A New Sieving-Style Information-Set Decoding Algorithm

The problem of decoding random codes is a fundamental problem for code-based cryptography, including recent code-based candidates in the NIST post-quantum standardization process. In this paper, we present a novel Sieving-style Information-set Decoding algorithm, addressing the task of solving the syndrome decoding problem. Our approach involves maintaining a list of weight-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2p$ </tex-math></inline-formula> solution vectors to a partial syndrome decoding problem and then creating new vectors by identifying pairs of vectors that collide in p positions. By gradually increasing the parity-check condition by one and repeating this process iteratively, we find the final solution(s). We show that our novel algorithm performs better than other ISDs in the memory-restricted scenario when applied to McEliece. Notably, in the case of problem instances with very low relative weight, the sieving approach uses significantly less memory compared to other ISD algorithms while being competitive in terms of performance.