Sparse Permutations with Low Differential Uniformity

Pascale Charpin (1) , Gohar M. Kyureghyan (2) , Valentin Suder (1)

1 SECRET - Security, Cryptology and Transmissions
2 Fakultät für Mathematik - Institut für Algebra und Geometrie

We study the functions View the $F_{s,t,\gamma}(x)=x^s+\gamma Tr(x^t)$ on $F_{2^n}$. We describe the set of such permutations and the explicit expressions of their compositional inverses. Further we consider special classes of such functions, for which we determine the size of their image set, the algebraic degree and the differential uniformity.

Mots clés: Permutation; Boolean function; Monomial function; Quadratic function; APN function; AB function; Cryptographic criteria; Differential uniformity

Domaines: Cryptographie et sécurité [cs.CR]; Mathématique discrète [cs.DM]

Pascale Charpin, Gohar M. Kyureghyan, Valentin Suder. Sparse Permutations with Low Differential Uniformity. Finite Fields and Their Applications, 2014, 28, pp.214-243. ⟨10.1016/j.ffa.2014.02.003⟩. ⟨hal-01068860⟩