A Complexity-Theoretic Approach to Proofs of Space

2026-08-09

AI Summary

This work addresses a critical gap in the foundations of Proofs of Space (PoS) by presenting a general framework that establishes their security under standard complexity-theoretic assumptions, thereby eliminating reliance on the random oracle model or ad hoc cryptographic hypotheses. For the first time, PoS security is reduced to the conjunction of classical complexity assumptions—such as the exponential hardness of E against nondeterministic circuits—and standard cryptographic primitives, including collision-resistant hash functions and SNARGs for languages in P. The framework yields succinct and non-trivial PoS constructions under relatively mild assumptions, and achieves near-optimal parameters and communication efficiency when instantiated under stronger complexity-theoretic conjectures.

Abstract

A Proof of Space, PoS, as introduced by Dziembowski et al. [CRYPTO'15], is a two-phase protocol that enables a Prover to convince an efficient Verifier that it has allocated a large amount of persistent memory to storing some information. To our knowledge, all existing PoS protocols are only known to be secure in the random oracle model (or under ad hoc assumptions about cryptographic assumptions). We provide an elementary framework for constructing PoS from a combination of derandomization assumptions and cryptographic assumptions. We provide a few simple instantiations of the framework. We show that non-trivial PoS follow from (a) $\mathsf{E}=\mathsf{DTIME[2^{O(n)}]}$ is hard for exponential-size nondeterministic circuits (an assumption introduced to show $\mathsf{AM}=\mathsf{NP}$), and (b) collision-resistant hash functions. We also show that PoS with nearly optimal parameters and interaction pattern follows from assumption (a) above and (c) SNARGs for $\mathsf{P}$.

Problem

• Proof of Space
• complexity theory
• derandomization
• cryptographic assumptions
• random oracle model

Innovation

• Proof of Space
• Complexity Theory
• Derandomization
• Collision-Resistant Hash Functions
• SNARGs