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Regular subgroups with large intersection. (English) Zbl 1455.20001

A block cipher (and the round functions composing such a cipher) can be regarded as a set of keyed permutations on the message space \(V=\mathbb{F}_2^n\). The security of the cipher can be measured by comparing these permutations to the set of affine functions on \(V\) (with respect to the XOR operation). In his Ph.D. thesis, M. Calderini [On Boolean functions, symmetric cryptography and algebraic coding theory. Trento: University of Trento (PhD Thesis) (2015)], studied a class of operations coming from copies of the usual translation group on \(V\) for investigating possible weaknesses in a block cipher with respect to these operations. A class of such operations were then used for investigating a possible differential cryptanalysis on bolck ciphers in [R. Civino et al., Des. Codes Cryptography 87, No. 2–3, 225–247 (2019; Zbl 1454.94059)]. These works motivated the present paper, which investigates pairs of regular elementary abelian subgroups of Sym(V), with the aim of finding information about their (affine) normalisers when the pairs have large intersection.

MSC:

20B35 Subgroups of symmetric groups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
94A60 Cryptography

Citations:

Zbl 1454.94059

Software:

PRESENT; Magma
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Full Text: DOI arXiv

References:

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