Entangled encodings and data entanglement

We introduce a new cryptographic tool that we dub entangled encoding scheme. An entangled encoding allows a set of users to encode their files into a single digital "clew" such that the following two properties are satisfied. (1) Privacy: The resulting encoding reveals no information about the files contained inside the clew; (2) All-or-nothing integrity (AONI): It is impossible to modify or delete any significant part of the encoding without affecting all files contained in the clew. We provide a concrete instantiation of an entangled encoding scheme with unconditional security, based on polynomial interpolation over a finite field. Finally, we show an appealing application of entangled encodings to the setting of secure cloud storage, where a set of users store their files at a potentially malicious cloud provider and want to ensure that their data remain safe and unblemished.