Code Based Cryptography and Steganography

  • Pascal Véron
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8080)

Abstract

For a long time, coding theory was only concerned by message integrity (how to protect against errors a message sent via some noisely channel). Nowadays, coding theory plays an important role in the area of cryptography and steganography. The aim of this paper is to show how algebraic coding theory offers ways to define secure cryptographic primitives and efficient steganographic schemes.

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References

  1. 1.
    Adams, C., Meijer, H.: Security-related comments regarding McEliece’s public-key cryptosystem. IEEE Trans. Inform. Theory 35, 454–455 (1989)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aguilar Melchor, C., Cayrel, P.-L., Gaborit, P.: A new efficient threshold ring signature scheme based on coding theory. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 1–16. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Ashikmin, A.E., Barg, A.: Minimal vectors in linear codes. IEEE Transaction on Information Theory 44(5) (1998)Google Scholar
  4. 4.
    Augot, D., Barbier, M., Couvreur, A.: List-decoding of binary goppa codes up to the binary johnson bound. In: IEEE, ITW 2011, pp. 229–233 (October 2011)Google Scholar
  5. 5.
    Augot, D., Finiasz, M., Gaborit, P., Manuel, S., Sendrier, N.: Sha-3 proposal: Fsb. Submission to NIST (2008)Google Scholar
  6. 6.
    Augot, D., Finiasz, M., Sendrier, N.: A family of fast syndrome based cryptographic hash functions. In: Dawson, E., Vaudenay, S. (eds.) Mycrypt 2005. LNCS, vol. 3715, pp. 64–83. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Baldi, M., Chiaraluce, F.: Cryptanalysis of a new instance of McEliece cryptosystem based on qc-ldpc codes. In: IEEE International Symposium on Information Theory, ISIT 2007, pp. 2591–2595 (June 2007)Google Scholar
  8. 8.
    Barg, S.: Some new NP-complete coding problems. Probl. Peredachi Inf. 30, 23–28 (1994)MathSciNetGoogle Scholar
  9. 9.
    Barreto, P.S.L.M., Cayrel, P.-L., Misoczki, R., Niebuhr, R.: Quasi-dyadic CFS signatures. In: Lai, X., Yung, M., Lin, D. (eds.) Inscrypt 2010. LNCS, vol. 6584, pp. 336–349. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Becker, A., Joux, A., May, A., Meurer, A.: Decoding random binary linear codes in 2n/20: How 1 + 1 = 0 improves information set decoding. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 520–536. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Bellare, M., Namprempre, C., Neven, G.: Security proofs for identity-based identification and signature schemes. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 268–286. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Berger, T.P., Cayrel, P.-L., Gaborit, P., Otmani, A.: Reducing key length of the McEliece cryptosystem. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 77–97. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Berlekamp, E.R., McEliece, R.J., van Tilborg, H.C.A.: On the intractability of certain coding problems. IEEE Transactions on Information Theory 24(3), 384–386 (1978)MATHCrossRefGoogle Scholar
  14. 14.
    Bernstein, D.J., Lange, T., Peters, C., Schwabe, P.: Really fast syndrome-based hashing. In: Nitaj, A., Pointcheval, D. (eds.) AFRICACRYPT 2011. LNCS, vol. 6737, pp. 134–152. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Bernstein, D.J.: Grover vs. McEliece (2008), http://cr.yp.to/papers.html
  16. 16.
    Bernstein, D.J.: List decoding for binary goppa codes (2008), http://cr.yp.to/codes/goppalist-20081107.pdf
  17. 17.
    Bernstein, D.J., Lange, T., Peters, C.: Attacking and defending the McEliece cryptosystem. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 31–46. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Bernstein, D.J., Lange, T., Peters, C.: Smaller decoding exponents: Ball-collision decoding. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 743–760. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  19. 19.
    Bernstein, D.J., Lange, T., Peters, C.: Smaller decoding exponents: Ball-collision decoding. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 743–760. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  20. 20.
    Bernstein, D.J., Lange, T., Peters, C.: Wild McEliece. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 143–158. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  21. 21.
    Beuchat, J.L., Sendrier, N., Tisserand, A., Villard, G.: Fpga implementation of a recently published signature scheme. Tech. Rep. 5158, Inria (March 2004)Google Scholar
  22. 22.
