Accession Number : ADA589912


Title :   Affine Equivalence and Constructions of Cryptographically Strong Boolean Functions


Descriptive Note : Doctoral thesis


Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CA


Personal Author(s) : Chung, Jong H


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a589912.pdf


Report Date : Sep 2013


Pagination or Media Count : 175


Abstract : In this thesis, we study a type of affine equivalence for the monomial rotation-symmetric (MRS) Boolean functions and two new construction techniques for cryptographic Boolean functions based on the affine equivalence of cryptographically strong base functions and fast Boolean operations. Affine equivalence of cryptographic Boolean functions presents a formidable challenge to researchers, due to its complexity and size of the search space. We focus on an affine equivalence based on permutation of variables for MRS Boolean functions and their relationship to circulant matrices over the binary field F2 and regular graphs. We first establish a relationship between generalized inverses of circulant matrices in F2 and their generating polynomials. We then apply the relationship to gain insight into necessary conditions for the affine equivalence, based on permutations of variables for MRS Boolean functions. We also propose a theoretical connection between regular graphs and MRS Boolean functions to further our study in affine equivalence. Finally, we present two constructions for Boolean functions with good cryptographic properties. The constructions take advantage of two affine-equivalent base functions with strong cryptographic properties. We analyze the cryptographic properties of the constructions and demonstrate an application with these base functions, called the hidden weighted-bit functions.


Descriptors :   *SPECIAL FUNCTIONS(MATHEMATICS) , CRYPTOGRAPHY


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE