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Algebraic cryptanalysis of a small-scale version of stream cipher Lex

Algebraic cryptanalysis of a small-scale version of stream cipher Lex

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  • Author(s): V. Velichkov 1, 2 ; V. Rijmen 1, 2, 3 ; B. Preneel 1, 2
    • View affiliations
    • Affiliations: 1: Department of Electrical Engineering ESAT/SCD-COSIC, Katholieke Universiteit Leuven, Heverlee, Belgium
      2: Department of Electrical Engineering ESAT/SCD-COSIC, Interdisciplinary Institute for BroadBand Technology (IBBT), Gent-Ledeberg, Belgium
      3: Institute for Applied Information Processing and Communications, Graz University of Technology, Graz, Austria
  • Source: Volume 4, Issue 2, June 2010, p. 49 – 61
    DOI:  10.1049/iet-ifs.2009.0118 , Print ISSN 1751-8709, Online ISSN 1751-8717
© The Institution of Engineering and Technology
Published

In this study, the authors analyse with respect to algebraic attacks a small-scale version of the stream cipher Lex. They base it on a small-scale version of the block cipher advanced encryption standard (AES) with 16-bit state and 16-bit key. They represent the small-scale Lex and its key schedule in two alternative ways: as a system of cubic boolean equations and as a system of quadratic boolean equations. The authors use Gröbner bases to solve the two systems for different number of rounds and sizes of the leak. They obtain the best results for the quadratic representation of the cipher. For this case they are able to recover the secret key in time less than 2 min by solving a system of 374 quadratic boolean equations in 208 unknowns resulting from 5 rounds of the cipher.

Inspec keywords: cryptography; Boolean algebra; block codes; algebraic codes

Other keywords: Grobner bases; cubic boolean equations; algebraic cryptanalysis; 16-bit key; stream cipher Lex; secret key; quadratic boolean equations; small scale version; block cipher advanced encryption standard; 16- bit state

Subjects: Algebra; Data security

References

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