2019/03/13 by Jinjin Chai, Zilong Wang, Chai, Jinjin +5
Computer Science · Engineering · #06E30 #42A38 #94A60 #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1903.05351
openalex publication_date 2019/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Correlation-immune (CI) multi-output Boolean functions have the property of keeping the same output distribution when some input variables are fixed. Recently, a new application of CI functions has appeared in the system of resisting side-channel attacks (SCA). In this paper, three new methods are proposed to characterize the t th-order CI multi-output Boolean functions (n-input and m-output). The first characterization is to regard the multi-output Boolean functions as the corresponding generalized Boolean functions. It is shown that a generalized Boolean functions fg is a t th-order CI function if and only if the Walsh transform of fg defined here vanishes at all points with Hamming weights between 1 and t. Compared to the previous Walsh transforms of component functions, our first method can reduce the computational complexity from (2m-1)∑tj=1\binomnj to m∑tj=1\binomnj. The last two methods are generalized from Fourier spectral characterizations. Especially, Fourier spectral characterizations are more efficient to characterize the symmetric multi-output CI Boolean functions.