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We consider the problem of sharing sensitive or valuable files across users while partially relying on a common, untrusted third-party, e.g., a Cloud Storage Provider (CSP). Although users can rely on a secure peer-to-peer (P2P) channel for file sharing, this introduces potential delay on the data transfer and requires the sender to remain active and connected while the transfer process occurs. Instead of using the P2P channel for the entire file, users can upload information about the file on a common CSP and share only the essential information that enables the receiver to download and recover the original file. This paper introduces Bifrost, an innovative file sharing system inspired by recent results on dual deduplication. Bifrost achieves the desired functionality and simultaneously guarantees that (1) the CSP can efficiently compress outsourced data; (2) the secure P2P channel is used only to transmit short, but crucial information; (3) users can check for data integrity, i.e., detect if the CSP alters the outsourced data; and (4) only the sender (data owner) and the intended receiver can access the file after sharing, i.e., the cloud or no malicious adversary can infer useful information about the shared file. We analyze compression and bandwidth performance using a proof-of-concept implementation. Our experiments show that secure file sharing can be achieved by sending only 650 bits on the P2P channel, irrespective of file size, while the CSP that aids the sharing can enjoy a compression rate of 86.9 %.