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Algebraic Cryptanalysis of SMS4: Gröbner Basis Attack and SAT Attack Compared

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Information, Security and Cryptology – ICISC 2009 (ICISC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5984))

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Abstract

The SMS4 block cipher is part of the Chinese WAPI wireless standard. This paper describes the specification and offers a specification for a toy version called simplified SMS4 (S-SMS4). We explore algebraic attacks on SMS4 and S-SMS4 using Gröbner basis attacks on equation systems over GF(2) and GF(28), as well as attacks using a SAT solver derived from the GF(2) model. A comparison of SAT and Gröbner basis attacks is provided.

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References

  1. 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)

    Chapter  Google Scholar 

  2. Courtois, N., Bard, G.V.: Algebraic cryptanalysis of the data encryption standard. In: Galbraith, S.D. (ed.) Cryptography and Coding 2007. LNCS, vol. 4887, pp. 152–169. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Lu, J.: Attacking reduced-round versions of the sms4 block cipher in the chinese wapi standard. In: Qing, S., Imai, H., Wang, G. (eds.) ICICS 2007. LNCS, vol. 4861, pp. 306–318. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Liu, F., Ji, W., Hu, L., Ding, J., Lv, S., Pyshkin, A., Weinmann, R.P.: Analysis of the sms4 block cipher. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds.) ACISP 2007. LNCS, vol. 4586, pp. 158–170. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  5. Ji, W., Hu, L.: New description of sms4 by an embedding over gf(28). In: Srinathan, K., Rangan, C.P., Yung, M. (eds.) INDOCRYPT 2007. LNCS, vol. 4859, pp. 238–251. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Ji, W., Hu, L., Ou, H.: Algebraic attack to sms4 and the comparison with aes. In: International Symposium on Information Assurance and Security, vol. 1, pp. 662–665 (2009)

    Google Scholar 

  7. Bosma, W., Cannon, J.J., Playoust, C.: The magma algebra system i: The user language. J. Symb. Comput. 24(3/4), 235–265 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Diffie, W., Ledin, G. (translators): Sms4 encryption algorithm for wireless networks. Cryptology ePrint Archive, Report 2008/329 (2008), http://eprint.iacr.org/

  9. Bard, G.V., Courtois, N.T., Jefferson., C.: Efficient methods for conversion and solution of sparse systems of low-degree multivariate polynomials over gf(2) via sat-solvers. Cryptology ePrint Archive, Report 2007/024 (2007), http://eprint.iacr.org/

  10. Cid, C., Leurent, G.: An analysis of the xsl algorithm. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 333–352. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Yang, B.Y., Chen, J.M., Courtois, N.: On asymptotic security estimates in xl and gröbner bases-related algebraic cryptanalysis. In: López, J., Qing, S., Okamoto, E. (eds.) ICICS 2004. LNCS, vol. 3269, pp. 401–413. Springer, Heidelberg (2004)

    Google Scholar 

  12. Ars, G., Faugère, J.C., Imai, H., Kawazoe, M., Sugita, M.: Comparison between XL and gröbner basis algorithms. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 354–371. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. The University of North Carolina at Chapel Hill, Chapel Hill, NC 27514

    Jeremy Erickson

  2. The University of Cincinnati, Cincinnati, OH 45221

    Jintai Ding

  3. South China University of Technology, Guangzhou, China

    Jintai Ding

  4. Northern Kentucky University, Highland Heights, KY 41099

    Chris Christensen

Authors
  1. Jeremy Erickson
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  2. Jintai Ding
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  3. Chris Christensen
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Editor information

Editors and Affiliations

  1. CIST (Center for Information Security Technologies), Korea University Anam Dong, Sungbuk Gu, Seoul, Korea

    Donghoon Lee

  2. Center for Information Security Technologies(CIST), Korea University, Seoul, Korea

    Seokhie Hong

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Erickson, J., Ding, J., Christensen, C. (2010). Algebraic Cryptanalysis of SMS4: Gröbner Basis Attack and SAT Attack Compared. In: Lee, D., Hong, S. (eds) Information, Security and Cryptology – ICISC 2009. ICISC 2009. Lecture Notes in Computer Science, vol 5984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14423-3_6

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  • DOI: https://doi.org/10.1007/978-3-642-14423-3_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14422-6

  • Online ISBN: 978-3-642-14423-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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