Boolean Functions for Cryptography and Coding Theory

A focused survey of Boolean functions in cryptography and coding theory

Boolean Functions for Cryptography and Coding Theory is a substantial research monograph by Claude Carlet that gathers the core theory, major results, and important applications of Boolean and vectorial functions in characteristic 2. It is written with researchers in mind, but the opening material and explanatory structure make it approachable for readers with a solid background in linear algebra and general mathematics.

The book’s central strength is its range. Rather than treating Boolean functions as an isolated topic, it shows how they sit at the intersection of cryptography, coding theory, and finite-field mathematics. Readers move through a carefully sequenced account of representations, transforms, cryptographic criteria, error-correcting codes, bent and plateaued functions, correlation immunity, algebraic immunity, and highly nonlinear vectorial functions.

What the book covers

• Foundations in cryptography, codes, Boolean functions, and vectorial functions
• General methods such as Fourier–Hadamard and Walsh transforms
• Cryptographic criteria for Boolean and vectorial functions
• Connections with Reed–Muller codes and other coding-theory structures
• Special classes of functions, including bent, plateaued, resilient, and algebraically immune functions
• Recent uses in side-channel resistance, fully homomorphic encryption, and local pseudorandom generators

Why it stands out

This is not a lightweight introduction. It is a revised and expanded monograph that aims to be as complete as possible within book form, while still giving proofs where they illuminate the theory. The result is a reference work that is especially valuable for graduate students, researchers, and advanced readers who want both the mathematical framework and the cryptographic motivation behind these functions.

A book for serious study 📘

If you work in cryptography, coding theory, discrete mathematics, or related areas of computer science, this title offers a clear route through a large and technically rich field. It is particularly useful when you want one volume that ties together definitions, criteria, constructions, and modern applications rather than scattering that material across papers.