A Scalable and Efficient Architecture for Binary Polynomial Multiplication in BIKE Utilizing Inter-/Inner-Wise Sparsity and Block-by-Block Pipeline

Efficient binary polynomial multiplication (BPM) implementations are crucial for the practical deployment of bit flipping key encapsulation (BIKE) postquantum cryptography (PQC) due to its computation-intensive nature. To speed up BPM, this brief proposes a scalable and efficient architecture. The proposed architecture employs a novel blockwise sparsity algorithm, which segments sparse polynomials into blocks and leverages interblock and inner block sparsity to eliminate invalid computations, thereby significantly reducing computational operations. Moreover, a scalable block-by-block pipeline structure, along with a multibank random access memory (RAM) for sparse polynomials, is designed to effectively process blocks, resulting in substantial enhancement in performance. Experimental results on Xilinx Artix-7 Field-Programmable Gate Arrays (FPGAs) demonstrate significant performance superiority on the proposed architecture, compared with existing approaches. Across different bandwidth settings of 16, 32, 64, or 128, our design can achieve <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.5\times \sim 35.1\times $ </tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.9\times \sim 78.8\times $ </tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.5\times \sim 112.7\times $ </tex-math></inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.5\times \sim 164.2\times $ </tex-math></inline-formula> speedup, respectively. Compared with state-of-the-art works, our design achieves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.8\times \sim 152.0\times $ </tex-math></inline-formula> improvements in area efficiency.