Differentially uniform mappings for cryptography
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
Cartesian authentication codes from functions with optimal nonlinearity
Theoretical Computer Science
Journal of Complexity - Special issue on coding and cryptography
Authentication Schemes from Highly Nonlinear Functions
Designs, Codes and Cryptography
A family of skew Hadamard difference sets
Journal of Combinatorial Theory Series A
On the construction of bent vectorial functions
International Journal of Information and Coding Theory
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
On the construction of highly nonlinear permutations
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Systematic authentication codes from highly nonlinear functions
IEEE Transactions on Information Theory
Linear codes from perfect nonlinear mappings and their secret sharing schemes
IEEE Transactions on Information Theory
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In this paper, the relationships between perfect nonlinear (in brief, PN) functions and optimal universal hash families are discussed. We point out the equivalence of constructions between them, i.e., from PN functions, one can obtain optimal universal hash families and vice versa. As an application of our construction, a message authentication code is proposed, which provides better resistance to substitution attack than a known construction given by Carlet et al. in 2006. More generally, the connections between functions with given differential uniformity and some universal hash families are studied.