The paper explores a novel cryptosystem for digital signatures based on linear equa-tions for logarithmic signatures. A logarithmic signature serves as a fundamental cryptographic primitive, characterized by properties such as nonlinearity, non-commutability, unidirectionality, and key-dependent factorability. The proposed cryptosystem ensures the secrecy of logarithmic signatures through its foundation in linear equations. Quantum security is achieved by eliminating any possible mapping between the input and output of the logarithmic signature, thereby rendering Grover's quantum attack ineffective. The public key sizes for the NIST security levels of 128, 192, and 256 bits are 1, 1.5, and 2 KB, respectively. The algorithm demonstrates scalability concerning computational costs, memory usage, and hardware limitations without compromising security. Its primary operation involves bitwise XOR over logarithmic arrays of 8, 16, 32, and 64 bits.

翻译：本文探讨了一种基于对数签名的线性方程数字签名新型密码体制。对数签名作为一种基本的密码学原语，具有非线性、不可交换性、单向性以及密钥依赖可分解性等特性。所提出的密码体制通过基于线性方程的设计，确保了对数签名的保密性。通过消除对数签名输入与输出之间任何可能的映射关系，该方案实现了量子安全性，从而使Grover量子攻击失效。在NIST安全级别为128、192和256比特时，其公钥大小分别为1、1.5和2 KB。该算法在计算成本、内存占用和硬件限制方面展现出良好的可扩展性，且不牺牲安全性。其主要运算涉及对8、16、32及64比特对数数组进行按位异或操作。