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Degree of composition of highly nonlinear functions and applications to higher order differential cryptanalysis. (English) Zbl 1056.94512
Knudsen, Lars (ed.), Advances in cryptology - EUROCRYPT 2002. 21st international conference on the theory and applications of cryptographic techniques, Amsterdam, the Netherlands, April 28 – May 2, 2002. Proceedings. Berlin: Springer (ISBN 3-540-43553-0). Lect. Notes Comput. Sci. 2332, 518-533 (2002).
Summary: 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 one 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 by H. Tanaka, K. Hisamatsu, and T. Kaneko [Lect. Notes Comput. Sci. 1719, 221–230 (1999; Zbl 0979.94042)] and by S. Babbage and L. Frisch [Lect. Notes Comput. Sci. 2015, 22–36 (2001; Zbl 0977.94020)].
For the entire collection see [Zbl 0984.00084].

MSC:
94A60 Cryptography
68P25 Data encryption (aspects in computer science)
94A55 Shift register sequences and sequences over finite alphabets in information and communication theory
06E30 Boolean functions
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