View More View Less
  • 1 University College London, UK
  • 2 Poznań University of Technology, Poland
  • 3 Université Catholique de Louvain, Belgium
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

Differential Cryptanalysis (DC) is one of the oldest known attacks on block ciphers. DC is based on tracking of changes in the differences between two messages as they pass through the consecutive rounds of encryption. However DC remains very poorly understood. In his textbook written in the late 1990s Schneier wrote that against differential cryptanalysis, GOST is “probably stronger than DES”. In fact Knudsen have soon proposed more powerful advanced differential attacks however the potential space of such attacks is truly immense. To this day there is no method which allows to evaluate the security of a cipher against such attacks in a systematic way. Instead, attacks are designed and improved in ad-hoc ways with heuristics [6–13,21]. The best differential attack known has time complexity of 2179 [13].

In this paper we show that for a given block cipher there exists an optimal size for advanced differential properties. This new understanding allows to considerably reduce the space to be searched for “good” truncated differential properties suitable for an attack.

  • [1]

    Albrecht, Martin and Leander, Gregor, An All-In-One Approach to Differential Cryptanalysis for Small Block Ciphers, preprint available at eprint.iacr.org/2012/401/.

    • Export Citation
  • [2]

    Babenko, Lyudmila K. and Ishchukova, Evgeniya, Differential analysis of GOST encryption algorithm, in: SIN 2010, pp. 149157, ACM (2010).

    • Search Google Scholar
    • Export Citation
  • [3]

    Biham, Eli and Shamir, Adi, Differential Cryptanalysis of DES-like Cryptosystems, Journal of Cryptology, vol. 4, pp. 372, IACR (1991).

    • Search Google Scholar
    • Export Citation
  • [4]

    Courtois, Nicolas, The Best Differential Characteristics and Subtleties of the Biham-Shamir Attacks on DES, on eprint.iacr.org/2005/202.

    • Export Citation
  • [5]

    Courtois, Nicolas, Security Evaluation of GOST 28147-89 In View Of International Standardisation, Cryptologia, Vol. 36 Iss. 1 pp. 213 (2012).

    • Search Google Scholar
    • Export Citation
  • [6]

    Courtois, Nicolas and Misztal, Michał, Aggregated Differentials and Cryptanalysis of PP-1 and GOST, in: CECC 2011, Periodica Mathematica Hungarica, Vol. 65 (2), pp. 11Ű26 (2012).

    • Search Google Scholar
    • Export Citation
  • [7]

    Courtois, Nicolas and Misztal, Michał, First Differential Attack On Full 32-Round GOST, in: ICICS′11, pp. 216227, Springer LNCS 7043 (2011).

    • Search Google Scholar
    • Export Citation
  • [8]

    Courtois, Nicolas and Misztal, Michał, Differential Cryptanalysis of GOST, in: Cryptology ePrint Archive, Report 2011/312. 14 June 2011, http://www.eprint.iacr.org/2011/312.

    • Search Google Scholar
    • Export Citation
  • [9]

    Courtois, Nicolas T., Misztal, Michał and Mourouzis, Theodosis, Enhanced Truncated Differential Cryptanalysis of GOST, in: SECRYPT 2013, 10th International Conference on Security and Cryptography, Reykjavik, Iceland, July 2931 (2013).

    • Search Google Scholar
    • Export Citation
  • [10]

    Courtois, Nicolas T. and Mourouzis, Theodosis, Propagation of Truncated Differentials in GOST, in: SECURWARE 2013, The Seventh InternationalConference on Emerging Security Information, Systems and Technologies, August 2531, 2013 — Barcelona, Spain.

    • Search Google Scholar
    • Export Citation
  • [11]

    Courtois, Nicolas T., Mourouzis, Theodosis, Misztal, Michał, Quisquater, Jean-Jacques and Song, Guangyan, Can GOST Be Made Secure Against Differential Cryptanalysis?, accepted to Cryptologia, to appear in 2014.

    • Export Citation
  • [12]

    Courtois, Nicolas, Algebraic Complexity Reduction and Cryptanalysis of GOST, Preprint 2010–2013, available at http://www.eprint.iacr.org/2011/626.

    • Search Google Scholar
    • Export Citation
  • [13]

    Courtois, Nicolas, An Improved Differential Attack on Full GOST, in: Cryptology ePrint Archive, Report 2012/138. 15 March 2012, http://www.eprint.iacr.org/2012/138.

    • Search Google Scholar
    • Export Citation
  • [14]

    Doganaksoy, Ali, Ege, Bariş, Koçak, Onur and Sulak, Fatih, Cryptographic Randomness Testing of Block Ciphers and Hash Functions, in: http://www.eprint.iacr.org/2010/564.

    • Export Citation
  • [15]

    Shorin, Vitaly V., Jelezniakov, Vadim V. and Gabidulin, Ernst M., Linear and Differential Cryptanalysis of Russian GOST, Preprint submitted to Elsevier Preprint, 4 April 2001.

    • Search Google Scholar
    • Export Citation
  • [16]

    Zabotin, I. A., Glazkov, G. P. and Isaeva, V. B., Cryptographic Protection for Information Processing Systems, Government Standard of the USSR, GOST 28147-89.

    • Search Google Scholar
    • Export Citation
  • [17]

    A Russian reference implementation of GOST implementing Russian algorithms as an extension of TLS v1.0. is available as a part of OpenSSL library. The file gost89.c contains eight different sets of S-boxes and is found in OpenSSL 0.9.8 and later: http://www.openssl.org/source/

    • Export Citation
  • [18]

    Knudsen, Lars R., Truncated and Higher Order Differentials, in: FSE 1994, pp. 196211, LNCS 1008, Springer.

  • [19]

    Poschmann, Axel, Ling, San and Wang, Huaxiong, 256 Bit Standardized Crypto for 650 GE -Ű GOST Revisited, in: CHES 2010, LNCS 6225, pp. 219233 (2010).

    • Search Google Scholar
    • Export Citation
  • [20]

    Rudskoy, Vladimir and Dmukh, Andrey, Algebraic and Differential Cryptanalysis of GOST: Fact or Fiction, in: CTCrypt 2012, 2 July 2012, Nizhny Novgorod, Russia. An extended abstract is available at: https://www.tc26.ru/invite/spisokdoc/CTCrypt_rudskoy.pdf. Slides are available at: https://www.tc26.ru/documentary%20materials/CTCrypt%202012/slides/CTCrypt_rudskoy_slides_final.pdf

    • Search Google Scholar
    • Export Citation
  • [21]

    Seki, H. and Kaneko, T., Differential Cryptanalysis of Reduced Rounds of GOST, in: SAC 2000, LNCS 2012, pp. 315323, Springer (2000).

    • Search Google Scholar
    • Export Citation
  • [22]

    Schneier, Bruce, Section 14.1 GOST, in: Applied Cryptography, Second Edition, John Wiley and Sons, 1996. ISBN 0-471-11709-9.

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE

 

  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • SCOPUS
  • The ISI Alerting Services

 

Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu