Advertisement

Grover vs. McEliece

  • Daniel J. Bernstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6061)

Abstract

This paper shows that quantum information-set-decoding attacks are asymptotically much faster than non-quantum information-set-decoding attacks.

Keywords

code-based cryptography post-quantum cryptography 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Proceedings of the twenty-eighth annual ACM symposium on the theory of computing, held in Philadelphia, PA, May 22-24. Association for Computing Machinery (1996), ISBN 0-89791-785-5. MR 97g:68005. See [13]Google Scholar
  2. 2.
    Barg, A., Zhou, S.: A quantum decoding algorithm of the simplex code. In: Proceedings of the 36th Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, September 23-25 (1998), http://www.enee.umd.edu/~abarg/reprints/rm1dq.pdf; Citations in this document: §2
  3. 3.
    Bernstein, D.J.: Cost analysis of hash collisions: Will quantum computers make SHARCS obsolete? In: Workshop Record of SHARCS ’09: Special-purpose Hardware for Attacking Cryptographic Systems (2009), http://cr.yp.to/papers.html#collisioncost; Citations in this document: §1
  4. 4.
    Bernstein, D.J., Buchmann, J., Dahmen, E. (eds.): Post-quantum cryptography. Springer, Heidelberg (2009), ISBN 978–3–540–88701–0.See [16], [20]zbMATHGoogle Scholar
  5. 5.
    Bernstein, D.J., Lange, T., Peters, C.: Attacking and defending the McEliece cryptosystem. In: [9], pp. 31–46 (2008), http://eprint.iacr.org/2008/318; Citations in this document: §2, §2
  6. 6.
    Bernstein, D.J., Lange, T., Peters, C., van Tilborg, H.: Explicit bounds for generic decoding algorithms for code-based cryptography. In: WCC 2009 (2009); Citations in this document: §1, §2, §2, §3Google Scholar
  7. 7.
    Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching (1996), http://arxiv.org/abs/quant-ph/9605034v1; Citations in this document: §3, §3
  8. 8.
    Brassard, G., Høyer, P., Tapp, A.: Quantum cryptanalysis of hash and claw- free functions. In: [18], pp. 163–169 (1998); MR 99g:94013. Citations in this document: §1 Google Scholar
  9. 9.
    Buchmann, J., Ding, J. (eds.): PQCrypto 2008. LNCS, vol. 5299. Springer, Heidelberg (2008); See [5]zbMATHGoogle Scholar
  10. 10.
    Cohen, G.D., Wolfmann, J. (eds.): Coding Theory 1988. LNCS, vol. 388. Springer, Heidelberg (1989)zbMATHGoogle Scholar
  11. 11.
    Gilbert, E.N., MacWilliams, F.J., Sloane, N.J.A.: Codes which detect deception. Bell System Technical Journal 53, 405–424 (1974), ISSN 0005–8580. MR 55:5306, http://cr.yp.to/bib/entries.html#1974/gilbert. Citations in this document: §1
  12. 12.
    Goldwasser, S. (ed.): 35th annual IEEE symposium on the foundations of computer science. Proceedings of the IEEE symposium held in Santa Fe, NM, November 20-22. IEEE, Los Alamitos (1994), ISBN 0-8186-6580-7. MR 98h:68008. See [21]Google Scholar
  13. 13.
    Grover, L.K.: A fast quantum mechanical algorithm for database search. In: [1], pp. 212–219 (1996); MR 1427516. Citations in this document: §1Google Scholar
  14. 14.
    Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Physical Review Letters 79, 325–328 (1997); Citations in this document: §1Google Scholar
  15. 15.
    Günther, C.G. (ed.): EUROCRYPT 1988. LNCS, vol. 330. Springer, Heidelberg (1988), ISBN 3–540–50251–3. MR 90a:94002. See [17]zbMATHGoogle Scholar
  16. 16.
    Hallgren, S., Vollmer, U.: Quantum computing. In: [4], pp. 15–34 (2009); Citations in this document: §1Google Scholar
  17. 17.
    Lee, P.J., Brickell, E.F.: An observation on the security of McEliece’s public-key cryptosystem. In: [15], pp. 275–280 (1988); Citations in this document: §3Google Scholar
  18. 18.
    Lucchesi, C.L., Moura, A.V. (eds.): LATIN 1998. LNCS, vol. 1380. Springer, Heidelberg (1998), ISBN 3-540-64275-7. MR 99d:68007. See [8]zbMATHGoogle Scholar
  19. 19.
    McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. JPL DSN Progress Report, 114–116 (1978), http://ipnpr.jpl.nasa.gov/progress_report2/42-44/44N.PDF; Citations in this document: §1
  20. 20.
    Overbeck, R., Sendrier, N.: Code-based cryptography. In: [4], pp. 95–145 (2009); Citations in this document: §1, §1, §2, §3, §3Google Scholar
  21. 21.
    Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: [12], pp. 124–134 (1994), see also newer version [22]. MR 1489242. Citations in this document: §1Google Scholar
  22. 22.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing 26, 1484–1509 (1997), see also older version [21]. MR 98i:11108Google Scholar
  23. 23.
    Stern, J.: A method for finding codewords of small weight. In: [10], pp. 106–113 (1989); Citations in this document: §2, §3Google Scholar
  24. 24.
    Zalka, C.: Fast versions of Shor’s quantum factoring algorithm (1998), http://arxiv.org/abs/quant-ph/9806084; Citations in this document: §1

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Daniel J. Bernstein
    • 1
  1. 1.Department of Computer Science (MC 152)The University of Illinois at ChicagoChicago

Personalised recommendations