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Construction and Analysis of Cryptographic Functions

  • Book
  • © 2014

Overview

Authors:
  1. Lilya Budaghyan

    1. Department of Informatics, University of Bergen, Bergen, Norway

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  • Examines two cryptographic functions which combat two of the most powerful attacks on symmetric cryptosystems
  • Demonstrates new methods for construction of these functions
  • Presents novel research used in many areas of mathematics and information theory, in particular, Boolean functions, symmetric cryptography, discrete mathematics, combinatorics, finite geometry, and coding theory
  • Includes supplementary material: sn.pub/extras

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    • Lilya Budaghyan
    Pages 1-9

  3. Generalities

    • Lilya Budaghyan
    Pages 11-37

  4. Equivalence Relations of Functions

    • Lilya Budaghyan
    Pages 39-61

  5. Bent Functions

    • Lilya Budaghyan
    Pages 63-99

  6. New Classes of APN and AB Polynomials

    • Lilya Budaghyan
    Pages 101-150

  7. Construction of Planar Functions

    • Lilya Budaghyan
    Pages 151-168
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Keywords

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.

Reviews

“The book deals with functions on finite fields that are used in cryptography. … Anybody who is not only interested in the construction of cryptographic relevant function, but who wants to learn also about the problem how to classify functions up to equivalence, should refer to this excellent text.” (Alexander Pott, zbMATH 1367.94001, 2017) 

Authors and Affiliations

  • Department of Informatics, University of Bergen, Bergen, Norway

    Lilya Budaghyan

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