SIGNLINE: Digital signature scheme based on linear equations cryptosystem

TL;DR

This paper introduces SIGNLINE, a new digital signature scheme based on linear equations and logarithmic signatures, offering quantum resistance and scalable performance for various security levels.

Contribution

The paper presents a novel cryptosystem leveraging linear equations for logarithmic signatures, enhancing quantum security and efficiency over existing schemes.

Findings

Quantum security achieved by eliminating input-output mappings.

Public key sizes are 1, 1.5, and 2 KB for 128, 192, and 256-bit security levels.

Algorithm scales well with computational and memory resources.

Abstract

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.