Degree of composition of highly nonlinear functions and applications to higher order cryptanalysis

Anne Canteaut 1 Marion Videau 1
1 CODES - Coding and cryptography
Inria Paris-Rocquencourt
Abstract : To improve the security of iterated block ciphers, the resistance against linear cryptanalysis has been formulated in terms of provable security which suggests the use of highly nonlinear functions as round functions. Here, we show that some properties of such functions enable to find a new upper bound for the degree of the product of its Boolean components. Such an improvement holds when all values occurring in the Walsh spectrum of the round function are divisible by a high power of 2. This result leads to a higher order differential attack on any 5-round Feistel ciphers using an almost bent substitution function. We also show that the use of such a function is precisely the origin of the weakness of a reduced version of MISTY1 reported in [23, 1].
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Lars R. Knudsen. EUROCRYPT 2002 : International Conference on the Theory and Applications of Cryptographic Techniques, Apr 2002, Amsterdam, Netherlands. Springer, 2332, pp.518-533, 2002, LNCS. 〈http://www.springerlink.com/content/c03nh08puehw9p5x/fulltext.pdf〉. 〈10.1007/3-540-46035-7_34〉
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Anne Canteaut, Marion Videau. Degree of composition of highly nonlinear functions and applications to higher order cryptanalysis. Lars R. Knudsen. EUROCRYPT 2002 : International Conference on the Theory and Applications of Cryptographic Techniques, Apr 2002, Amsterdam, Netherlands. Springer, 2332, pp.518-533, 2002, LNCS. 〈http://www.springerlink.com/content/c03nh08puehw9p5x/fulltext.pdf〉. 〈10.1007/3-540-46035-7_34〉. 〈hal-00675316〉

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