Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
The Nonhomomorphicity of Boolean Functions
SAC '98 Proceedings of the Selected Areas in Cryptography
On Binary Cyclic Codes with d=3
On Binary Cyclic Codes with d=3
Linear structures in blockciphers
EUROCRYPT'87 Proceedings of the 6th 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
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The most important building blocks of symmetric cryptographic primitives such as the DES or the AES, are vectorial Boolean functions, also called S-boxes. In this paper, we extend the definition of normality for Boolean functions into several new affine invariant properties for vectorial Boolean functions. We compute the probability of occurrence of these properties and present practical algorithms for each of these new properties. We find a new structural property for the AES S-box, which also holds for a large class of permutation functions when the dimension n is even. Moreover, we prove a relation with the propagation characteristics of a vectorial function and extend the scope of non-APN functions for n even.