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Solving Structured Polynomial Systems and Applications to Cryptology

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Computer Algebra in Scientific Computing (CASC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5743))

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Abstract

Cryptography is a collection of mathematical techniques used to secure the transmission and storage of information. A fundamental problem in cryptography is to evaluate the security of cryptosystems against the most powerful techniques. To this end, several general methods have been proposed: linear cryptanalysis, differential cryptanalysis, ... Extensively used cryptographic standards - such as AES [1] - are all resistant against linear and differential attacks. In this talk, we will describe another general method - Algebraic Cryptanalysis - which can be used to evaluate the security of such cryptosystems.

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References

  1. Daemen, J., Rijmen, V.: The Design of Rijndael: The Wide Trail Strategy. Springer, Heidelberg (2001)

    MATH  Google Scholar 

  2. Buchberger, B.: An Algorithm for Finding the Basis Elements in the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal (German), PhD Thesis, Univ of Innsbruck, Math. Institute, Austria, English Translation: J. of Symbolic Computation, Special Issue on Logic, Math and Comp Science: Interactions 41(3-4), 475-511 (1965)

    Google Scholar 

  3. Bardet, M., Faugère, J.-C., Salvy, B., Yang, B.-Y.: Asymptotic Behaviour of the Degree of Regularity of Semi-Regular Polynomial Systems. In: Proc. of MEGA 2005, Eighth International Symposium on Effective Methods in Algebraic Geometry (2005)

    Google Scholar 

  4. Garey, M.R., Johnson, D.B.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)

    MATH  Google Scholar 

  5. Courtois, N.: Efficient Zero-knowledge Authentication Based on a Linear Algebra Problem MinRank. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, p. 402. Springer, Heidelberg (2001)

    Chapter  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. Faugère, J.-C., Levy-dit-Vehel, F., Perret, L.: Cryptanalysis of MinRank. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 280–296. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Faugère, J.-C.: A New Efficient Algorithm for Computing Gröbner Basis without Reduction to Zero: F5. In: Proceedings of ISSAC, July 2002, pp. 75–83. ACM press, New York (2002)

    Google Scholar 

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Faugère, JC. (2009). Solving Structured Polynomial Systems and Applications to Cryptology. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_7

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  • DOI: https://doi.org/10.1007/978-3-642-04103-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04102-0

  • Online ISBN: 978-3-642-04103-7

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