Generalized Feistel Ciphers for Efficient Prime Field Masking

A recent work from Eurocrypt 2023 suggests that prime-field masking has excellent potential to improve the efficiency vs. security tradeoff of masked implementations against side-channel attacks, especially in contexts where physical leakages show low noise. We pick up on the main open challenge that this seed result leads to, namely the design of an optimized prime cipher able to take advantage of this potential. Given the interest of tweakable block ciphers with cheap inverses in many leakage-resistant designs, we start by describing the FPM (Feistel for Prime Masking) family of tweakable block ciphers based on a generalized Feistel structure. We then propose a first instantiation of FPM, which we denote as small-pSquare. It builds on the recent observation that the square operation (which is non-linear in Fp) can lead to masked gadgets that are more efficient than those for multiplication, and is tailored for efficient masked implementations in hardware. We analyze the mathematical security of the FPM family of ciphers and the small-pSquare instance, trying to isolate the parts of our study that can be re-used for other instances. We additionally evaluate the implementation features of small-pSquare by comparing the efficiency vs. security tradeoff of masked FPGA circuits against those of a state-of-the art binary cipher, namely SKINNY, confirming significant gains in relevant contexts.