Protocols for decentralized networks

A method comprising:

• receiving, at a verifier, the frequency of input challenges that a prover will receive;
• receiving at a verifier, an output proof, the output proof having been generated by steps comprising:
• receiving data at a prover;
• performing a seal operation on the data;
• receiving, at the prover, an initial input challenge;
• producing an output proof, wherein producing the output proof comprises:
• producing an initial proof responsive to the initial input challenge, the initial proof proving that the prover is storing specified data;
• generating a new input challenge based at least in part on the initial proof,
• producing a new proof responsive to the new input challenge, the new proof proving that the prover is storing the specified data;
• and
• repeating the generating step and the producing a new proof responsive to the new input challenge step a specified number of times resulting in an output proof, wherein the generating a new input challenge is based at least in part on a most recent new proof, and wherein performing the seal operation is several orders of magnitude slower than producing an output proof,
• receiving the output proof at the verifier;
• and
• verifying, at the verifier, the output proof.

A system comprising:

• one or more computers and one or more storage devices on which are stored instructions that are operable, when executed by the one or more computers, to cause the one or more computers to perform operations comprising:
• receiving, at a verifier, the frequency of input challenges that a prover will receive;
• receiving at a verifier, an output proof, the output proof having been generated by steps comprising:
• receiving, at a prover, an initial input challenge;
• producing, at the prover, an output proof proving that the prover has access to specified data for a specified time, wherein producing the output proof comprises:
• producing, at the prover, an initial proof responsive to the initial input challenge, the initial proof proving that the prover is storing specified data;
• generating, at the prover, a new input challenge based at least in part on the initial proof;
• producing, at the prover, a new proof responsive to the new input challenge, the new proof proving that the prover is storing the specified data;
• and
• repeating, at the prover, the generating step and the producing a new proof responsive to the new input challenge step a number of times, the repeating step generating sequential proofs of storage to determine time of storage, wherein each generating step is based at least in part on a most recent new proof, and
• receiving the output proof at the verifier;
• and
• verifying, at the verifier, the output proof.