A Heuristic Algorithm for LPN Decoding with Improved Memory and Time Efficiency

Abstract

The LPN problem, which forms the basis of many lightweight and post-quantum cryptographic schemes, has recently received considerable attention. The solution to this problem typically involves two distinct phases, namely the reduce phase and the decode phase. While current research primarily focuses on the reduce phase, the most advanced decoding algorithm, FWHT, suffers from high computational costs in terms of time and space complexity. In this article, we propose a novel LPN decoding algorithm, GNS, which utilizes a heuristic approach to achieve significantly reduced memory and time complexity compared to FWHT. Experimental comparisons between the FWHT and GNS algorithms were conducted, with the computational results demonstrating that the proposed GNS algorithm is both efficient and superior to FWHT.