Paper 2023/1530
Proofs of Space with Maximal Hardness
Abstract
In a proof of space, a prover performs a complex computation with a large output. A verifier periodically checks that the prover still holds the output. The security goal for a proof of space construction is to ensure that a prover who erases even a portion of the output has to redo a large portion of the complex computation in order to satisfy the verifier. In existing constructions of proofs of space, the computation that a cheating prover is forced to redo is a small fraction (vanishing or small constant) of the original complex computation. The only exception is a construction of Pietrzak (ITCS 2019) that requires extremely depthrobust graphs, which result in impractically high complexity of the initialization process. We present the first proof of space of reasonable complexity that ensures that the prover has to redo almost the entire computation (fraction arbitrarily close to 1) when trying to save even an arbitrarily small constant fraction of the space. Our construction is a generalization of an existing construction called SDR (Fisch, Eurocrypt 2019) deployed on the Filecoin blockchain. Our improvements, while general, also demonstrate that the already deployed construction has considerably better security than previously shown. Technically, our construction can be viewed as amplifying predecessorrobust graphs. These are directed acyclic graphs in which every subgraph of sufficient relative size $\pi$ contains a large singlesink connected component of relative size $\alpha_\pi$. We take a predecessorrobust graph with constant parameters $(\pi, \alpha_\pi)$, and build a bigger predecessorrobust graph with a nearoptimal set of parameters and additional guarantees on sink placement, while increasing the degree only by a small additive constant.
Metadata
 Available format(s)
 Category
 Cryptographic protocols
 Publication info
 Published elsewhere. Major revision. FOCS 2024
 Keywords
 Proof of SpaceGraphsPebblingDepthRobust GraphsPredecessorRobust Graphs
 Contact author(s)
 leonid reyzin @ gmail com
 History
 20240920: last of 2 revisions
 20231006: received
 See all versions
 Short URL
 https://ia.cr/2023/1530
 License

CC BY
BibTeX
@misc{cryptoeprint:2023/1530, author = {Leonid Reyzin}, title = {Proofs of Space with Maximal Hardness}, howpublished = {Cryptology {ePrint} Archive, Paper 2023/1530}, year = {2023}, url = {https://eprint.iacr.org/2023/1530} }