Linkable ring signature schemes play an important role in developing anonymous cryptocurrencies. Nevertheless, the inherent transparency of transaction information in traditional cryptocurrencies, especially blockchains, can lead to exposure of users’ identities, undermining anonymity. Moreover, the traditional cryptographic algorithms utilized by blockchain systems face challenges in effectively resisting quantum attacks. In this paper, we propose a novel NIZK-based linkable ring signature (ZLRS) scheme based on lattices to overcome these existing limitations and enhance the privacy aspects of blockchain transactions. Using the NIZK protocol with sub-linear communication complexity, the ZLRS scheme effectively protects the completeness and confidentiality of transaction messages. Moreover, we implement a blockchain transaction system based on the ZLRS scheme, thereby establishing an environment of complete anonymity and reinforcing security measures against quantum attacks for users within the blockchain system. Finally, an evaluation exhibits the efficacy of the ZLRS scheme in terms of efficiency and conciseness, showing its superiority when compared to similar schemes.