In 2002, Asiacrypt made a publication of Nicolas Courtois and Josef Pieprzyk [1] where they propose a theoretical model of AES, which ensure characterization it as a quadratic equations system, the system consists on 8000 equations with 1600 binary variables, however, the attack failed in trying to break AES, as Courtois mentioned in [2]. In addition, several cryptography experts have commented that there are mathematics problems behind the attack, the authors have probably made a mistake, despite this, considering the orderly shape and the mathematical complete structure of AES, it is possible that this type of cryptanalysis can become one of the most powerful to break AES.
Other known publications are:
- Impossible Differentials Attack: there is an attack of this type on 5 rounds of AES, requiring 2^{29} chosen plaintext, 2^{30} encryptions, 2^{42} bytes of memory, 2^{26} precalculus steps. These conditions were improved in [3] and [4] to achieve an attack on 6 rounds of AES.
- Square Attack: is an attack aimed at a type of Rijndael algorithm, it has been designed based on bytes structures. Just the first such attack was made on the predecessor algorithm called "Square". This attack can break Rijndael on 6-7 rounds, which may be upgraded to attack on 9 rounds of AES-256 with 2^{77} plaintexts, 2^{56} related keys and 2^{224} encryptions [5].
- Collision Attack: it tries to find two inputs that produce the same hash value, i.e., a hash collision. This attack affects all versions of AES, 128, 192 and 256 with 7 rounds [6].
References
- Nicolas C & Josef P. 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 (2002), pp. 267-287.
- http://www.cryptosystem.net/aes/
- J H C, M K, K K, J L & S K. Improved Impossible Differential Cryptanalysis of Rijndael and Crypton. ICISC (2001) LNCS 2288: pp. 39-49.
- Raphael CP & M U S. Generalised impossible differentials of advanced encryption standard. IEE Electronics Letters (2001) Vol. 37, Issue 14: pp. 896-898.
- N F, J K, S L, B S, M S, D W, D W & D W. Improved cryptanalysis of Rijndael. FSE 00, LNCS 1978, pp. 213-230.
- H G & M M. A collision Attack on 7 rounds of Rijndael. AES3papers, pp. 2-11.