Private blockchain networks are used by enterprises to manage decentralized processes without trusted mediators and without exposing their assets publicly on an open network like Ethereum. Yet external parties that cannot join such networks may have a compelling need to be informed about certain data items on their shared ledgers along with certifications of data authenticity; e.g., a mortgage bank may need to know about the sale of a mortgaged property from a network managing property deeds. These parties are willing to compensate the networks in exchange for privately sharing information with proof of authenticity and authorization for external use. We have devised a novel and cryptographically secure protocol to effect a fair exchange between rational network members and information recipients using a public blockchain and atomic swap techniques. Using our protocol, any member of a private blockchain can atomically reveal private blockchain data with proofs in exchange for a monetary reward to an external party if and only if the external party is a valid recipient. The protocol preserves confidentiality of data for the recipient, and in addition, allows it to mount a challenge if the data turns out to be inauthentic. We also formally analyze the security and privacy of this protocol, which can be used in a wide array of practical scenarios.