Blockchain technologies have been boosting the development of data-driven decentralized services in a wide range of fields. However, with the spirit of full transparency, many public blockchains expose all types of data to the public such as Ethereum. Besides, the on-chain persistence of large data is significantly expensive technically and economically. These issues lead to the difficulty of sharing fairly large private data while preserving attractive properties of public blockchains. Although direct encryption for on-chain data persistence can introduce confidentiality, new challenges such as key sharing, access control, and legal rights proving are still open. Meanwhile, cross-chain collaboration still requires secure and effective protocols, though decentralized storage systems such as IPFS bring the possibility for fairly large data persistence. In this paper, we propose Sunspot, a decentralized framework for privacy-preserving data sharing with access control on transparent public blockchains, to solve these issues. We also show the practicality and applicability of Sunspot by MyPub, a decentralized privacy-preserving publishing platform based on Sunspot. Furthermore, we evaluate the security, privacy, and performance of Sunspot through theoretical analysis and experiments.