Advertisement

RankSynd a PRNG Based on Rank Metric

  • Philippe Gaborit
  • Adrien Hauteville
  • Jean-Pierre Tillich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9606)

Abstract

In this paper, we consider a pseudo-random generator based on the difficulty of the syndrome decoding problem for rank metric codes. We also study the resistance of this problem against a quantum computer. Our results show that with rank metric it is possible to obtain fast PRNG with small public data, without considering additional structure for public matrices like quasi-cyclicity for Hamming distance.

References

  1. 1.
    Banerjee, A., Peikert, C., Rosen, A.: Pseudorandom functions and lattices. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 719–737. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    Berbain, C., Gilbert, H., Patarin, J.: QUAD: a practical stream cipher with provable security. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 109–128. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Berlekamp, E., McEliece, R., van Tilborg, H.: On the inherent intractability of certain coding problems. IEEE Trans. Inform. Theor. 24(3), 384–386 (1978)CrossRefzbMATHGoogle Scholar
  4. 4.
    Bernstein, D.J.: Grover vs. McEliece. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 73–80. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Blum, L., Blum, M., Shub, M.: A simple unpredictable pseudo-random number generator. SIAM J. comput. 15(2), 364–383 (1986)CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudorandom bits. SIAM J. Comput. 13(4), 850–864 (1984)CrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching. Fortsch. Phys. 46, 493 (1998)CrossRefGoogle Scholar
  8. 8.
    Chabaud, F., Stern, J.: The cryptographic security of the syndrome decoding problem for rank distance codes. In: Kim, K., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 368–381. Springer, Heidelberg (1996)Google Scholar
  9. 9.
    Courtois, N.T.: Efficient zero-knowledge authentication based on a linear algebra problem minrank. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, p. 402. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Cramer, R., Ducas, L., Peikert, C., Regev, O.: Recovering short generators of principal ideals in cyclotomic rings. Cryptology ePrint Archive, Report 2015/313 (2015). http://eprint.iacr.org/
  11. 11.
    Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)CrossRefGoogle Scholar
  12. 12.
    Fischer, J.-B., Stern, J.: An efficient pseudo-random generator provably as secure as syndrome decoding. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 245–255. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  13. 13.
    Gaborit, P., Lauradoux, C., Sendrier, N.: SYND: a fast code-based stream cipher with a security reduction. In: Proceedings of the IEEE International Symposium on Information Theory - ISIT, pp. 186–190, Nice (2007)Google Scholar
  14. 14.
    Gaborit, P., Ruatta, O., Schrek, J.: On the complexity of the rank syndrome decoding problem. CoRR (2013). arXiv:org/abs/1301.1026
  15. 15.
    Gaborit, P., Zémor, G.: On the hardness of the decoding and the minimum distance problems for rank codes. CoRR (2014). arXiv:org/abs/1404.3482
  16. 16.
    Gibson, J.K.: The security of the Gabidulin public key cryptosystem. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 212–223. Springer, Heidelberg (1996)Google Scholar
  17. 17.
    Goubin, L., Courtois, N.T.: Cryptanalysis of the TTM cryptosystem. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, p. 44. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  18. 18.
    Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325 (1997)CrossRefGoogle Scholar
  19. 19.
    Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)CrossRefMathSciNetzbMATHGoogle Scholar
  20. 20.
    Hauteville, A., Tillich, J.-P.: New algorithms for decoding in the rank metric and an attack on the LRPC cryptosystem (2015). arXiv:org/abs/1504.05431
  21. 21.
    Kipnis, A., Shamir, A.: Cryptanalysis of the HFE public key cryptosystem by relinearization. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, p. 19. Springer, Heidelberg (1999)Google Scholar
  22. 22.
    Levin, L.A.: One way functions and pseudorandom generators. Combinatorica 7(4), 357–363 (1987)CrossRefMathSciNetzbMATHGoogle Scholar
  23. 23.
    Lévy-dit-Vehel F., Perret, L.: Algebraic decoding of codes in rank metric. In: Proceedings of YACC06, Porquerolles, France (2006). http://grim.univ-tln.fr/YACC06/abstracts-yacc06.pdf
  24. 24.
    Lidl, R., Niederreiter, H.: Finite Fields, Volume 20 of Encyclopedia of Mathematics and its Applications, 2nd edn. Cambridge University Press, Cambridge (1997)Google Scholar
  25. 25.
    McEliece, R.J.: A public-key system based on algebraic coding theory. DSN Progress Report 44, pp. 114–116. Jet Propulsion Lab (1978)Google Scholar
  26. 26.
    Meziani, M., Cayrel, P.-L., Hoffmann, G.: Improving the performance of the SYND stream cipher. In: Mitrokotsa, A., Vaudenay, S. (eds.) AFRICACRYPT 2012. LNCS, vol. 7374, pp. 99–116. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  27. 27.
    Ourivski, A.V., Johansson, T.: New technique for decoding codes in the rank metric and its cryptography applications. Prob. Inf. Transm. 38(3), 237–246 (2002)CrossRefzbMATHGoogle Scholar
  28. 28.
    Spaenlenhauer, P.-J.: Résolution de systèmes multi-homogènes et determinantiels. Ph.D. thesis, Univ. Pierre et Marie Curie- Paris 6 (2012)Google Scholar
  29. 29.
    Yao, A.C.: Theory and application of trapdoor functions. In: 23rd Annual Symposium on Foundations of Computer Science, SFCS 2008, pp. 80–91. IEEE (1982)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Philippe Gaborit
    • 1
  • Adrien Hauteville
    • 1
    • 2
  • Jean-Pierre Tillich
    • 2
  1. 1.XLIM-DMIUniversité de LimogesLimoges CedexFrance
  2. 2.InriaLe ChesnayFrance

Personalised recommendations