The Spectra of Des S-Boxes

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.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 2014
Accession Number
ADA607778

Entities

People

  • Mathew B. Fukuzawa

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Cyber
  • Energy and Power Technologies
  • Engineered Resilient Systems

DTIC Thesaurus Topics

  • Boolean Algebra
  • Communication Systems
  • Computer Programs
  • Computer Science
  • Cryptography
  • Data Encryption
  • Graph Theory
  • Information Processing
  • Information Security
  • Linear Algebra
  • Mathematics
  • Network Science
  • Number Theory
  • Parallel Computing
  • Secure Communications
  • Signal Processing
  • United States

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Computer Programming and Software Development.
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms
  • Cyber
  • Cyber - Cryptography