Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for establishing a proof of storage over a specified period of time.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for establishing a proof of storage over a specified period of time.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for establishing a proof of storage over a specified period of time.

Abstract: One method includes: (a) forwarding an input challenge to a prover at a start time, the input challenge having a time-stamp; (b) receiving a proof of storage responsive to the input challenge from the prover; (c) generating a new input challenge based on the proof of storage and forwarding the new input challenge to the prover; (d) repeating steps (b) and (c) resulting in a final proof; (e) receiving a proof result based on the final proof, the proof result having a time-stamp; (f) determining that the time between the start time time-stamp and the proof result time-stamp is less than a specified period of time; and (g) determining a winning prover from a plurality of candidate provers where a probability of a candidate prover being a winning prover is proportional to the candidate prover's assigned storage which is indicated at least in part by the candidate miner's proof result.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for replication-related protocols for decentralized networks. One method includes: receiving, at a prover, a file to be stored; encoding the file to be stored using an encoding function to produce an encoded stored file wherein the time to encode using the encoding function takes at least a minimum encoding time; receiving a challenge at the prover; producing a proof at the prover in response to the challenge within a verify time period, wherein the proof is determined in part by decoding the encoded stored file and wherein the verify time period is less than the minimum encoding time; and taking an action (e.g., rewarding a storage miner/prover) in response to the proof.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for establishing a proof of storage over a specified period of time. One of the methods includes: (a) receiving, at a prover, an input challenge at a start time; (b) producing a proof responsive to the input challenge, wherein the proof is based at least in part on a proof of storage; (c) generating a new input challenge based at least in part on the proof; (d) repeating steps (b)-(c) a number of times resulting in a final proof; (e) receiving a proof result based at least in part on the final proof from the prover within a specified period of time from the start time; and (f) forwarding, to the verifier, the proof result.