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.

翻译：本文对基于初等阿贝尔2-群上矩阵代数构建的LINEture后量子数字签名方案的安全参数进行了全面的密码学分析。我们研究了三个主要参数对密码强度的影响：首先是字长m（呈现二次方影响），其次是向量维度l，最后是会话密钥中子矩阵的数量q（呈现线性影响）。我们的分析揭示了参数l的双重特性：根据先前分析，它不影响对猜测攻击的抵抗能力；而对验证机制的深入研究表明，l建立了l×m比特的验证屏障。我们确立了阈值关系l < (q-1)×m，当低于此阈值时参数l将成为安全关键因素。为获得最大密码效率，提出了最优选择规则l ≈ (q-1)×m。文中提供了与NIST后量子密码标准的对比分析及实际参数建议。