Design theory
Nonlinearity criteria for cryptographic functions
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
A proposal for a new block encryption standard
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Construction of relative difference sets in p-groups
Discrete Mathematics
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
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
The Design of Rijndael
Nonlinear functions in abelian groups and relative difference sets
Discrete Applied Mathematics - Optimal discrete structure and algorithms (ODSA 2000)
Journal of Complexity - Special issue on coding and cryptography
A family of skew Hadamard difference sets
Journal of Combinatorial Theory Series A
Generalized boolean bent functions
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
Almost difference sets and their sequences with optimal autocorrelation
IEEE Transactions on Information Theory
A new APN function which is not equivalent to a power mapping
IEEE Transactions on Information Theory
A new characterization of group action-based perfect nonlinearity
Discrete Applied Mathematics
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Perfect nonlinear functions are used to construct DES-like cryptosystems that are resistant to differential attacks. We present generalized DES-like cryptosystems where the XOR operation is replaced by a general group action. The new cryptosystems, when combined with G-perfect nonlinear functions (similar to classical perfect nonlinear functions with one XOR replaced by a general group action), allow us to construct systems resistant to modified differential attacks. The more general setting enables robust cryptosystems with parameters that would not be possible in the classical setting. We construct several examples of G-perfect nonlinear functions, both $${\mathbb{Z}}_2$$ -valued and $${\mathbb{Z}}_2^a$$ -valued. Our final constructions demonstrate G-perfect nonlinear planar permutations (from $${\mathbb{Z}}_2^a$$ to itself), thus providing an alternative implementation to current uses of almost perfect nonlinear functions.