A Differential and Linear Analysis of the Inversion Mapping in Odd-Characteristic Finite Fields
Substitution boxes (S-boxes) based on the inversion mapping (S[x] = x) in even-characteristic finite fields are widely used components in the design of cryptographic primitives such as block ciphers (notably the AES cipher). This report focuses on the inversion mapping in finite fields GF(pn) where p is a (small) odd prime and n is a (small) integer. We compare the differential and linear profiles of S-boxes over oddand even-characteristic fields, which also motivates the design and analysis of AES variants operating in fields of odd characteristic. Even for GF(2n), the study of S-boxes which are APN permutations (odd-valued n) already shows resistance to differential and linear cryptanalysis after three rounds.