Affine equivalence and constructions of cryptographically strong Boolean functions
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Authors
Chung, Jong Ho
Subjects
Boolean Function
Cryptography
Affine Equivalence
Cryptography
Affine Equivalence
Advisors
Stanica, Pantelimon
Date of Issue
2013-09
Date
Sep-13
Publisher
Monterey, California: Naval Postgraduate School
Language
Abstract
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.
Type
Thesis
Description
Series/Report No
Department
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
Funder
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.