Publication Type : Journal Article
Publisher : Journal of Mathematical Cryptology, Walter de Gruyter GmbH.
Source : Journal of Mathematical Cryptology, Walter de Gruyter GmbH, Volume 10, Number 3-4, p.145-156 (2016)
Url : https://www.scopus.com/inward/record.uri?eid=2-s2.0-84998890570&doi=10.1515%2fjmc-2016-0042&partnerID=40&md5=aa284b96a294dd41441636d75415f16e
Campus : Coimbatore
School : School of Engineering
Center : TIFAC CORE in Cyber Security
Year : 2016
Abstract : There have been efforts to investigate the affine equivalence of Boolean functions. Due to the complexity of the general problem, only affine equivalence under certain groups of permutations is usually considered. Boolean functions which are invariant under the action of cyclic rotation of the input variables are known as rotation symmetric (RS) Boolean functions. Due to their speed of computation and the prospect of being good cryptographic Boolean functions, this class of Boolean functions has received a lot of attention from cryptographic researchers. In this paper, we study affine equivalence for the simplest rotation symmetric Boolean functions, called MRS functions, which are generated by the cyclic permutations of a single monomial. Using Pólya's enumeration theorem, we compute the number of equivalence classes, under certain large groups of permutations, for these MRS functions in any number n of variables. If n is prime, we obtain the number of equivalence classes under the group of all permutations of the variables.
Cite this Research Publication : T. W. Cusick, Dr. Lakshmy K. V., and Sethumadhavan, M., “Affine equivalence of monomial rotation symmetric Boolean functions: A Pólya's theorem approach”, Journal of Mathematical Cryptology, vol. 10, pp. 145-156, 2016.