Graph Eigenvalues and Walsh Spectrum of Boolean Functions

Abstract

In this paper we consider the Cayley graph G(f) associated to a Boolean function f and we use it to investigate some of the cryptographic properties of f. We derive necessary (but not sufficient) conditions for a Boolean function to be bent. We also find a complete characterization of the propagation characteristics of f using the topology of its associated Cayley graph G(f) . Finally, some inequalities between the cardinality of the spectrum of G(f) and the Hamming weight of functions are obtained, and some problems are raised.

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Document Details

Document Type
Technical Report
Publication Date
Aug 28, 2006
Accession Number
ADA573186

Entities

People

  • Pantelimon Stanica

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Coefficients
  • Differential Equations
  • Eigenvalues
  • Equations
  • Exclusion Principle
  • Graph Theory
  • Inequalities
  • Mathematical Analysis
  • Mathematics
  • Notation
  • Number Theory
  • Numbers
  • Spectra
  • Theorems
  • Triangles
  • Vector Spaces

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Approximation Theory.
  • Computer Programming and Software Development.
  • Operations Research