On the Signal-to-Noise Ratio for Boolean Functions

Abstract

The notion of the signal-to-noise ratio (SNR), proposed by Guilley, et al. in 2004, is a property that attempts to characterize the resilience of (n,m)-functions F=(f₁,...,f_m) (cryptographic S-boxes) against differential power analysis. But how to study the signal-to-noise ratio for a Boolean function still appears to be an important direction. In this paper, we give a tight upper and tight lower bounds on SNR for any (balanced) Boolean function. We also deduce some tight upper bounds on SNR for balanced Boolean function satisfying propagation criterion. Moreover, we obtain a SNR relationship between an n-variable Boolean function and two (n-1)-variable decomposition functions. Meanwhile, we give SNR(f⊞g) and SNR(f⊡g) for any balanced Boolean functions f,g. Finally, we give a lower bound on SNR(F), which determined by SNR(f_i) (1≤i≤m), for (n,m)-function F=(f₁,f₂,…,f_m).