Books on Boolean Functions

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9783319129907-big.jpg 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.

9780511780448i.jpg 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.

9780511780448i.jpg 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.jpeg 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. 

9780521460941.jpg Introduction to Finite Fields and their Applications
Rudolf Lidl & Harald Niederreiter
 A standard textbook on the theory of finite fields and other elementary topics.

9781439873786.jpg Handbook of Finite Fields
Gary L. Mullen & Daniel Panario
A comprehensive survey on results in the area of finite fields.

Index.jpg Bent functions: results and applications to cryptography
Natalia Tokareva
Bent Functions: Results and Applications to Cryptography offers a unique survey of the objects of discrete mathematics known as Boolean bent functions. As these maximal, nonlinear Boolean functions and their generalizations have many theoretical and practical applications in combinatorics, coding theory, and cryptography, the text provides a detailed survey of their main results, presenting a systematic overview of their generalizations and applications, and considering open problems in classification and systematization of bent functions. The text is appropriate for novices and advanced researchers, discussing proofs of several results, including the automorphism group of bent functions, the lower bound for the number of bent functions, and more.