Three characterizations of non-binary correlation-immune and resilient functions
Designs, Codes and Cryptography
Generalization of Siegenthaler Inequality and Schnorr-Vaudenay Multipermutations
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Transitive q-Ary Functions over Finite Fields or Finite Sets: Counts, Properties and Applications
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Enumeration of Homogeneous Rotation Symmetric Functions over Fp
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
De Bruijn sequences and complexity of symmetric functions
Cryptography and Communications
Resilient functions over finite fields
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Balanced Symmetric Functions Over
IEEE Transactions on Information Theory
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A function over finite rings is a function from a ring $E_{q}^{n}$ to a ring Er, where Ek is ℤ /k ℤ. These functions are well used in cryptography: cipher design, hash function design and in theoretical computer science. In this paper, we are especially interested in symmetric functions. We give practical ways of computing their ANF and their Walsh Spectrum in $\mathcal{O}\left({ n+q-1 \choose q-1 }^2\right)$ using linear algebra. Thus, we achieve a better complexity both in time and memory than the fast Fourier transform which is in $\mathcal{O}\left( q^nn\log(q) \right)$.