A Distributed Weighted Threshold Signature with Packing for Weight-Differentiated Blockchains

In blockchain systems, threshold signatures are widely employed for their ability to distribute trust among multiple participants, thereby enhancing both security and decentralization. However, existing threshold signature schemes encounter several challenges in blockchain scenarios. First, they fail to accommodate weight-differentiated environments, such as proof-of-stake (PoS) systems. Second, key generation in most existing schemes usually depends on a trusted third-party dealer. Finally, their efficiency remains limited in large-scale applications. To overcome these issues, we propose a distributed weighted Schnorr threshold signature scheme with a packing property. The proposed scheme removes the need for a trusted dealer through distributed key generation (DKG) and integrates packed secret sharing with a hyper-invertible matrix to enable the efficient generation of multiple threshold signatures in a single execution. Moreover, by adopting the concept of a party controlling multiple evaluation points, the scheme naturally achieves weighted signing functionality. Security evaluations indicate that the proposed scheme effectively resists forgery attacks, and empirical experiments further verify its feasibility in practice. In general, our scheme achieves high efficiency and security, making it particularly suitable for PoS and other weight-differentiated blockchain systems.