Advertisement

Preventing Timing Attacks Against RQC Using Constant Time Decoding of Gabidulin Codes

  • Slim Bettaieb
  • Loïc Bidoux
  • Philippe GaboritEmail author
  • Etienne Marcatel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11505)

Abstract

This paper studies the resistance of the code-based encryption scheme RQC to timing attacks. We describe two chosen ciphertext timing attacks that rely on a correlation between the weight of the error to be decoded and the running time of Gabidulin code’s decoding algorithm. These attacks are of theoretical interest as they outperform the best known algorithm to solve the rank syndrome decoding problem in term of complexity. Nevertheless, they are quite impracticable in real situations as they require a huge number of requests to a timing oracle. We also provide a constant-time algorithm for the decoding of Gabidulin codes that prevent these attacks without any performance cost for honest users.

Keywords

RQC Gabidulin decoding Timing attack Rank metric 

Supplementary material

References

  1. 1.
    Aguilar-Melchor, C., et al.: Hamming Quasi-Cyclic (HQC) (2017)Google Scholar
  2. 2.
    Aguilar-Melchor, C., et al.: Rank Quasi-Cyclic (RQC) (2017)Google Scholar
  3. 3.
    Aguilar-Melchor, C., Blazy, O., Deneuville, J.-C., Gaborit, P., Zémor, G.: Efficient encryption from random quasi-cyclic codes. IEEE Transact. Inf. Theory 64(5), 3927–3943 (2018)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Aragon, N., Gaborit, P., Hauteville, A., Tillich, J.P.: A new algorithm for solving the rank syndrome decoding problem. In: 2018 IEEE International Symposium on Information Theory (ISIT), pp. 2421–2425 (2018)Google Scholar
  5. 5.
    Augot, D., Loidreau, P., Robert, G.: Generalized Gabidulin codes over fields of any characteristic. Des. Codes Crypt. 86(8), 1807–1848 (2018)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gabidulin, E.M.: Theory of codes with maximum rank distance. Problemy Peredachi Informatsii 21(1), 3–16 (1985)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Gaborit, P., Zémor, G.: On the hardness of the decoding and the minimum distance problems for rank codes. IEEE Transact. Inf. Theory 62(12), 7245–7252 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hofheinz, D., Hövelmanns, K., Kiltz, E.: A modular analysis of the Fujisaki-Okamoto transformation. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 341–371. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70500-2_12CrossRefzbMATHGoogle Scholar
  9. 9.
    Loidreau, P.: A Welch–Berlekamp like algorithm for decoding Gabidulin codes. In: Ytrehus, Ø. (ed.) WCC 2005. LNCS, vol. 3969, pp. 36–45. Springer, Heidelberg (2006).  https://doi.org/10.1007/11779360_4CrossRefGoogle Scholar
  10. 10.
    Ore, O.: On a special class of polynomials. Transact. Am. Math. Soc. 35(3), 559–584 (1933)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Slim Bettaieb
    • 1
  • Loïc Bidoux
    • 1
  • Philippe Gaborit
    • 2
    Email author
  • Etienne Marcatel
    • 3
  1. 1.WorldlineSeclinFrance
  2. 2.University of Limoges, XLIM-DMILimogesFrance
  3. 3.AtosLes Clayes-sous-BoisFrance

Personalised recommendations