Construction and Analysis of Cryptographic Functions

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.

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

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