Boolean Functions for Cryptography and Coding Theory

A complete, accessible book on single and multiple output Boolean functions in cryptography and coding, with recent applications and problems.

Claude Carlet (Author)

9781108473804, Cambridge University Press

Hardback, published 7 January 2021

574 pages
26 x 18.1 x 3.6 cm, 1.2 kg

Boolean functions are essential to systems for secure and reliable communication. This comprehensive survey of Boolean functions for cryptography and coding covers the whole domain and all important results, building on the author's influential articles with additional topics and recent results. A useful resource for researchers and graduate students, the book balances detailed discussions of properties and parameters with examples of various types of cryptographic attacks that motivate the consideration of these parameters. It provides all the necessary background on mathematics, cryptography, and coding, and an overview on recent applications, such as side channel attacks on smart cards, cloud computing through fully homomorphic encryption, and local pseudo-random generators. The result is a complete and accessible text on the state of the art in single and multiple output Boolean functions that illustrates the interaction between mathematics, computer science, and telecommunications.

1. Introduction to cryptography, codes, Boolean and vectorial functions
2. Generalities on Boolean and vectorial functions
3. Boolean functions, vectorial functions and cryptography
4. Boolean functions, vectorial functions and error correcting codes
5. Functions with weights, Walsh spectra and nonlinearities easier to study
6. Bent functions and plateaued functions
7. Correlation immune and resilient functions
8. Functions satisfying SAC, PC, EPC, or having good GAC
9. Algebraic immune functions
10. Particular classes of Boolean functions
11. Highly nonlinear vectorial functions with low differential uniformity
12. Recent uses of Boolean and vectorial functions and related problems
13. Open questions
14. Appendix.

Subject Areas: Computer networking & communications [UT], Combinatorics & graph theory [PBV], Coding theory & cryptology [GPJ]