Hiding Higher-Order Univariate Leakages by Shuffling Polynomial Masking Schemes: A More Efficient, Shuffled, and Higher-Order Masked AES S-box

Polynomial masking is a glitch-resistant and higher-order masking scheme based upon Shamir's secret sharing scheme and multi-party computation protocols. Polynomial masking was first introduced at CHES 2011, while a 1st-order implementation of the AES S-box on FPGA was presented at CHES 2013. In this latter work, the authors showed a 2nd-order univariate leakage by side-channel collision analysis on a tuned measurement setup. This negative result motivates the need to evaluate the performance, area-costs, and security margins of combined \shuffled\ and higher-order polynomially masking schemes to counteract trivial univariate leakages. In this work, we provide the following contributions: first, we introduce additional principles for the selection of efficient addition chains, which allow for more compact and faster implementations of cryptographic S-boxes. Our 1st-order AES S-box implementation requires approximately 27% less registers, 20% less clock cycles, and 5% less random bits than the CHES 2013 implementation. Then, we propose a lightweight shuffling countermeasure, which inherently applies to polynomial masking schemes and effectively enhances their univariate security at negligible area expenses. Finally, we present the design of a \combined\ \shuffled\ \and\ higher-order polynomially masked AES S-box in hardware, while providing ASIC synthesis and side-channel analysis results in the Electro-Magnetic (EM) domain.