The recent decades have witnessed the rapid development of the satellite technology and low-earth-orbit (LEO) satellite networks. However, future satellite networks will involve multiple institutions and platforms, making it a real challenge to protect user privacy during the information dissemination across these management entities. To this end, this paper proposes a Blockchain-based Privacy Protection Protocol using Smart Contracts (BPPSC) which solves the problem of privacy protection under cross-platform information dissemination scenarios. First of all, a four-stage dissemination process with smart contracts is designed, i.e., the user registration stage, information upload stage, information dissemination stage, and the termination stage. Using smart contracts not only makes the information dissemination more controllable, but also improves the Information query efficiency. Secondly, in the dissemination process, the scope of dissemination is limited based on the user privacy preference, so as to improve the security of user information dissemination. Thirdly, we analyze the security and resistance of the proposed method against the malicious information owner attack, malicious disseminator attack, malicious service platform attack and man-in-the-middle attack. Finally, through the simulation results of the Ethereum blockchain test network and NS2 simulator, the efficacy and security of the proposed privacy protection method are verified, and the response delay of on-chain transactions is significantly reduced compared with existing popular methods such as the APPF protocol.