A Low-Cost Local Masking Radix-4 NTT Against Soft-Analytical Side-Channel Attacks

The number theoretic transform (NTT) is essential for accelerating polynomial multiplication in lattice-based cryptography. However, it is vulnerable to soft-analytical side-channel attacks (SASCAs). Although local masking countermeasure provides theoretical resistance against such attacks, its direct implementation in Radix-4 NTT architecture leads to more than a 4 times increase in modular multiplications, resulting in substantial hardware overhead. To address this challenge, we propose the modular multiplication parallel mask sharing (MMPMS) scheme, which optimizes the modular multiplication parallelism of the Radix-4 butterfly units and shares random twiddle factors, thereby achieving a balance between hardware overhead and security. Then, we construct a complete local masking NTT/INTT algorithm and efficiently implement it on the Artix-7 field-programmable gate array (FPGA). Experimental results show that compared with the state-of-the-art local masking NTT, our scheme reduces the equivalent area and ATP overhead by more than 8.24 times and 6.74 times, respectively. In addition, a nonspecifict-test analysis indicates no significant side-channel leakage.