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Computational aspects of the expected differential probability of 4-round AES and AES-like ciphers. (English) Zbl 1171.14017
The authors study the security of the AES and AES-like block cipher against differential cryptanalysis. They start with a general presentation of basic terms and mathematical background of the AES encryption model and continuing by studying particular characteristic of the cipher system show the security of $$S$$-boxes against differential attack. The entire work represents a good exposure of the AES model study and can be a part of cryptographically analysis in order to improve the security of the model in certain cases.

##### MSC:
 94A60 Cryptography
LEX
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##### References:
 [1] Beth T, Ding C (1993) On Almost Perfect Nonlinear Permutations. In: EUROCRYPT. Lecture Notes in Computer Science, vol 765. Springer, Heidelberg, pp 65–76 · Zbl 0951.94524 [2] Biham E, Shamir A (1990) Differential Cryptanalysis of DES-like Cryptosystems. In: Menezes A, Vanstone SA (eds) CRYPTO. Lecture Notes in Computer Science, vol 537. Springer, Heidelberg, pp 67–75 · Zbl 0729.68017 [3] Biryukov A (2007) The design of a stream Cipher LEX. Selected areas in cryptography. Lecture Notes in Computer Science, vol 4356. Springer, Heidelberg, pp 67–75 · Zbl 1161.94387 [4] Daemen J, Rijmen V (2002) The design of Rijndael: AES–the advanced encryption standard. Springer, Heidelberg · Zbl 1065.94005 [5] Daemen J, Rijmen V (2005) The Pelican MAC Function. Cryptology ePrint Archive, Report 2005/088. http://eprint.iacr.org/ · Zbl 1140.68385 [6] Daemen J, Rijmen V (2006) Understanding two-round differentials in AES. In: De Prisco R, Yung M (eds) SCN. Lecture Notes in Computer Science, vol 4116. Springer, Heidelberg, pp 78–94 · Zbl 1152.94413 [7] Fisher SD (1966) Classroom notes: matrices over a finite field. Am Math Mon 73(6): 639–641 · Zbl 0138.01202 · doi:10.2307/2314805 [8] Hong S, Lee S, Lim J, Sung J, Cheon DH, Cho I (2000) Provable Security against Differential and Linear Cryptanalysis for the SPN Structure. In: Schneier B (eds) FSE. Lecture Notes in Computer Science, vol 1978. Springer, Heidelberg, pp 273–283 · Zbl 0994.68505 [9] Keliher L, Meijer H, Tavares SE (2001) New method for upper bounding the maximum average linear hull probability for SPNs. In: Pfitzmann B (eds) EUROCRYPT. Lecture Notes in Computer Science, vol 2045. Springer, Heidelberg, pp 420–436 · Zbl 1015.94546 [10] Keliher L (2004) Refined analysis of bounds related to linear and differential cryptanalysis for the AES. In: Dobbertin H, Rijmen V, Sowa A (eds) AES4 Conference Lecture Notes in Computer Science, vol 3373. Springer, Heidelberg, pp 42–57 · Zbl 1117.94323 [11] Keliher L, Sui J (2007) Exact maximum expected differential and linear probability for 2-round advanced encryption standard (AES). IET Inf Secur 1(2): 53–57 · doi:10.1049/iet-ifs:20060161 [12] Lai X, Massey JL, Murphy S (1991) Markov ciphers and differential cryptanalysis. In: Advances in Cryptology–EUROCRYPT ’91 (Brighton, 1991). Lecture Notes in Computer Science, vol 547. Springer, Berlin, pp 17–38 [13] Lidl R, Niederreiter H (1997) Finite fields, Encyclopedia of mathematics and its applications, 2nd edn. Cambridge University Press, Cambridge [14] Matsui M (1993) Linear Cryptoanalysis Method for DES Cipher EUROCRYPT. In: Helleseth T (eds) Lecture Notes in Computer Science, vol 765. Springer, Heidelberg, pp 386–397 · Zbl 0951.94519 [15] Minematsu K, Tsunoo Y (2006) Provably secure MACs from differentially-uniform permutations and AES-based implementations. In: Robshaw M (eds) FSE. Lecture Notes in Computer Science, vol 4047. Springer, Heidelberg, pp 226–241 · Zbl 1234.94058 [16] Park S, Sung SH, Chee S, Yoon E-J, Lim J (2002) On the security of Rijndael-like structures against differential and linear cryptanalysis. In: Zheng Y (eds) ASIACRYPT. Lecture Notes in Computer Science, vol 2501. Springer, Heidelberg, pp 176–191 · Zbl 1065.68530 [17] Park S, Sung SH, Lee S, Lim J (2003) Improving the upper bound on the maximum differential and the maximum linear hull probability for SPN structures and AES. In: Johansson T (eds) FSE. Lecture Notes in Computer Science, vol 2887. Springer, Heidelberg, pp 247–260 · Zbl 1254.94040
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