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When Stream Cipher Analysis Meets Public-Key Cryptography

  • Matthieu Finiasz
  • Serge Vaudenay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4356)

Abstract

Inspired by fast correlation attacks on stream ciphers, we present a stream cipher-like construction for a public-key cryptosystem whose security relies on two problems: finding a low-weight multiple of a given polynomial and a Hidden Correlation problem. We obtain a weakly secure public-key cryptosystem we call TCHo (as for Trapdoor Cipher, Hardware Oriented). Using the Fujisaki-Okamoto construction, we can build an hybrid cryptosystem, TCHo n  − FO, resistant against adaptive chosen ciphertext attacks.

Keywords

Encryption Scheme Random Oracle Stream Cipher Random Oracle Model Iterative Decode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Avoine, G., Oechslin, P.: A scalable and provably secure hash-based RFID protocol. In: PerSec 2005 (2005)Google Scholar
  2. 2.
    Camion, P., Mihaljević, M.J., Imai, H.: Two alerts for design of certain stream ciphers: Trapped LFSR and weak resilient function over GF(q). In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 196–213. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    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)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Canteaut, A., Trabbia, M.: Improved fast correlation attacks using parity check equations of weight 4 and 5. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 573–588. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Chepyshov, V.V., Johansson, T., Smeets, B.: A simple algorithm for fast correlation attacks on stream ciphers. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 181–195. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient algorithms for solving overdefined systems of multivariate polynomial equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392–407. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Courtois, N., Meier, W.: Algebraic attacks on stream ciphers with linear feedback. In: Biham, E. (ed.) Advances in Cryptology – EUROCRPYT 2003. LNCS, vol. 2656, pp. 345–359. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Courtois, N., Pieprzyk, J.: Cryptanalysis of block ciphers with overdefined systems of equations. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 267–287. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Dalai, D.K., Gupta, K.C., Maitra, S.: Results on algebraic immunity for cryptographically significant boolean functions. In: Canteaut, A., Viswanathan, K. (eds.) INDOCRYPT 2004. LNCS, vol. 3348, pp. 92–106. Springer, Heidelberg (2004)Google Scholar
  10. 10.
    Faugère, J.-C.: A new efficient algorithm for computing gröbner bases (F4). Journal of Pure and Applied Algebra 139, 61–88 (1999)CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Faugère, J.-C.: A new efficient algorithm for computing gröbner bases without reduction to zero (F5). In: ISSAC 2002, Lille, France, July 2002, pp. 75–83. ACM, New York (2002)CrossRefGoogle Scholar
  12. 12.
    Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 537–554. Springer, Heidelberg (1999)Google Scholar
  13. 13.
    Johansson, T., Jönsson, F.: Fast correlation attacks based on turbo code techniques. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 181–197. Springer, Heidelberg (1999)Google Scholar
  14. 14.
    Johansson, T., Jönsson, F.: Improved fast correlation attacks on stream ciphers via convolutional codes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 347–362. Springer, Heidelberg (1999)Google Scholar
  15. 15.
    Johansson, T., Jönsson, F.: Fast correlation attacks through reconstruction of linear polynomials. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 300–315. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    Lu, Y.: Applied Stream Ciphers in Mobile Communications. Phd thesis num. 3491, EPFL (2006), http://library.epfl.ch/theses/?nr=3491
  18. 18.
    Lu, Y., Meier, W., Vaudenay, S.: The conditional correlation attack: A practical attack on bluetooth encryption. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 97–117. Springer, Heidelberg (2005)Google Scholar
  19. 19.
    Lu, Y., Vaudenay, S.: Faster correlation attack on bluetooth keystream generator E0. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 407–425. Springer, Heidelberg (2004)Google Scholar
  20. 20.
    Meier, W., Staffelbach, O.: Fast correltaion attacks on stream ciphers. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 301–314. Springer, Heidelberg (1988)Google Scholar
  21. 21.
    Mihaljevic, M.J., Fossorier, M.P.C., Imai, H.: A low-complexity and high-performance algorithm for the fast correlation attack. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 196–212. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  22. 22.
    Molland, H., Mathiassen, J.E., Helleseth, T.: Improved fast correlation attack using low rate codes. In: Paterson, K.G. (ed.) Cryptography and Coding. LNCS, vol. 2898, pp. 67–81. Springer, Heidelberg (2003)Google Scholar
  23. 23.
    Molnar, D., Wagner, D.: Privacy and security in library RFID: issues, practices, and architectures. In: Atluri, V., Pfitzmann, B., McDaniel, P.D. (eds.) CCS 2004, pp. 210–219. ACM Press, New York (2004)CrossRefGoogle Scholar
  24. 24.
    Rivest, R.L, Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM 21(2), 120–126 (1978)CrossRefMathSciNetzbMATHGoogle Scholar
  25. 25.
    Shamir, A.: An efficient identification scheme based on permuted kernels (extended abstract). In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 606–609. Springer, Heidelberg (1990)Google Scholar
  26. 26.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)CrossRefMathSciNetzbMATHGoogle Scholar
  27. 27.
    Shoup, V.: NTL: A library for doing number theory. Available online from http://www.shoup.net/ntl/
  28. 28.
    Siegenthaler, T.: Cryptanalysts representation of nonlinearly filtered ML-sequences. In: Pichler, F. (ed.) EUROCRYPT 1985. LNCS, vol. 219, pp. 103–110. Springer, Heidelberg (1986)CrossRefGoogle Scholar
  29. 29.
    von zur Gathen, J., Gerhard, J.: Modern Computer Algebra, 2nd edn. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  30. 30.
    Wagner, D.: A generalized birthday problem. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 288–304. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Matthieu Finiasz
    • 1
  • Serge Vaudenay
    • 1
  1. 1.EPFL, CH-1015 LausanneSwitzerland

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