Boolean Functions and Their Walsh Transforms

Boolean functions are fundamental building blocks for many cryptographic algorithms. This chapter introduces basic concepts and operations of Boolean functions, including Walsh transforms and basic cryptographic properties of Boolean functions.

[1]  Tore Herlestam,et al.  On Functions of Linear Shift Register Sequences , 1985, EUROCRYPT.

[2]  Joos Vandewalle,et al.  Propagation Characteristics of Boolean Functions , 1991, EUROCRYPT.

[3]  Willi Meier,et al.  Nonlinearity Criteria for Cryptographic Functions , 1990, EUROCRYPT.

[4]  Palash Sarkar,et al.  Cryptographically significant Boolean functions with five valued Walsh spectra , 2002, Theor. Comput. Sci..

[5]  Claude Carlet,et al.  Boolean Functions for Cryptography and Error-Correcting Codes , 2010, Boolean Models and Methods.

[6]  Amr M. Youssef,et al.  Comment on "Bounds on the Number of Functions Satisfying the Strict Avalanche Criterion" , 1996, Inf. Process. Lett..

[7]  Thomas W. Cusick,et al.  Boolean Functions Satisfying a Higher Order Strict Avalanche Criterion , 1994, EUROCRYPT.

[8]  Subhamoy Maitra Highly nonlinear balanced Boolean functions with good local and global avalanche characteristics , 2002, Inf. Process. Lett..

[9]  B. Sankur,et al.  Applications of Walsh and related functions , 1986 .

[10]  Joos Vandewalle,et al.  On the design of high speed self-synchronizing stream ciphers , 1992, [Proceedings] Singapore ICCS/ISITA `92.

[11]  Palash Sarkar A note on the spectral characterization of correlation immune Boolean functions , 2000, Inf. Process. Lett..

[12]  Claude E. Shannon,et al.  The synthesis of two-terminal switching circuits , 1949, Bell Syst. Tech. J..

[13]  Yixian Yang,et al.  Further enumerating boolean functions of cryptographic significance , 2004, Journal of Cryptology.

[14]  Christian Ronse Feedback Shift Registers , 1984, Lecture Notes in Computer Science.

[15]  Sheelagh Lloyd,et al.  Counting Functions Satisfying a Higher Order Strict Avalanche Criterion , 1990, EUROCRYPT.

[16]  Thomas W. Cusick,et al.  Bounds on the Number of Functions Satisfying the Strict Avalanche Criterion , 1996, Inf. Process. Lett..

[17]  S. Lloyd Counting binary functions with certain cryptographic properties , 2004, Journal of Cryptology.

[18]  Solomon W. Golomb,et al.  Shift Register Sequences , 1981 .

[19]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[20]  Kaoru Kurosawa,et al.  Design of SAC/PC(l) of Order k Boolean Functions and Three Other Cryptographic Criteria , 1997, EUROCRYPT.

[21]  Réjane Forré,et al.  A Fats Correlation Attack on Nonlinearly Feedforward Filtered Shift-Register Sequences , 1990, EUROCRYPT.

[22]  Babbage On the relevance of the strict avalanche criterion , 1990 .

[23]  Réjane Forré,et al.  The Strict Avalanche Criterion: Spectral Properties of Boolean Functions and an Extended Definition , 1988, CRYPTO.

[24]  Hideki Imai,et al.  A Recursive Construction Method of S-boxes Satisfying Strict Avalanche Criterion , 1990, CRYPTO.

[25]  Sheelagh Lloyd Balance, Uncorrelatedness and the Strict Avalanche Criterion , 1993, Discret. Appl. Math..

[26]  Kaoru Kurosawa,et al.  Generalization of Higher Order SAC to Vector Output Boolean Functions , 1996, ASIACRYPT.

[27]  Pascale Charpin,et al.  On Propagation Characteristics of Resilient Functions , 2002, Selected Areas in Cryptography.

[28]  Luke James O'Connor An analysis of product ciphers based on the properties of boolean functions , 1992 .

[29]  Jennifer Seberry,et al.  Improving the Strict Avalanche Characteristics of Cryptographic Functions , 1994, Inf. Process. Lett..