  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 %.
