An efficient multivariate linkable group signature scheme

Group signature schemes are vital for privacy-preserving applications, such as electronic voting and electronic ten-dering, where anonymity, traceability, and linkability are essential. However, existing multivariate group signature schemes face limitations, including large signature sizes, high computational cost, and suboptimal use of the Multivariate Quadratic (MQ) prob-lem's complexity. This paper proposes an enhanced Multivariate Linkable Group Signature Scheme (MLGS), ensuring stronger security by leveraging an under-determined MQ system. The scheme introduces compact signatures, scalable batch verification, and modular arithmetic optimizations, significantly reducing computational and storage overhead. These improvements make the scheme not only quantum resistant but also practical for large-scale applications such as blockchain-based voting and tendering. Benchmarking and theoretical analysis demonstrate the security, efficiency, and scalability of the proposed scheme, highlighting its potential to address the gaps in existing multivariate schemes.