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On Asymptotic Security Estimates in XL and Gröbner Bases-Related Algebraic Cryptanalysis

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Information and Communications Security (ICICS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3269))

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Abstract

“Algebraic Cryptanalysis” against a cryptosystem often comprises finding enough relations that are generally or probabilistically valid, then solving the resultant system. The security of many schemes (most important being AES) thus depends on the difficulty of solving multivariate polynomial equations. Generically, this is NP-hard.

The related methods of XL (eXtended Linearization), Gröbner Bases, and their variants (of which a large number has been proposed) form a unified approach to solving equations and thus affect our assessment and understanding of many cryptosystems.

Building on prior theory, we analyze these XL variants and derive asymptotic formulas giving better security estimates under XL-related algebraic attacks; through this examination we have hopefully improved our understanding of such variants. In particular, guessing a portion of variables is a good idea for both XL and Gröbner Bases methods.

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Author information

Authors and Affiliations

  1. Tamkang University, Tamsui, Taiwan

    Bo-Yin Yang

  2. Chinese Data Security Inc, & Nat’l Taiwan U., Taipei

    Jiun-Ming Chen

  3. Axalto Smartcards, Paris, France

    Nicolas T. Courtois

Authors
  1. Bo-Yin Yang
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  2. Jiun-Ming Chen
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  3. Nicolas T. Courtois
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Editor information

Editors and Affiliations

  1. Department of Information and Communication Technologies, University of A Coruña, Spain

    Javier Lopez

  2. Chinese Academy of Sciences, Institute of Softwear, 100080, Beijing, China

    Sihan Qing

  3. Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, 305-8573, Ibaraki, Japan

    Eiji Okamoto

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© 2004 Springer-Verlag Berlin Heidelberg

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Yang, BY., Chen, JM., Courtois, N.T. (2004). On Asymptotic Security Estimates in XL and Gröbner Bases-Related Algebraic Cryptanalysis. In: Lopez, J., Qing, S., Okamoto, E. (eds) Information and Communications Security. ICICS 2004. Lecture Notes in Computer Science, vol 3269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30191-2_31

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  • DOI: https://doi.org/10.1007/978-3-540-30191-2_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23563-7

  • Online ISBN: 978-3-540-30191-2

  • eBook Packages: Springer Book Archive

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