Publication:
The spectra of DES S-Boxes

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Authors
Fukuzawa, Mathew B.
Subjects
Data Encryption Standard
Boolean Function
Cayley Graph
Graph Spectra
Advisors
Stǎnicǎ, Pantelimon
Date of Issue
2014-06
Date
Jun-14
Publisher
Monterey, California: Naval Postgraduate School
Language
Abstract
We typically do not associate the field of graph theory with the field of cryptography. In graph theory, the aim is to model relationships with a graph and examine properties of that graph. The goal of cryptography is to design a communication system over a nonsecure channel. One connection between the two fields can be found with Cayley graphs and Boolean functions (BF). Accordingly, we can represent a cryptographic Boolean function with a Cayley graph and examine its properties. In this thesis, we convert the substitution boxes within the Data Encryption Standard (DES) to Boolean functions and represent them with Cayley graphs. From the Cayley graph, we analyze the graph spectra and attempt to determine a relationship with the cryptographic properties of the corresponding Boolean functions. With the spectra, we also make some inferences about the structure of the Cayley graph.
Type
Thesis
Description
Department
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
Funder
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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.
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