In this study, a new data-sharing method is proposed that uses a private InterPlanetary File System—a decentralized storage system operated within a closed network—to distribute data to external entities while making its authenticity verifiable. Among the two operational modes of IPFS, public and private, this study focuses on the method for using private IPFS. Private IPFS is not open to the general public; although it poses a risk of data tampering when distributing data to external parties, the proposed method ensures the authenticity of the received data. In particular, this method applies a type of zero-knowledge proof, namely, the Groth16 protocol of zk-SNARKs, to ensure that the data corresponds to the content identifier in a private IPFS. Moreover, the recipient’s name is embedded into the distributed data to prevent unauthorized secondary distribution. Experiments confirmed the effectiveness of the proposed method for an image data size of up to 120 × 120 pixels. In future studies, the proposed method will be applied to larger and more diverse data types.