    Biswas, B., Sendrier, N.: McEliece cryptosystem implementation: Theory and practice. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 47–62. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  23. 23.
    Brickell, E., Odlyzko, A.: Cryptanalysis: A survey of recent results. In: Comtemporary Cryptology - the Science of Information Integrity, pp. 501–540 (1992)Google Scholar
  24. 24.
    Canteaut, A.: Attaques de cryptosystèmes à mots de poids faible et construction de fonctions t-résilientes. PhD thesis, Université Paris VI (1996)Google Scholar
  25. 25.
    Canteaut, A., Chabaud, F.: A new algorithm for finding minimum-weight words in a linear code: Application to McEliece’s cryptosystem and to narrow-sense bch codes of length 511. IEEE Transactions on Information Theory 44(1), 367–378 (1998)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Canteaut, A., Sendrier, N.: Cryptanalysis of the original McEliece cryptosystem. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 187–199. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  27. 27.
    Cayrel, P.-L., Dusart, P.: McEliece/niederreiter pkc: sensitivity to fault injection. In: International Workshop on Future Engineering, Applications and Services, FEAS (2010)Google Scholar
  28. 28.
    Cayrel, P.-L., El Yousfi Alaoui, S.M., Hoffmann, G., Véron, P.: An improved threshold ring signature scheme based on error correcting codes. In: Özbudak, F., Rodríguez-Henríquez, F. (eds.) WAIFI 2012. LNCS, vol. 7369, pp. 45–63. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  29. 29.
    Cayrel, P.-L., Gaborit, P., Girault, M.: Identity-based identification and signature schemes using correcting codes. In: Augot, D., Sendrier, N., Tillich, J.P. (eds.) WCC 2007. INRIA (2007)Google Scholar
  30. 30.
    Cayrel, P.-L., Véron, P., El Yousfi Alaoui, S.M.: A zero-knowledge identification scheme based on the q-ary syndrome decoding problem. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 171–186. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  31. 31.
    Chabanne, H., Courteau, B.: Application de la méthode de décodage itérative d’omura à la cryptanalyse du système de mc eliece. Rapport de Recherche 122, Université de Sherbrooke (October 1993)Google Scholar
  32. 32.
    Courtois, N.T., Finiasz, M., Sendrier, N.: How to achieve a McEliece-based digital signature scheme. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 157–174. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  33. 33.
    Crandall, R.: Some notes on steganography (1998), Posted on the steganography mailing listGoogle Scholar
  34. 34.
    Dallot, L.: Towards a concrete security proof of courtois, finiasz and sendrier signature scheme. In: Lucks, S., Sadeghi, A.-R., Wolf, C. (eds.) WEWoRC 2007. LNCS, vol. 4945, pp. 65–77. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  35. 35.
    Dallot, L., Vergnaud, D.: Provably secure code-based threshold ring signatures. In: Parker, M.G. (ed.) Cryptography and Coding 2009. LNCS, vol. 5921, pp. 222–235. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  36. 36.
    Damgård, I.B.: A design principle for hash functions. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 416–427. Springer, Heidelberg (1990)Google Scholar
  37. 37.
    Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Transactions on Information Theory IT-22(6), 644–654 (1976)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Dowsley, R., Müller-Quade, J., Nascimento, A.C.A.: A CCA2 secure public key encryption scheme based on the McEliece assumptions in the standard model. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 240–251. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  39. 39.
    Eisenbarth, T., Güneysu, T., Heyse, S., Paar, C.: Microeliece: Mceliece for embedded devices. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 49–64. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  40. 40.
    El Yousfi Alaoui, S.M., Dagdelen, Ö., Véron, P., Galindo, D., Cayrel, P.-L.: Extended Security Arguments for Signature Schemes. In: Mitrokotsa, A., Vaudenay, S. (eds.) AFRICACRYPT 2012. LNCS, vol. 7374, pp. 19–34. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  41. 41.
    Faugère, J.C., Otmani, A., Perret, L., Tillich, J.P.: A distinguisher for high rate McEliece cryptosystems. IACR Eprint archive, 2010/331 (2010)Google Scholar
  42. 42.
    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
  43. 43.
