Performance-Optimized Group Signature Schemes Based on the Discrete Logarithm Problem and Bilinear Maps

Abstract

Group signature schemes are essential cryptographic primitives that enable authorized members to sign messages on behalf of a group while maintaining anonymity against verifiers. However, many existing schemes face challenges regarding computational efficiency, public key scalability, and robust security against coalition attacks. This study addresses these limitations by proposing three novel group signature constructions. The first scheme is based on the Discrete Logarithm Problem (DLP) and focuses on providing high-speed verification. The second scheme introduces an identitybased (ID-based) structure utilizing both factoring and DLP to simplify key management. The third scheme leverages the algebraic properties of bilinear pairings to create an ID-based group signature that achieves short signature lengths and resists key escrow issues. Formal security analysis demonstrates that the proposed schemes satisfy critical requirements, including unforgetability, anonymity, linkability, traceability, and coalition resistance. Furthermore, a performance comparison indicates that the proposed structures significantly reduce computational complexity in signature generation and verification phases compared to established models like the Lee and Wang-Fu schemes. These findings suggest that the integrated approach of using DLP and bilinear pairings offers a scalable and secure framework suitable for modern digital infrastructure, including e-voting and anonymous electronic tendering systems.