Paper 2018/702

Tight Proofs of Space and Replication

Ben Fisch

Abstract

We construct a concretely practical proof-of-space (PoS) with arbitrarily tight security based on stacked depth robust graphs and constant-degree expander graphs. A proof-of-space (PoS) is an interactive proof system where a prover demonstrates that it is persistently using space to store information. A PoS is arbitrarily tight if the honest prover uses exactly N space and for any $\epsilon > 0$ the construction can be tuned such that no adversary can pass verification using less than $1-\epsilon N$ space. Most notably, the degree of the graphs in our construction are independent of $\epsilon$, and the number of layers is only $O(\log(1/\epsilon))$. The proof size is $O(d/\epsilon)$. The degree $d$ depends on the depth robust graphs, which are only required to maintain $\Omega(N)$ depth in subgraphs on 80% of the nodes. Our tight PoS is also secure against parallel attacks. Tight proofs of space are necessary for proof-of-replication (PoRep), which is a publicly verifiable proof that the prover is dedicating unique resources to storing one or more retrievable replicas of a file. Our main PoS construction can be used as a PoRep, but data extraction is as inefficient as replica generation. We present a second variant of our construction called ZigZag PoRep that has fast/parallelizable data extraction compared to replica generation and maintains the same space tightness while only increasing the number of levels by roughly a factor two.

Metadata
Available format(s)
PDF
Publication info
Preprint. MINOR revision.
Keywords
proof of spaceproof of replicationtight security
Contact author(s)
benafisch @ gmail com
History
2018-08-16: revised
2018-08-01: received
See all versions
Short URL
https://ia.cr/2018/702
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2018/702,
      author = {Ben Fisch},
      title = {Tight Proofs of Space and Replication},
      howpublished = {Cryptology ePrint Archive, Paper 2018/702},
      year = {2018},
      note = {\url{https://eprint.iacr.org/2018/702}},
      url = {https://eprint.iacr.org/2018/702}
}
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