    Finiasz, M.: Nouvelles constructions utilisant des codes correcteurs d’erreurs en cryptographie à clé publique. PhD thesis, Ecole Polytechnique (2004)Google Scholar
  44. 44.
    Finiasz, M.: Parallel-CFS: Strengthening the CFS McEliece-based signature scheme. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 159–170. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  45. 45.
    Finiasz, M., Gaborit, P., Sendrier, N.: Improved fast syndrome based cryptographic hash function. In: ECRYPT Hash Workshop 2007 (2007)Google Scholar
  46. 46.
    Finiasz, M., Sendrier, N.: Security bounds for the design of code-based cryptosystems. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 88–105. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  47. 47.
    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
  48. 48.
    Fouque, P.-A., Leurent, G.: Cryptanalysis of a hash function based on quasi-cyclic codes. In: Malkin, T. (ed.) CT-RSA 2008. LNCS, vol. 4964, pp. 19–35. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  49. 49.
    Fridrich, J.: Asymptotic behavior of the ZZW embedding construction. IEEE Transactions on Information Forensics and Security 4(1), 151–153 (2009)CrossRefGoogle Scholar
  50. 50.
    Fridrich, J., Goljan, M., Lisonek, P., Soukal, D.: Writing on wet paper. IEEE Trans. on Signal Processing 53(10), 3923–3935 (2005)MathSciNetCrossRefGoogle Scholar
  51. 51.
    Fridrich, J.: Steganography in Digital Media: Principles, Algorithms, and Applications, 1st edn. Cambridge University Press, New York (2009)Google Scholar
  52. 52.
    Gaborit, P.: Shorter keys for code based cryptography. In: Proceeedings of WCC 2005, pp. 81–90 (2005)Google Scholar
  53. 53.
    Gaborit, P., Girault, M.: Lightweight code-based identification and signature. In: Proceeedings of ISIT 2007 (2007)Google Scholar
  54. 54.
    Gaborit, P., Laudauroux, C., Sendrier, N.: Synd: a fast code-based stream cipher with a security reduction. In: Proceeedings of ISIT 2007 (2007)Google Scholar
  55. 55.
    Gaborit, P., Zémor, G.: Asymptotic improvement of the gilbert-varshamov bound for linear codes. In: Proceeedings of ISIT 2006, pp. 287–291 (2006)Google Scholar
  56. 56.
    Garey, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)MATHGoogle Scholar
  57. 57.
    Gauthier Umana, V., Leander, G.: Practical key recovery attacks on two McEliece variants. IACR Eprint archive, 2009/509 (2009)Google Scholar
  58. 58.
    Gibson, J.K.: Equivalent goppa codes and trapdoors to McEliece’s public key cryptosystem. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 517–521. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  59. 59.
    Girault, M.: A (non-practical) three-pass identification protocol using coding theory. In: Seberry, J., Pieprzyk, J.P. (eds.) AUSCRYPT 1990. LNCS, vol. 453, pp. 265–272. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  60. 60.
    Girault, M., Stern, J.: On the length of cryptographic hash-values used in identification schemes. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 202–215. Springer, Heidelberg (1994)Google Scholar
  61. 61.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM, Journal of Computing 18, 186–208 (1989)MathSciNetMATHCrossRefGoogle Scholar
  62. 62.
    Goppa, V.D.: A new class of linear error correcting codes. Probl. Pered. Inform., 24–30 (1970)Google Scholar
  63. 63.
    Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, STOC 1996, pp. 212–219. ACM, New York (1996)CrossRefGoogle Scholar
  64. 64.
    Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)CrossRefGoogle Scholar
  65. 65.
    Harari, S.: A new authentication algorithm. In: Wolfmann, J., Cohen, G. (eds.) Coding Theory 1988. LNCS, vol. 388, pp. 91–105. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  66. 66.
    Heyse, S., Moradi, A., Paar, C.: Practical power analysis attacks on software implementations of McEliece. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 108–125. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  67. 67.
    Housley, R.: Using advanced encryption standard (aes) counter mode with ipsec encapsulating security payload (esp). RFC 3686, Network Working Group (January 2004)Google Scholar
  68. 68.
