Security Parameter Analysis of the LINEture Post-Quantum Digital Signature Scheme

Abstract: This paper presents a comprehensive cryptographic analysis of the security parameters of the LINEture post-quantum digital signature scheme, which is constructed using matrix algebra over elementary abelian 2-groups. We investigate the influence of three principal parameters. First, the word size m (exhibiting quadratic impact), the second is a vector dimension l, and the third is a number of submatrices in the session key q (exhibiting linear impact) on cryptographic strength. Our analysis reveals a dualistic nature of the parameter l. According to the previous analysis, it does not affect resistance to guessing attacks. A deeper examination of the verification mechanism demonstrates that l establishes a kind of verification barrier of l times m bits. We establish the threshold relationship l less q minus 1 times m, below which parameter l becomes security-critical. The optimal selection rule l near q minus 1 times m is proposed for maximum cryptographic efficiency. Comparative analysis with NIST PQC standards and practical parameter recommendations are provided.