On the Complexity of Scrypt and Proofs of Space in the Parallel Random Oracle Model

We investigate lower bounds in terms of time and memory on the parallel complexity of an adversary A computing labels of randomly selected challenge nodes in direct acyclic graphs, where the w-bit label of a node is the hash h (modelled as a random oracle with w-bit output) of the labels of its parents. Specific instances of this general problem underlie both proofs-of-space protocols [Dziembowski et al. CRYPTO’15] as well as memory-hardness proofs including scrypt, a widely deployed password hashing and key-derivation function which is e.g. used within Proofs-of-Work for digital currencies like Litecoin. Current lower bound proofs for these problems only consider restricted algorithms A which perform only a single h query at a time and which only store individual labels (but not arbitrary functions thereof). This paper substantially improves this state of affairs; Our first set of results shows that even when allowing multiple parallel h queries, the “cumulative memory complexi...

• Type: Journal
• Year: 2016
• Where: IACR
• Authors: Joël Alwen, Binyi Chen, Chethan Kamath, Vladimir Kolmogorov, Krzysztof Pietrzak, Stefano Tessaro
• Keywords: Biometrics, IACR 2016