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Square Code Attack on a Modified Sidelnikov Cryptosystem

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Codes, Cryptology, and Information Security (C2SI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9084))

Abstract

This paper presents a cryptanalysis of a modified version of the Sidelnikov cryptosystem which is based on Reed-Muller codes. This modified scheme consists in inserting random columns in the secret generating matrix or parity check matrix. The cryptanalysis relies on the computation of the squares of the public code. The particular nature of Reed-Muller which are defined by means of multivariate binary polynomials, permits to predicate the value of dimension of the square codes and then to fully recover in polynomial time the secret positions of the random columns. Our work shows that the insertion of random columns in the Sidelnikov scheme does not bring any security improvement.

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Author information

Authors and Affiliations

  1. LITIS, University of Rouen, 76821, Mont-Saint-Aignan, France

    Ayoub Otmani

  2. Department of Mathematics, University of Yaounde 1, ERAL, Yaoundé, Cameroon

    Hervé Talé Kalachi

Authors
  1. Ayoub Otmani
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  2. Hervé Talé Kalachi
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Corresponding author

Correspondence to Ayoub Otmani .

Editor information

Editors and Affiliations

  1. University of Mohammed V, Rabat, Morocco

    Said El Hajji

  2. University of Caen, Caen, France

    Abderrahmane Nitaj

  3. LAGA,Universities of Paris 8 and Paris 13, Saint-Denis Cedex 02, France

    Claude Carlet

  4. University of Mohammed V, Rabat, Morocco

    El Mamoun Souidi

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Otmani, A., Kalachi, H.T. (2015). Square Code Attack on a Modified Sidelnikov Cryptosystem. In: El Hajji, S., Nitaj, A., Carlet, C., Souidi, E. (eds) Codes, Cryptology, and Information Security. C2SI 2015. Lecture Notes in Computer Science(), vol 9084. Springer, Cham. https://doi.org/10.1007/978-3-319-18681-8_14

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  • DOI: https://doi.org/10.1007/978-3-319-18681-8_14

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18680-1

  • Online ISBN: 978-3-319-18681-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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