CBM-TI: Code-Based Masking against Glitches by Hybridization with Threshold Implementation

Code-Based Masking (CBM) has been introduced to enhance high-order Boolean masking by increasing its resistance order via further decorrelating the coordinates of each symbol involved in the computation. Additionally, CBM enables cost amortization and fault detection. Notably, as demonstrated at CHES 2024, CBM facilitates the computation of provably masked operations under the Strong Non-Interference (SNI) security assumption with quasi-linear complexity. On the other hand, Threshold Implementation (TI) serves as an extension of Boolean masking, armoring it against combinational hazards. In this article, we show that merits of CBM and TI can be combined, paving the way to more secure hardware (high-order) masked implementations. We demonstrate CBM-TI, which is proven secure as well under SNI assumption and security when glitches worsen the leakage model.The security of CBM-TI is studied in a n-share setting, where n = 3 (minimal random splitting order required for TI). We analyzed CBM-TI in simulation and in real hardware (FPGA) to validate its security property. Leveraging high-order T-test leakage detection tool, we show that CBM-TI is endowed with higher-order security. Namely, TI leaks at order d = 3, whereas CBM-TI does not. We study several CBM-TI variants and show that the smallest leaking order of CBM-TI can be tuned to be as high as 7. This represents a significant progress over TI as each marginally improved order translates into exponentially more traces to attack the implementation.