    Massey, J.L.: Minimal codewords and secret sharing. In: 6th Joint Swedish-Russian Workshop on Information Theory, pp. 276–279 (1993)Google Scholar
  69. 69.
    Johansson, T., Jönsson, F.: On the complexity of some cryptographic problems based on the general decoding problem. IEEE Transactions on Information Theory 48(10), 2669–2678 (2002)MATHCrossRefGoogle Scholar
  70. 70.
    Lee, P.J., Brickell, E.F.: An observation on the security of McEliece’s public-key cryptosystem. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 275–280. Springer, Heidelberg (1988)CrossRefGoogle Scholar
  71. 71.
    Leon, J.S.: A probabilistic algorithm for computing minimum weights of large error-correcting codes. IEEE Transactions on Information Theory 34(5), 1354–1359 (1988)MathSciNetCrossRefGoogle Scholar
  72. 72.
    Li, Y.X., Deng, R.H., Wang, X.M.: On the equivalence of McEliece’s and niederreiter’s public-key cryptosystems. IEEE Transactions on Information Theory 40(1), 271–273 (1994)MathSciNetMATHCrossRefGoogle Scholar
  73. 73.
    Loidreau, P., Sendrier, N.: Weak keys in the McEliece public-key cryptosystem. IEEE Transactions on Information Theory 47(3), 1207–1211 (2001)MathSciNetMATHCrossRefGoogle Scholar
  74. 74.
    MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Code. North-Holland (1977)Google Scholar
  75. 75.
    May, A., Meurer, A., Thomae, E.: Decoding random linear codes in \(\tilde{\mathcal{O}}(2^{0.054n})\). In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 107–124. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  76. 76.
    McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. JPL DSN Progress Report, pp. 114–116 (1978)Google Scholar
  77. 77.
    McEliece, R.J., Sarwate, D.V.: On sharing secrets and Reed-Solomon codes. Communications of the ACM 24(9), 583–584 (1981)MathSciNetCrossRefGoogle Scholar
  78. 78.
    Merkle, R., Hellman, M.: Hiding information and signatures in trapdoor knapsacks. IEEE Trans. Inform. Theory 24, 525–530 (1978)CrossRefGoogle Scholar
  79. 79.
    Misoczki, R., Barreto, P.S.L.M.: Compact McEliece keys from goppa codes. In: Jacobson Jr., M.J., Rijmen, V., Safavi-Naini, R. (eds.) SAC 2009. LNCS, vol. 5867, pp. 376–392. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  80. 80.
    Molter, H., Stöttinger, M., Shoufan, A., Strenzke, F.: A simple power analysis attack on a McEliece cryptoprocessor. Journal of Cryptographic Engineering 1, 29–36 (2011)CrossRefGoogle Scholar
  81. 81.
    Munuera, C., Barbier, M.: Wet paper codes and the dual distance in steganography. Advances in Mathematics of Communications 6(3), 237–285 (2012)MathSciNetCrossRefGoogle Scholar
  82. 82.
    Munuera, C.: Steganography from a coding theory point of view. Series on Coding Theory and Cryptology, vol. 8. World Scientific Publishing Co. Pte. Ltd. (2013)Google Scholar
  83. 83.
    Niederreiter, H.: Knapsack-type cryptosystems and algebraic coding theory. Problems Control Inform. Theory 15(2), 159–166 (1986)MathSciNetMATHGoogle Scholar
  84. 84.
    Nojima, R., Imai, H., Kobara, K., Morozov, K.: Semantic security for the McEliece cryptosystem without random oracles. Designs, Codes and Cryptography 49, 289–305 (2008), doi:10.1007/s10623-008-9175-9MathSciNetMATHCrossRefGoogle Scholar
  85. 85.
    Otmani, A., Tillich, J.P., Dallot, L.: Cryptanalysis of two McEliece cryptosystems based on quasi-cyclic codes. Mathematics in Computer Science 3, 129–140 (2010)MathSciNetMATHCrossRefGoogle Scholar
  86. 86.
    Peters, C.: Information-set decoding for linear codes over F q. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 81–94. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  87. 87.
    Prange, E.: The use of information sets in decoding cyclic codes. IRE Trans. IT-8, 85–89 (1962)MathSciNetGoogle Scholar
  88. 88.
