An iterative correction method for practically LPN solving

Abstract

The LPN problem, lying at the core of many cryptographic constructions for lightweight and post-quantum cryptography, has recently received much attention. Accordingly, BKW, Gauss algorithm, and their improved or hybrid variants have been proposed to solve the LPN problem. In this paper, we propose an intelligent method for LPN solving from a wholly new perspective by iterative correcting the secret, which can successfully reduce the dimension of the LPN problem. While the challenge is that there are so many independent secret variables of the given checking parity equations with noise in LPN problems, a set of rules should be developed to effectively direct and correct the secret. To solve this problem, we skillfully introduce the genetic algorithm to simulate the process of iterative correction and further add vaccination technology to guide and speed up the iterative process. Owing to the small memory and data consumption of our algorithm, we conducted experiments and, for the first time, solved the largest practical LPN(256,1/8) instance in 30 days, which shows the superiority of our method. To the best of our knowledge, this is the first time the iterative correction method and the intelligent algorithm have been successfully applied to LPN problems.