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I'm looking for a way to prove that a certain amount of data was stored, through some easily verifiable piece of information. Similarly to how proof-of-work can prove through a hash that a certain amount of work was done to generate such hash.

I don't need this "proof" to tell me whether that data is currently stored somewhere, I'm just interested in proving that a certain amount of data was stored (anytime in the past) via some sort of hash or other piece of information.

For instance, imagine I have to prove to someone that I was able to store 5 GB. Doesn't matter where, I could use many different computers. One requirement I guess is that the proof should be easy to validate.

Any ideas?

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Proof of Storage is what you are looking for (also called Proof of Data Possession). The timestamp will prove that the data was stored at a certain time, as per your question. From Wikipedia:

...instead of showing that space is available for solving a puzzle, the prover shows that space is actually used to store a piece of data correctly at the time of proof.

See Storj, which is decentralized cloud storage.

The concept of Proof of Existence is another way. In Blockchain, it is done by cryptographic hashing. The amount of data and a time stamp are hashed and added to the public distributed ledger.

Simply by a process of Blockchain registering and timestamping, Proof of Existence enables anyone to anonymously and securely store an online distributed proof of existence for any document. Documents are not stored in a centralized database or in the Bitcoin Blockchain, so all data stays private. All that is stored is a cryptographic digest of the file, linked to the time in which the document was submitted.

Proof of Capacity (space is available for solving a puzzle) is another concept used in Blockchain, but this is merely related to what you are looking for. Basically, you allocate disk space and then prove that you have done so. Burstcoin (Signum) uses this.

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