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Towards Algebraic Cryptanalysis of HFE Challenge 2

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 200))

Abstract

In this paper, we present an experimental analysis of HFE Challenge 2 (144 bit) type systems. We generate scaled versions of the full challenge fixing and guessing some unknowns. We use the MXL3 algorithm, an efficient algorithm for computing Gröbner basis, to solve these scaled versions. We review the MXL3 strategy and introduce our experimental results.

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References

  1. Bard, G.V.: Accelerating cryptanalysis with the Method of Four Russians. Report 251, Cryptology ePrint Archive (2006)

    Google Scholar 

  2. 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)

    Chapter  Google Scholar 

  3. Courtois, N.T., 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 

  4. Courtois, N.T., Pieprzyk, J.: Cryptanalysis of Block Ciphers with Overdefined Systems of Equations. Technical Report 2002/044, Cryptology ePrint Archive (2002)

    Google Scholar 

  5. Ding, J., Buchmann, J., Mohamed, M.S.E., Moahmed, W.S.A., Weinmann, R.-P.: MutantXL. In: Proceedings of the 1st International Conference on Symbolic Computation and Cryptography (SCC 2008), pp. 16–22. LMIB, Beijing (2008)

    Google Scholar 

  6. Faugère, J.-C., Joux, A.: Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44–60. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Mohamed, M.S.E., Cabarcas, D., Ding, J., Buchmann, J., Bulygin, S.: MXL3: An efficient algorithm for computing gröbner bases of zero-dimensional ideals. In: Lee, D., Hong, S. (eds.) ICISC 2009. LNCS, vol. 5984, pp. 87–100. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Mohamed, M.S.E., Mohamed, W.S.A.E., Ding, J., Buchmann, J.: MXL2: Solving polynomial equations over GF(2) using an improved mutant strategy. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 203–215. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Patarin, J.: Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33–48. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  10. Penzhorn, W.: Algebraic attacks on cipher systems. In: Proceedings of 7th AFRICON Conference in Africa (AFRICON), vol. 2, pp. 969–974. IEEE, Los Alamitos (2004)

    Google Scholar 

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© 2011 Springer-Verlag Berlin Heidelberg

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Mohamed, M.S.E., Ding, J., Buchmann, J. (2011). Towards Algebraic Cryptanalysis of HFE Challenge 2. In: Kim, Th., Adeli, H., Robles, R.J., Balitanas, M. (eds) Information Security and Assurance. ISA 2011. Communications in Computer and Information Science, vol 200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23141-4_12

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  • DOI: https://doi.org/10.1007/978-3-642-23141-4_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23140-7

  • Online ISBN: 978-3-642-23141-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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