Affine equivalence and constructions of cryptographically strong Boolean functions
Chung, Jong Ho
MetadataShow full item record
In this thesis, we study a type of affine equivalence for the monomial rotation-symmetric (MRS) Boolean func-tions 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.
Approved for public release; distribution is unlimited
Showing items related by title, author, creator and subject.
Gangopadhyay, Sugata; Gangopadhyay, Aditi Kar; Pollatos, Spyridon; Stănică, Pantelimon (2015-07-31);While performing cryptanalysis, it is of interest to approximate a Boolean function in n variables f : Fn → F2 by affine functions. Usually, it is assumed that all the input vectors to a Boolean function are equiprobable ...
The Fourier Entropy-Influence Conjecture Holds for a Log-Density 1 Class of Cryptographic Boolean Functions Stănică, Pantelimon; Gangopadhyay, Sugata (2014-01-25);We consider the Fourier Entropy-Infl uence (FEI) conjecture in the context of cryptographic Boolean functions. We show that the FEI con jecture is true for the functions satisfying the strict avalanche criterion, ...
The Fourier Entrophy-Influence Conjecture Holds for a Log-Density 1 Class of Cryptographic Boolean Functions Gangopadhyay, Sugata; Stanica, Pantelimon (2014);We consider the Fourier Entropy-Infuence (FEI) conjecture in the context of cryptographic Boolean functions. We show that the FEI conjecture is true for the functions satisfying the strict avalanche criterion, which forms ...