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
Almost perfect nonlinear power functions on GF (2n): the Niho case
Information and Computation
Codes, Bent Functions and Permutations Suitable For DES-likeCryptosystems
Designs, Codes and Cryptography
Provable Security Against Differential Cryptanalysis
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Almost perfect nonlinear power functions on GF(2n): the Welch case
IEEE Transactions on Information Theory
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Cryptographic Functions and Design Criteria for Block Ciphers
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
The Simplest Method for Constructing APN Polynomials EA-Inequivalent to Power Functions
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
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We study the functions from F2m into F2m for odd m which oppose an optimal resistance to linear cryptanalysis. These functions are called almost bent. It is known that almost bent functions are also almost perfect nonlinear, i.e. they also ensure an optimal resistance to differential cryptanalysis but the converse is not true. We here give a necessary and sufficient condition for an almost perfect nonlinear function to be almost bent. This notably enables us to exhibit some infinite families of power functions which are not almost bent.