Cryptology ePrint Archive: Report 2020/1166

A Differential and Linear Analysis of the Inversion Mapping in Odd-Characteristic Finite Fields

Jorge Nakahara Jr

Abstract: Substitution boxes (S-boxes) based on the inversion mapping 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(p^n) where p is a (small) odd prime and n is a (small) integer. We compare the differential and linear profiles of S-boxes over odd- and even-characteristic fields, which also motivates the design and analysis of AES variants operating in fields of odd-characteristic. Even for GF(2^n), the study of S-boxes which are APN permutations (odd-valued n)already shows resistance to differential and linear cryptanalysis after three rounds.

Category / Keywords: secret-key cryptography / odd-characteristic finite fields, inversion mapping, S-box, APN permutations

Date: received 24 Sep 2020

Contact author: jorge_nakahara at yahoo com br

Available format(s): PDF | BibTeX Citation

Version: 20200925:184820 (All versions of this report)

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