Hardware Design of Polynomial Multiplication for Byte-Level Ring-LWE Based Cryptosystem

摘要

An ideal lattice is defined over a ring learning with errors (Ring-LWE) problem. Polynomial multiplication over the ring is the most computational and time-consuming block in lattice-based cryptography. This paper presents the first hardware design of the polynomial multiplication for LAC, one of the Round-2 candidates of the NIST PQC Standardization Process, which has byte-level modulus p=251. The proposed architecture supports polynomial multiplications for different degree n (n=512/1024/2048). For designing the scheme, we used the Vivado HLS compiler, a high-level synthesis based hardware design methodology, which is able to optimize software algorithms into actual hardware products. The design of the scheme takes 274/280/291 FFs and 204/217/208 LUTs on the Xilinx Artix-7 family FPGA, requested by NIST PQC competition for hardware implementation. Multiplication core uses only 1/1/2 pieces of 18Kb BRAMs, 1/1/1 DSPs, and 90/94/95 slices on the board. Our timing result achieved in an alternative degree n with 5.052/4.3985/5.133ns.