The Design of Rijndael
A Simple Algebraic Representation of Rijndael
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Essential Algebraic Structure within the AES
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of Block Ciphers with Overdefined Systems of Equations
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
In How Many Ways Can You Write Rijndael?
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Efficient algorithms for solving overdefined systems of multivariate polynomial equations
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Automatic search of attacks on round-reduced AES and applications
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
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Since being officially selected as the new Advanced Encryption Standard (AES), Rijndael has continued to receive great attention and has had its security continuously evaluated by the cryptographic community. Rijndael is a cipher with a simple, elegant and highly algebraic structure. Its selection as the AES has led to a growing interest in the study of algebraic properties of block ciphers, and in particular algebraic techniques that can be used in their cryptanalysis. In these notes we will examine some algebraic aspects of the AES and consider a number of algebraic techniques that could be used in the analysis of the cipher. In particular, we will focus on the large, though surprisingly simple, systems of multivariate quadratic equations derived from the encryption operation, and consider some approaches that could be used when attempting to solve these systems. These notes refer to an invited talk given at the Fourth Conference on the Advanced Encryption Standard (AES4) in May 2004, and are largely based on[4].