2024/05/25 by Gennady Khalimov, Yevgen Kotukh, Khalimov, Gennady +7
Computer Science · #Chaos-based Image/Signal Encryption #Cryptography and Data Security #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2405.16227
openalex publication_date 2024/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.