Construction and Analysis of Cryptographic Functions

  • Lilya¬†Budaghyan

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Lilya Budaghyan
    Pages 1-9
  3. Lilya Budaghyan
    Pages 11-37
  4. Lilya Budaghyan
    Pages 39-61
  5. Lilya Budaghyan
    Pages 63-99
  6. Lilya Budaghyan
    Pages 101-150
  7. Lilya Budaghyan
    Pages 151-168

About this book


This book covers novel research on construction and analysis of optimal cryptographic functions such as almost perfect nonlinear (APN), almost bent (AB), planar and bent functions. These functions have optimal resistance to linear and/or differential attacks, which are the two most powerful attacks on symmetric cryptosystems. Besides cryptographic applications, these functions are significant in many branches of mathematics and information theory including coding theory, combinatorics, commutative algebra, finite geometry, sequence design and quantum information theory. The author analyzes equivalence relations for these functions and develops several new methods for construction of their infinite families. In addition, the book offers solutions to two longstanding open problems, including the problem on characterization of APN and AB functions via Boolean, and the problem on the relation between two classes of bent functions.


Almost bent function Almost perfect nonlinear function Bent function Boolean function CCZ-equivalence Commutative semifield EA-equivalence Nonlinearity Planar function S-box

Authors and affiliations

  • Lilya¬†Budaghyan
    • 1
  1. 1.Department of InformaticsUniversity of BergenBergenNorway

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-12990-7
  • Online ISBN 978-3-319-12991-4
  • About this book