Publicly verifiable proofs of space

1. An apparatus, comprising:

at least one processing device comprising a processor coupled to a memory, the at least one processing device implementing a verifying entity of a decentralized system configured:

to receive information associated with at least one ledger entry of a distributed ledger of the decentralized system;

to verify at least a portion of one or more computations associated with the received information;

to generate evidence of at least one error in said at least a portion of the one or more computations associated with the received information; and

to associate the generated evidence with a public key of the verifying entity;

wherein the decentralized system comprises a proof of space based mining system, and wherein said at least one ledger entry of the distributed ledger comprises at least one proof of space for the proof of space based mining system;

wherein the verifying entity is further configured to provide, to one or more mining operator entities in the proof of space based mining system, a proof of knowledge of said at least one error; and

wherein submission of the proof of knowledge of said at least one error entitles the verifying entity to a bounty, the bounty comprising at least a fraction of a value obtained by successful mining in the proof of space based mining system.

2. The apparatus of claim 1 wherein the public key is associated with a secret key, the secret key being associated with a financial capability of the verifying entity.

3. The apparatus of claim 1 wherein the verifying entity comprises a bounty hunter entity in the proof of space based mining system, the bounty hunter entity being configured to verify said at least a portion of the one or more computations associated with the received information to enforce one or more policies in the proof of space based mining system.

4. The apparatus of claim 1 wherein the proof of knowledge of said at least one error comprises a proof of knowledge of a secret key associated with the public key.

5. An apparatus, comprising:

at least one processing device comprising a processor coupled to a memory, the at least one processing device implementing a verifying entity of a decentralized system configured:

to receive information associated with at least one ledger entry of a distributed ledger of the decentralized system;

to verify at least a portion of one or more computations associated with the received information;

to generate evidence of at least one error in said at least a portion of the one or more computations associated with the received information; and

to associate the generated evidence with a public key of the verifying entity;

wherein the decentralized system comprises a proof of space based mining system, and wherein said at least one ledger entry of the distributed ledger comprises at least one proof of space for the proof of space based mining system;

wherein the verifying entity is further configured to provide, to one or more mining operator entities in the proof of space based mining system, a proof of knowledge of said at least one error; and

wherein providing the proof of knowledge of said at least one error comprises:

submitting, at a first point in time, a first transaction to the distributed ledger comprising the public key and an encryption of the generated evidence; and

submitting, at a second point in time, a second transaction to the distributed ledger comprising a decryption key for decrypting the encryption of the generated evidence in the first transaction.

6. The apparatus of claim 1 wherein the one or more computations associated with the received information comprise a plurality of iterations of hash function, and wherein the generated evidence comprises a value that is a preimage to a node value which, when the hash function is applied, does not produce the node value.

7. A method comprising:

receiving information associated with at least one ledger entry of a distributed ledger of a decentralized system;

verifying at least a portion of one or more computations associated with the received information;

generating evidence of at least one error in said at least a portion of the one or more computations associated with the received information; and

associating the generated evidence with a public key of the verifying entity;

wherein the method is performed by at least one processing device comprising a processor coupled to a memory implementing a verifying entity of the decentralized system;

wherein the decentralized system comprises a proof of space based mining system, and wherein said at least one ledger entry of the distributed ledger comprises at least one proof of space for the proof of space based mining system;

wherein the method further comprises providing, from the verifying entity to one or more mining operator entities in the proof of space based mining system, a proof of knowledge of said at least one error; and

wherein submission of the proof of knowledge of said at least one error entitles the verifying entity to a bounty, the bounty comprising at least a fraction of a value obtained by successful mining in the proof of space based mining system.

8. The method of claim 7 wherein the verifying entity comprises a bounty hunter entity in the proof of space based mining system, the bounty hunter entity being configured to verify said at least a portion of the one or more computations associated with the received information to enforce one or more policies in the proof of space based mining system.

9. A computer program product comprising a non-transitory processor-readable storage medium having stored therein program code of one or more software programs, wherein the program code when executed by the at least one processing device causes the at least one processing device to perform the steps of the method of claim 7 .

10. An apparatus comprising:

at least one processing device comprising a processor coupled to a memory, the at least one processing device implementing a mining operator entity of a decentralized system configured:

to generate a challenge based at least in part on at least a portion of content of a distributed ledger of the decentralized system;

to select, based at least in part on the generated challenge, at least one first node of a graph stored by the mining operator entity;

to select, based at least in part on the at least one first node, at least one second node of the graph;

to generate, based at least in part on the at least one second node, a response to the generated challenge;

to determine a value of a quality function that takes as input the generated response to the generated challenge; and

to submit, based at least in part on the determined value of the quality function, an entry to the distributed ledger, the entry comprising at least a portion of the generated response to the generated challenge;

wherein the decentralized system comprises a proof of space based mining system, and wherein said at least one ledger entry of the distributed ledger comprises at least one proof of space for the proof of space based mining system;

wherein the mining operator entity is configured to receive, from a verifying entity in the proof of space based mining system, a proof of knowledge of said at least one error; and

wherein submission of the proof of knowledge of said at least one error entitles the verifying entity to a bounty, the bounty comprising at least a fraction of a value obtained by successful mining in the proof of space based mining system.

11. The apparatus of claim 10 wherein the entry further comprises at least a portion of the generated challenge.

12. The apparatus of claim 10 wherein the entry is associated with at least one of a public key and a secret key generated by the mining operator entity.

13. The apparatus of claim 10 wherein the mining operator entity is further configured, prior to generating the challenge, to register the graph in the decentralized system.

14. The apparatus of claim 13 wherein registering the graph in the decentralized system comprises the mining operator entity committing to the graph.

15. The apparatus of claim 14 wherein committing to the graph comprises submitting a value representative of the graph to be stored on the distributed ledger.

16. The apparatus of claim 5 wherein the public key is associated with a secret key, the secret key being associated with a financial capability of the verifying entity.

17. The apparatus of claim 5 wherein the verifying entity comprises a bounty hunter entity in the proof of space based mining system, the bounty hunter entity being configured to verify said at least a portion of the one or more computations associated with the received information to enforce one or more policies in the proof of space based mining system.

18. The method of claim 7 herein the public key is associated with a secret key, the secret key being associated with a financial capability of the verifying entity.

19. The method of claim 7 wherein providing the proof of knowledge of said at least one error comprises:

submitting, at a first point in time, a first transaction to the distributed ledger comprising the public key and an encryption of the generated evidence; and

submitting, at a second point in time, a second transaction to the distributed ledger comprising a decryption key for decrypting the encryption of the generated evidence in the first transaction.