Differential Properties of Power Functions

Céline Blondeau (1) , Anne Canteaut (1) , Pascale Charpin (1)

1 SECRET - Security, Cryptology and Transmissions

Some properties of power permutations, that is, monomials bijective mappings on F2n , are investigated. In particular, the differential spectrum of these functions is shown to be of great interest for estimating their resistance to some variants of differential cryptanalysis. The relationships between the differential spectrum of a power permutation and the weight enumerator of a cyclic code with two zeroes are provided. The functions with a two-valued differential spectrum are also studied and the differential spectra of several infinite families of exponents are computed.

Mots clés: differential uniformity; APN function; almost perfect non-linear function; boolean function; power function; permutation; cyclic codes; weight enumerator; differential cryptanalysis

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Céline Blondeau, Anne Canteaut, Pascale Charpin. Differential Properties of Power Functions. ISIT 2010 - IEEE International Symposium on Information Theory, Jun 2010, Austin, United States. ⟨hal-00610114⟩