The Correlation of a Boolean Function with Its Variables
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
Computation of the Fast Walsh-Fourier Transform
IEEE Transactions on Computers
Counting all bent functions in dimension eight 99270589265934370305785861242880
Designs, Codes and Cryptography
Further constructions of resilient Boolean functions with very high nonlinearity
IEEE Transactions on Information Theory
Algebraic immunity for cryptographically significant Boolean functions: analysis and construction
IEEE Transactions on Information Theory
Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions
Finite Fields and Their Applications
| Hi-index | 7.29 |
The problem of counting Boolean functions with specified number s of Walsh coefficients @w in their Walsh spectrum is discussed in this paper. Strategies to solve this problem shall help solving many more problems related to desired cryptographic features of Boolean functions such as nonlinearity, resiliency, algebraic immunity, etc. In an attempt to study this problem, we present a new framework of solutions. We give results for |@w|=2^n^-^1 and for all s, in line with a previous work of Wu (1998) [12]. We also provide various results such as existence and construction for some s when @w=0, multiplicities for all @w and naive bounds on s for @w2^n^/^2.