ALGEBRAIC CRYPTANALYSIS OF AES USING GRÖBNER BASIS

Abstract: Algebraic cryptanalysis is a potentially powerful attack on symmetric key block ciphers. This paper presents Algebraic cryptanalysis on Rijndael AES,based on its rich algebraic structure.The paper beginsby defining the mathematical model of AES then constructing a system of mostly nonlinear polynomial equations representing S-Box. Then applying a powerful algebraic tool; Gröbner basis; to overcome the nonlinearity features of S-Box. Finally, it shows that howapplying Gröbnerbasis of AES constructs a spare matrix which makes the system easy to be solved. Moreover, we have proved the "Resistance of Algebraic Attack" RAA value (G) has been reduced.

Keywords: Algebraic cryptanalysis, multivariate quadratic polynomial equation system, S-box, Gröbner bases, Rijndael AES, RAA.