Differentially uniform mappings for cryptography
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
On almost perfect nonlinear permutations
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Linear cryptanalysis method for DES cipher
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
The Number of Classes of Invertible Boolean Functions
Journal of the ACM (JACM)
On Asymptotic Estimates in Switching and Automata Theory
Journal of the ACM (JACM)
The Design of Rijndael
Provable Security Against Differential Cryptanalysis
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
APN functions in odd characteristic
Discrete Mathematics - Special issue: Combinatorics 2000
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
A toolbox for cryptanalysis: linear and affine equivalence algorithms
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
FOX: a new family of block ciphers
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
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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 : Fpm→ Fpnbased 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.