2017: 0.293
Source Normalized Impact per Paper (SNIP) 2017: 1.117

Mathematical Citation Quotient (MCQ) 2017: 0.51

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Volume 3, Issue 3


Numerical solvers and cryptanalysis

Mario Lamberger / Tomislav Nad / Vincent Rijmen
Published Online: 2010-01-20 | DOI: https://doi.org/10.1515/JMC.2009.015


In this paper, we present an approach to apply numerical methods in the cryptanalysis of modern cryptographic algorithms. We focus on the stream cipher Trivium. It is a stream cipher recommended by the eStream project in the hardware category. We use numerical methods to attack a reduced version of Trivium – called Bivium A. We first set up a system of equations describing the internal state of the cipher and convert it into a system over the reals. Four different techniques for the conversion are discussed. At this point we are able to apply numerical methods. We choose the DIRECT algorithm by D. R. Jones et al. and the Interior Reflective Newton Method by Coleman and Li. Results, occurring problems in this approach and possible future research directions are discussed.

Keywords.: Numerical solver; numerical analysis; Boolean equations; Trivium; Bivium; stream ciphers; cryptanalysis; optimization

About the article

Received: 2008-12-30

Revised: 2009-09-29

Published Online: 2010-01-20

Published in Print: 2009-09-01

Citation Information: Journal of Mathematical Cryptology, Volume 3, Issue 3, Pages 249–263, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/JMC.2009.015.

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Journal of Mathematical Cryptology, 2011, Volume 4, Number 4

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