MS-LW-TI: Primitive-Based First-Order Threshold Implementation for 4 × 4 S-boxes

Threshold implementation (TI) is a lightweight countermeasure against side-channel attacks when glitches happen. As to masking schemes, an S-box is the key part to protection. In this paper, we propose a general first-order lightweight TI scheme for 4 × 4 S-boxes and name it as MiniSat-lightweight-threshold implementation (MS-LW-TI). First, we use MiniSat to optimally decompose an S-box into the least number of three different logic gate operations, AND, OR, and XOR. Among these operations, we define two primitives and the extension of two primitives for TI design. Furthermore, we prove that the primitives and their extensions strictly comply with the security properties. Finally, we implement MS-LW-TI on Xilinx Spartan-6 Field Programmable Gate Array (FPGA) to show that the S-boxes of PRESENT, GIFT, and PICCOLO consume only 17, 15, and 13 look-up-tables (LUTs), 16, 9, and 16 flip-flops (FFs), 6, 5, and 6 slices, respectively. Compared with the existing lightweight TI design, our TI for PRESENT S-box has a 22%, 38%, and 25% reduction of LUTs, FFs, and slices to the design by Shahmirzadi and Moradi at IACR Transactions on Cryptographic Hardware and Embedded Systems (TCHES) 2021, and our TI for GIFT S-box has a 6%, 25%, and 28% reduction of LUTs, FFs, and slices to the design by Jati et al., which is the smallest.