The Data Encryption Standard (DES) and its strength against attacks
IBM Journal of Research and Development
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
Handbook of Applied Cryptography
Handbook of Applied Cryptography
The Design of Rijndael
White-Box Cryptography and an AES Implementation
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Provable Security Against Differential Cryptanalysis
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
On the Distribution of Characteristics in Composite Permutations
CRYPTO '93 Proceedings of the 13th Annual International Cryptology Conference on Advances in Cryptology
The Data Base of Selected Permutations (Extended Abstract)
ASIACRYPT '91 Proceedings of the International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
A toolbox for cryptanalysis: linear and affine equivalence algorithms
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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This paper presents an iterative construction method for building composite permutations. Its efficiency is based on the concepts of pre-computation and equivalence classes. Equivalence class representatives of permutations on four bits are pre-computed. These class representatives can serve as input to the construction method, however, the results are also of independent interest for applications in cryptography. A well-known example of a cryptosystem using composite permutations for its Substitution boxes (S-boxes) is the Data Encryption Standard (DES). Throughout the paper, DES-like S-boxes are defined as mappings satisfying all design criteria as disclosed by one of the designers of DES. All permutations on four bits with DES-like properties are identified. Starting with pre-computed representatives of classes with such permutations, two iterations of a specialized version of the algorithm are applied to obtain bounds on the minimum differential uniformity and minimum non-linear uniformity of DES-like S-boxes. It is established that the two values cannot be less than eight, and that DES-like S-boxes for which the values are both equal to 12 do exist. In addition, if the non-linear uniformity of each of the four permutations in a DES-like S-box is at most six, as in all DES S-boxes, then its non-linear uniformity cannot be less than ten and its minimum differential uniformity equals 12.