    Quisquater, J.-J., Guillou, L.C., Berson, T.: How to explain zero-knowledge protocols to your children. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 628–631. Springer, Heidelberg (1990)Google Scholar
  89. 89.
    Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 26(1), 96–99 (1983)CrossRefGoogle Scholar
  90. 90.
    Saarinen, M.-J.O.: Linearization attacks against syndrome based hashes. In: Srinathan, K., Rangan, C.P., Yung, M. (eds.) INDOCRYPT 2007. LNCS, vol. 4859, pp. 1–9. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  91. 91.
    Sendrier, N.: Efficient generation of binary words of given weight. In: Boyd, C. (ed.) Cryptography and Coding 1995. LNCS, vol. 1025, pp. 184–187. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  92. 92.
    Sendrier, N.: On the structure of a randomly permuted concateneted code. In: EUROCODE 1994, 169–173. Inria (1994)Google Scholar
  93. 93.
    Sendrier, N.: Finding the permutation between equivalent linear codes: The support splitting algorithm. IEEE Transactions on Information Theory 46(4), 1193–1203 (2000)MathSciNetMATHCrossRefGoogle Scholar
  94. 94.
    Shamir, A.: How to Share a Secret. Communications of the ACM 22(11), 612–613 (1979)MathSciNetMATHCrossRefGoogle Scholar
  95. 95.
    Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  96. 96.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 20–22 (1994)Google Scholar
  97. 97.
    Shoufan, A., Strenzke, F., Molter, H.G., Stöttinger, M.: A Timing Attack against Patterson Algorithm in the McEliece PKC. In: Lee, D., Hong, S. (eds.) ICISC 2009. LNCS, vol. 5984, pp. 161–175. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  98. 98.
    Sidelnikov, V., Shestakov, S.: On cryptosystems based on generalized reed-solomon codes. Diskretnaya Math. 4, 57–63 (1992)MathSciNetGoogle Scholar
  99. 99.
    Stern, J.: A method for finding codewords of small weight. In: Wolfmann, J., Cohen, G. (eds.) Coding Theory 1988. LNCS, vol. 388, pp. 106–113. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  100. 100.
    Stern, J.: A new identification scheme based on syndrome decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 13–21. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  101. 101.
    Strenzke, F.: A smart card implementation of the McEliece PKC. In: Samarati, P., Tunstall, M., Posegga, J., Markantonakis, K., Sauveron, D. (eds.) WISTP 2010. LNCS, vol. 6033, pp. 47–59. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  102. 102.
    Strenzke, F., Tews, E., Molter, H.G., Overbeck, R., Shoufan, A.: Side channels in the McEliece PKC. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 216–229. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  103. 103.
    Sugiyama, Y., Kasahara, M., Hirasawa, S., Namekawa, T.: Further results on goppa codes and their applications to constructing efficient binary codes. IEEE Transactions on Information Theory 22, 518–526 (1976)MathSciNetMATHCrossRefGoogle Scholar
  104. 104.
    van Tilburg, J.: On the McEliece public-key cryptosystem. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 119–131. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  105. 105.
    Véron, P.: Cryptanalysis of harari’s identification scheme. In: Boyd, C. (ed.) Cryptography and Coding 1995. LNCS, vol. 1025, pp. 264–269. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  106. 106.
    Véron, P.: Improved identification schemes based on error-correcting codes. Appl. Algebra Eng. Commun. Comput. 8(1), 57–69 (1996)CrossRefGoogle Scholar
  107. 107.
    Véron, P.: Public key cryptography and coding theory. In: Woungang, I., Misra, S., Misra, S. (eds.) Selected Topics in Information and Coding Theory, vol. 7. World Scientific Publications (March 2010)Google Scholar
  108. 108.
    Wagner, D.: A generalized birthday problem. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 288–304. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  109. 109.
    Westfeld, A.: F5-A steganographic algorithm. In: Moskowitz, I.S. (ed.) IH 2001. LNCS, vol. 2137, pp. 289–302. Springer, Heidelberg (2001)CrossRefGoogle Scholar

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Authors and Affiliations

  • Pascal Véron
    • 1
  1. 1.IMATHUniversité du Sud Toulon-VarLa Garde CedexFrance

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