Power Efficiency of S-Boxes: From a Machine-Learning-Based Tool to a Deterministic Model

Abstract

Designing cryptographically good and power-efficient $4\times 4$ S-boxes is a challenging problem in the era of lightweight cryptography. Although the optimal cryptographic properties are easy to determine, verifying the power efficiency of an S-box is nontrivial. The conventional approach of determining the power consumption using commercially available CAD tools is highly time-consuming, which becomes formidable while dealing with a large pool of S-boxes. This mandates the development of automation that should quickly characterize the power efficiency from the Boolean function representation of an S-box. In this paper, we present a supervised machine-learning-assisted automated framework to resolve the problem for $4\times 4$ S-boxes, which turns out to be 14 times faster than the traditional approach. The key idea is to extrapolate the knowledge of literal counts, AND–OR–NOT gate counts in the sum-of-products (SOP) form of the underlying Boolean functions to predict the dynamic power efficiency. We demonstrate the effectiveness of our framework by reporting on a set of power-efficient (involutive) optimal S-boxes from a large set of S-boxes. We also develop a deterministic model using results obtained from supervised learning to predict the dynamic power of an S-box that can be used in an evolutionary algorithm to generate cryptographically good and low-power S-boxes.