Boolean Functions for Cryptography and Coding Theory

« 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. »-- Quatrième de couverture Copyright Contents Preface Acknowledgments Notation 1 Introduction to cryptography, codes, Boolean, and vectorial functions 1.1 Cryptography 1.2 Error-correcting codes 1.3 Boolean functions 1.4 Vectorial functions 2 Generalities on Boolean and vectorial functions 2.1 A hierarchy of equivalence relations over Boolean and vectorial functions 2.2 Representations of Boolean functions and vectorial functions 2.3 The Fourier–Hadamard transform and the Walsh transform 2.4 Fast computation of S-boxes 3 Boolean functions, vectorial functions, and cryptography 3.1 Cryptographic criteria (and related parameters) for Boolean functions 3.2 Cryptographic criteria for vectorial functions in stream and block ciphers 3.3 Cryptographic criteria and parameters for vectorial functions in stream ciphers 3.4 Cryptographic criteria and parameters for vectorial functions in block ciphers 3.5 Search for functions achieving the desired features 3.6 Boolean and vectorial functions for diffusion, secret sharing, and authentication 4 Boolean functions, vectorial functions, and error-correcting codes 4.1 Reed–Muller codes 4.2 Other codes related to Boolean functions 5 Functions with weights, Walsh spectra, and nonlinearities easier to study 5.1 Affine functions and their combinations 5.2 Quadratic functions and their combinations 5.3 Cubic functions 5.4 Indicators of flats 5.5 Functions admitting (partial) covering sequences 5.6 Functions with low univariate degree and related functions 6 Bent functions and plateaued functions 6.1 Bent Boolean functions 6.2 Partially-bent and plateaued Boolean functions 6.3 Bent4 and partially-bent4 functions 6.4 Bent vectorial functions 6.5 Plateaued vectorial functions 7 Correlation immune and resilient functions 7.1 Correlation immune and resilient Boolean functions 7.2 Resilient vectorial Boolean functions 8 Functions satisfying SAC, PC, and EPC, or having good GAC 8.1 PC(l) criterion 8.2 PC(l) of order k and EPC(l) of order k criteria 8.3 Absolute indicator 9 Algebraic immune functions 9.1 Algebraic immune Boolean functions 9.2 Algebraic immune vectorial functions 10 Particular classes of Boolean functions 10.1 Symmetric functions 10.2 Rotation symmetric, idempotent, and other similar functions 10.3 Direct sums of monomials 10.4 Monotone functions 11 Highly nonlinear vectorial functions with low differential uniformity 11.1 The covering radius bound; bent/perfect nonlinear functions 11.2 The Sidelnikov–Chabaud–Vaudenay bound 11.3 Almost perfect nonlinear and almost bent functions 11.4 The known infinite classes of AB functions 11.5 The known infinite classes of APN functions 11.6 Differentially uniform functions 12 Recent uses of Boolean and vectorial functions and related problems 12.1 Physical attacks and related problems on functions and codes 12.2 Fully homomorphic encryption and related questions on Boolean functions 12.3 Local pseudorandom generators and related criteria on Boolean functions 12.4 The Gowers norm on pseudo-Boolean functions 13 Open questions 13.1 Questions of general cryptography dealing with functions 13.2 General questions on Boolean functions and vectorial functions 13.3 Bent functions and plateaued functions 13.4 Correlation immune and resilient functions 13.5 Algebraic immune functions 13.6 Highly nonlinear vectorial functions with low differential uniformity 13.7 Recent uses of Boolean and vectorial functions and related problems 14 Appendix: finite fields 14.1 Prime fields and fields with four, eight, and nine elements 14.2 General finite fields: construction, primitive element 14.3 Representation (additive and multiplicative); trace function 14.4 Permutations on a finite field 14.5 Equations over finite fields References Index "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"-- Provided by publisher This complete and accessible survey of Boolean functions for cryptography and coding, written for researchers and graduate students, balances all necessary background with comprehensive state of the art coverage, and tackles recent problems and applications like side channel attacks, Gowers norm, and cloud computing.