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Lower Bounds for Key Length of k-wise Almost Independent Permutations and Certain Symmetric-Key Encryption Schemes

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Advances in Information and Computer Security (IWSEC 2016)

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Abstract

The k-wise almost independent permutations are one of important primitives for cryptographic schemes and combinatorial constructions. Kaplan, Naor, and Reingold showed a general construction for k-wise almost independent permutations, and Kawachi, Takebe, and Tanaka provided symmetric-key encryption schemes that achieve multi-message approximate secrecy and multi-ciphertext approximate non-malleability based on Kaplan et al.’s construction. In this paper, we show lower bounds of key length for these constructions. In particular, they are nearly optimal for k-wise almost independent permutations and multi-message approximate secrecy if the approximation parameter is a constant.

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References

  1. Naor, M., Reingold, O.: On the construction of pseudorandom permutations: Luby-Rackoff revisited. J. Cryptol. 12(1), 29–66 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hoory, S., Magen, A., Myers, S., Rackoff, C.: Simple permutations mix well. Theor. Comput. Sci. 348(2–3), 251–261 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cameron, P.J.: Permutation groups. In: Graham, R.L., Grötschel, M., Lovász, L. (eds.) Handbook of Combinatorics, vol. 1, pp. 611–645. MIT Press, Cambridge (1995)

    Google Scholar 

  4. Kuperberg, G., Lovett, S., Peled, R.: Probabilistic existence of rigid combinatorial structures. In: Karloff, H.J., Pitassi, T. (eds.) STOC, pp. 1091–1106. ACM (2012)

    Google Scholar 

  5. Luby, M., Rackoff, C.: How to construct pseudorandom permutations from pseudorandom functions. SIAM J. Comput. 17(2), 373–386 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  6. Brodsky, A., Hoory, S.: Simple permutations mix even better. Random Struct. Algorithms 32(3), 274–289 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kaplan, E., Naor, M., Reingold, O.: Derandomized constructions of k-wise (almost) independent permutations. Algorithmica 55(1), 113–133 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kawachi, A., Takebe, H., Tanaka, K.: Symmetric-key encryption scheme with multi-ciphertext non-malleability. In: Hanaoka, G., Yamauchi, T. (eds.) IWSEC 2012. LNCS, vol. 7631, pp. 123–137. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  9. Dodis, Y.: Shannon impossibility. In: Smith, A. (ed.) ICITS 2012. LNCS, vol. 7412, pp. 100–110. Springer, Heidelberg (2012). Revisited

    Chapter  Google Scholar 

  10. Shannon, C.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656–715 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kawachi, A., Portmann, C., Tanaka, K.: Characterization of the relations between information-theoretic non-malleability, secrecy, and authenticity. In: Fehr, S. (ed.) ICITS 2011. LNCS, vol. 6673, pp. 6–24. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. Hanaoka, G.: Some information theoretic arguments for encryption: non-malleability and chosen-ciphertext security (invited talk). In: Safavi-Naini, R. (ed.) ICITS 2008. LNCS, vol. 5155, pp. 223–231. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Bierbrauer, J., Johansson, T., Kabatianskii, G.A., Smeets, B.J.M.: On families of hash functions via geometric codes and concatenation. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 331–342. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  14. Hanaoka, G., Shikata, J., Hanaoka, Y., Imai, H.: Unconditionally secure anonymous encryption and group authentication. Comput. J. 49(3), 310–321 (2006)

    Article  MATH  Google Scholar 

  15. McAven, L., Safavi-Naini, R., Yung, M.: Unconditionally secure encryption under strong attacks. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol. 3108, pp. 427–439. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Acknowledgements

This work is partially supported by the JSPS Grant-in-Aid for Scientific Research (A) No.16H01705 and the ELC project (Grant-in-Aid for Scientific Research on Innovative Areas MEXT Japan, KAKENHI No. 24106009).

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Authors and Affiliations

  1. Tokushima University, Tokushima, Japan

    Akinori Kawachi

  2. Kanazawa University, Kanazawa, Japan

    Hirotoshi Takebe

  3. Tokyo Institute of Technology and JST CREST, Tokyo, Japan

    Keisuke Tanaka

Authors
  1. Akinori Kawachi
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  2. Hirotoshi Takebe
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  3. Keisuke Tanaka
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Corresponding author

Correspondence to Akinori Kawachi .

Editor information

Editors and Affiliations

  1. Japan Broadcasting Corporation, Tokyo, Japan

    Kazuto Ogawa

  2. Yokohama National University, Yokohama, Japan

    Katsunari Yoshioka

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Kawachi, A., Takebe, H., Tanaka, K. (2016). Lower Bounds for Key Length of k-wise Almost Independent Permutations and Certain Symmetric-Key Encryption Schemes. In: Ogawa, K., Yoshioka, K. (eds) Advances in Information and Computer Security. IWSEC 2016. Lecture Notes in Computer Science(), vol 9836. Springer, Cham. https://doi.org/10.1007/978-3-319-44524-3_12

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  • DOI: https://doi.org/10.1007/978-3-319-44524-3_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44523-6

  • Online ISBN: 978-3-319-44524-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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