In this paper we present an extension of the generalized linear equivalence relation, proposed in [7]. This mathematical tool can be helpful for the classification of non-linear functions f : F p m → F p n based on their cryptographic properties. It thus can have relevance in the design criteria for substitution boxes (S-boxes), the latter being commonly used to achieve non-linearity in most symmetric key algorithms. First, we introduce a simple but effective representation of the cryptographic properties of S-box functions when the characteristic of the underlying finite field is odd; following this line, we adapt the linear cryptanalysis technique, providing a generalization of Matsui’s lemma. This is done in order to complete the proof of Theorem 2 in [7], also by considering the broader class of generalized affine transformations. We believe that the present work can be a step towards the extension of known cryptanalytic techniques and concepts to finite fields with odd characteristic.

A complete formulation of generalized affine equivalence

BREVEGLIERI, LUCA ODDONE;CAIRONI, MARIO;CHERUBINI, ALESSANDRA;MACCHETTI, MARCO
2005-01-01

Abstract

In this paper we present an extension of the generalized linear equivalence relation, proposed in [7]. This mathematical tool can be helpful for the classification of non-linear functions f : F p m → F p n based on their cryptographic properties. It thus can have relevance in the design criteria for substitution boxes (S-boxes), the latter being commonly used to achieve non-linearity in most symmetric key algorithms. First, we introduce a simple but effective representation of the cryptographic properties of S-box functions when the characteristic of the underlying finite field is odd; following this line, we adapt the linear cryptanalysis technique, providing a generalization of Matsui’s lemma. This is done in order to complete the proof of Theorem 2 in [7], also by considering the broader class of generalized affine transformations. We believe that the present work can be a step towards the extension of known cryptanalytic techniques and concepts to finite fields with odd characteristic.
THEORETICAL COMPUTER SCIENCE
INF; Boolean functions; generalized linear equivalence; linear cryptanalysis; S-boxes; cryprography
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/269072
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