Construction and Analysis of Cryptographic Functions

by Lilya Budaghyan

Overview

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.

Product Details

ISBN-13:	9783319129907
Publisher:	Springer International Publishing
Publication date:	01/07/2015
Edition description:	2014
Pages:	168
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Introduction.- Generalities.- Equivalence relations of functions.- Bent functions.- New classes of APN and AB polynomials.- Construction of planar functions.

Editorial 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)

From the Publisher