# Books on Boolean Functions

 Construction and Analysis of Cryptographic Functions Lilya Budaghyan 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.

 Boolean Functions for Cryptography and Error Correcting Codes Claude Carlet (chapter in "Boolean Models and Methods in Mathematics, Computer Science, and Engineering") A comprehensive survey on the subject of Boolean functions and their applications to cryptography.

 Vectorial Boolean Functions for Cryptography Claude Carlet (chapter in "Boolean Models and Methods in Mathematics, Computer Science, and Engineering") A comprehensive survey on the subject of vectorial Boolean functions and their applications to cryptography.

 Bent Functions: Fundamentals and Results Sihem Mesnager This book gives a detailed survey of the main results on bent functions over finite fields, presents a systematic overview of their generalizations, variations and applications, considers open problems in classification and systematization of bent functions, and discusses proofs of several results. This book uniquely provides a necessary comprehensive coverage of bent functions.It serves as a useful reference for researchers in discrete mathematics, coding and cryptography. Students and professors in mathematics and computer science will also find the content valuable, especially those interested in mathematical foundations of cryptography. It can be used as a supplementary text for university courses on discrete mathematics, Boolean functions, or cryptography, and is appropriate for both basic classes for under-graduate students and advanced courses for specialists in cryptography and mathematics.

 Introduction to Finite Fields and their Applications Rudolf Lidl & Harald Niederreiter A standard textbook on the theory of finite fields and other elementary topics.

 Handbook of Finite Fields Gary L. Mullen & Daniel Panario A comprehensive survey on results in the area of finite fields.