Paper 2016/333

Proof of Space from Stacked Expanders

Ling Ren and Srinivas Devadas


Recently, proof of space (PoS) has been suggested as a more egalitarian alternative to the traditional hash-based proof of work. In PoS, a prover proves to a verifier that it has dedicated some specified amount of space. A closely related notion is memory-hard functions (MHF), functions that require a lot of memory/space to compute. While making promising progress, existing PoS and MHF have several problems. First, there are large gaps between the desired space-hardness and what can be proven. Second, it has been pointed out that PoS and MHF should require a lot of space not just at some point, but throughout the entire computation/protocol; few proposals considered this issue. Third, the two existing PoS constructions are both based on a class of graphs called superconcentrators, which are either hard to construct or add a logarithmic factor overhead to efficiency. In this paper, we construct PoS from stacked expander graphs. Our constructions are simpler, more efficient and have tighter provable space-hardness than prior works. Our results also apply to a recent MHF called Balloon hash. We show Balloon hash has tighter space-hardness than previously believed and consistent space-hardness throughout its computation.

Available format(s)
Cryptographic protocols
Publication info
Published by the IACR in TCC 2016
Proof of spacegraph pebbling
Contact author(s)
renling @ mit edu
2016-08-25: last of 2 revisions
2016-03-25: received
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      author = {Ling Ren and Srinivas Devadas},
      title = {Proof of Space from Stacked Expanders},
      howpublished = {Cryptology ePrint Archive, Paper 2016/333},
      year = {2016},
      note = {\url{}},
      url = {}
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