A New System of Multivariate Quadratic Equations for Rijndael

Li Na; Chen Wei-hong

Volume 26 Issue 12

Dec. 2004

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Li Na, Chen Wei-hong. A New System of Multivariate Quadratic Equations for Rijndael[J]. Journal of Electronics & Information Technology, 2004, 26(12): 1990-1995.

Citation:

Li Na, Chen Wei-hong. A New System of Multivariate Quadratic Equations for Rijndael[J]. Journal of Electronics & Information Technology, 2004, 26(12): 1990-1995.

Li Na, Chen Wei-hong. A New System of Multivariate Quadratic Equations for Rijndael[J]. Journal of Electronics & Information Technology, 2004, 26(12): 1990-1995.

Citation:

Li Na, Chen Wei-hong. A New System of Multivariate Quadratic Equations for Rijndael[J]. Journal of Electronics & Information Technology, 2004, 26(12): 1990-1995.

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A New System of Multivariate Quadratic Equations for Rijndael

Received Date: 2003-07-25
Rev Recd Date: 2004-01-12
Publish Date: 2004-12-19

Abstract

Abstract

Because the algebraic expression of Rijndael S box is a composition of the converse function with a q-polynomial over GF(28), in this paper the variables of S box are supposed rationally and the relations between these variables are analyzed, then a new system of multivariate quadratic equations over GF(28) are used to describe completely Rijndael, the cryptanalysis of Rijndael can be written as a problem of solving the system of multivariate quadratic equations. This system is simpler than Murphy and Robshaws, and has a lower complexity while applying XSL technique.

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References(1)

References

Daemen J, Rijmen V. AES proposal: Rijndael, AES Round 1 Technical Evaluation CD-1: Documentation. National Institute of Standards and Technology, available from:http:∥www.nist.gov/aes, Aug. 1998.[2]Courtois N, Pieprzyk J. Cryptanalysis of block ciphers with overdefined systems of equations.Advances in Cryptology-ASIACRYPT 2002, Berlin: Springer-Verlag, 2002: 267-287.Murphy S, Robshaw M. Essential algebraic structure within the AES. Advances in Cryptology-CRYPTO 2002, Berlin: Springer-Verlag, 2002: 1-16.[3]Murphy S, Robshaw M. Comments on the security of the AES and the XSL technique, available from: http:∥www.cosic.esat.kuleuven.ac.be, Sep. 2002.

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