On Inverses of APN Exponents

Gohar Kyureghyan (1) , Valentin Suder (2)

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

In this extended abstract we present results on the inverses modulo 2n − 1 of the known APN exponents. In particular, we describe explicitly the inverses of the Welch and Dobbertin exponents and give the main ideas of their proofs. Further, we observe that the inverse of the Dobbertin exponent defines an APN function on F2n of algebraic degree n+3 , which 2 is the first example of such a function.

Domaines: Cryptographie et sécurité [cs.CR]

Gohar Kyureghyan, Valentin Suder. On Inverses of APN Exponents. IEEE International Symposium on Information Theory - ISIT 2012, Jul 2012, Cambridge, MA, United States. pp.1207-1211, ⟨10.1109/ISIT.2012.6283047⟩. ⟨hal-00879498⟩