Steps Towards Redesigning Cryptosystems by a Non-associative Algebra of IP-Loops

Abstract

In block ciphers, the substitution boxes (S-boxes) are used with the purpose to induce confusion in cryptosystems. For the last three decades most of algebraic and chaotic S-boxes are based on the associative algebras of Galois fields. However, recently a little but remarkable work on the designing of S-boxes over some local associative algebras have been published, which is in fact a mock of the associative algebras of Galois fields. The main purpose of these establishments is to hide data and improve the security levels of crypto algorithms. In this study we redesign S-boxes over the elements of inverse property loop. The fascinating features of this structure are; it’s non-associativity and the existence of the inverse of zero element. These properties not only increase the availability of the number of structures but also provide easy approach in constructing S-boxes. The newly designed S-boxes are assessed by various analyses, which include nonlinearity, strict avalanche criterion, bit independence criterion, linear approximation probabilities, and differential approximation probabilities. Majority logic criterion is also performed to evaluate its application in various encryption systems.