描述Rijndael的一个新的方程组
A New System of Multivariate Quadratic Equations for Rijndael
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摘要: 由于Rijndael的S盒的代数表达式是逆函数合成GF(28)上一个q-多项式，该文合理假设S盒的变量并通过讨论各变量之间的关系，把Rijndael用GF(28)上一个多变量二次方程组来表示，使得Rijndael的密钥恢复等同于求解这个方程组.该方程组较Murphy-Robshaw方程组更简单，用XSL技术求解复杂度更低。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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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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