Improved Lattice-Based Attack on Mersenne Low Hamming Ratio Search Problem

This paper investigates the Mersenne number-based AJPS cryptosystem, with a particular focus on its associated hard problem. Specifically, we aim to enhance the existing lattice-based attack on the Mersenne low Hamming ratio search problem. Unlike the previous approach of directly employing lattice reduction algorithm, we apply the lattice-based method to solving polynomial equations derived from the above problem. We extend the search range for vulnerabilities in weak keys and increase the success probability of key recovery attack. To validate the efficacy and accuracy of our proposed improvements, we conduct numerical computer experiments. These experiments serve as a concrete validation of the practicality and effectiveness of our improved attack.