Improved Plantard Arithmetic for Lattice-based Cryptography

This paper presents an improved Plantard’s modular arithmetic (Plantard arithmetic) tailored for Lattice-Based Cryptography (LBC). Based on the Plantard arithmetic, we present faster implementations of two LBC schemes, Kyber and NTTRU, running Cortex-M4. The intrinsic advantage is that one multiplication can be saved from a constant. However, original not very practical in schemes because limitation unsigned input range. In this paper, improve customize it existing with theoretical proof. only inherits its aforementioned but also accepts signed inputs, produces output, enlarges range compared design. Moreover, state-of-the-art Montgomery has larger smaller output range, which allows better lazy reduction strategies during NTT/INTT implementation current schemes. All these merits make possible to replace some platforms. After applying novel method NTTRU using 16-bit NTT Cortex-M4 devices, show proposed design outperforms known fastest uses Barrett arithmetic. Specifically, implementation, results speedup 25.02% 18.56% INTT, respectively. Compared reference our INTT achieve by 83.21% 78.64%, As KEM set new speed records