A Complexity-Theoretic Approach to Proofs of Space

• URL: http://arxiv.org/abs/2608.08993v1
• Date: Mon, 10 Aug 2026 01:28:01 GMT
• Title: A Complexity-Theoretic Approach to Proofs of Space
• Abstract summary: We provide an elementary cryptographic framework for constructing PoS from a combination of derandomization assumptions and cryptographic assumptions.<n>PoS with nearly optimal parameters and interaction pattern follows from assumption (a) above and (c) SNARGs for $mathsfP$.
• Score: 5.160781170457704
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\mathsf{P}$.

Related papers

• Verified Pythagorean Composition for Adaptive Cryptographic Games: Noise Flooding in Homomorphic Encryption [45.00791460144501]
  Noise flooding is a standard defense against decryption attacks on approximate homomorphic encryption.<n>Our proof constructs a new relational program logic over SSProve semantics.
  arXiv  Detail & Related papers  (2026-08-14T00:40:29Z)
• Multi-Prover Interactive Proof Systems with Leakage [1.0960289997471082]
  We introduce two techniques to approach the setting where communication between provers is allowed but bounded.<n>We show that for any $p$, we can construct two-prover one-round $mathsfMIP$ and $mathsfMIPast$ protocols for $mathsfNEXP$ and $mathsfRE$.
  arXiv  Detail & Related papers  (2026-05-11T01:58:44Z)
• Cloning Games, Black Holes and Cryptography [50.022147589030304]
  We introduce a new toolkit for analyzing cloning games.<n>This framework allows us to analyze a new cloning game based on binary phase states.<n>We show that the binary phase variantally optimal bound offers quantitative insights into information scrambling in idealized models of black holes.
  arXiv  Detail & Related papers  (2024-11-07T14:09:32Z)
• Projection by Convolution: Optimal Sample Complexity for Reinforcement Learning in Continuous-Space MDPs [56.237917407785545]
  We consider the problem of learning an $varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Key to our solution is a novel projection technique based on ideas from harmonic analysis. Our result bridges the gap between two popular but conflicting perspectives on continuous-space MDPs.
  arXiv  Detail & Related papers  (2024-05-10T09:58:47Z)
• Lossy Cryptography from Code-Based Assumptions [7.880958076366762]
  A proliferation of advanced cryptographic primitives imply hard problems in the complexity class $SZK$. This poses a barrier for building advanced primitives from code-based assumptions. We propose a new code-based assumption: Dense-Sparse, that falls in the complexity class $BPPSZK$ and is conjectured to be secure against subexponential time adversaries.
  arXiv  Detail & Related papers  (2024-02-06T02:17:08Z)
• A Fast Algorithm for the Real-Valued Combinatorial Pure Exploration of Multi-Armed Bandit [55.2480439325792]
  We study the real-valued pure exploration problem in the multi-armed bandit (R-CPE-MAB)<n>We introduce an algorithm named the gap-based exploration (CombGapE) algorithm, whose sample complexity upper bound matches the lower bound up to a problem-dependent constant factor.<n>We numerically show that the CombGapE algorithm outperforms existing methods significantly in both synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-06-15T15:37:31Z)
• Fast Rates for Maximum Entropy Exploration [52.946307632704645]
  We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. We study the maximum entropy exploration problem two different types. For visitation entropy, we propose a game-theoretic algorithm that has $widetildemathcalO(H3S2A/varepsilon2)$ sample complexity. For the trajectory entropy, we propose a simple algorithm that has a sample of complexity of order $widetildemathcalO(mathrmpoly(S,
  arXiv  Detail & Related papers  (2023-03-14T16:51:14Z)
• Quantum Cryptography in Algorithmica [0.7524721345903025]
  We show that in a black-box setting, quantum cryptography based on pseudorandom states is possible even if one-way functions do not exist. We also introduce a conjecture that would generalize our results to multi-copy secure pseudorandom states.
  arXiv  Detail & Related papers  (2022-12-01T21:33:38Z)
• Reward-Mixing MDPs with a Few Latent Contexts are Learnable [75.17357040707347]
  We consider episodic reinforcement learning in reward-mixing Markov decision processes (RMMDPs) Our goal is to learn a near-optimal policy that nearly maximizes the $H$ time-step cumulative rewards in such a model.
  arXiv  Detail & Related papers  (2022-10-05T22:52:00Z)
• Learning a Single Neuron with Adversarial Label Noise via Gradient Descent [50.659479930171585]
  We study a function of the form $mathbfxmapstosigma(mathbfwcdotmathbfx)$ for monotone activations. The goal of the learner is to output a hypothesis vector $mathbfw$ that $F(mathbbw)=C, epsilon$ with high probability.
  arXiv  Detail & Related papers  (2022-06-17T17:55:43Z)
• Quantum Resources Required to Block-Encode a Matrix of Classical Data [56.508135743727934]
  We provide circuit-level implementations and resource estimates for several methods of block-encoding a dense $Ntimes N$ matrix of classical data to precision $epsilon$. We examine resource tradeoffs between the different approaches and explore implementations of two separate models of quantum random access memory (QRAM) Our results go beyond simple query complexity and provide a clear picture into the resource costs when large amounts of classical data are assumed to be accessible to quantum algorithms.
  arXiv  Detail & Related papers  (2022-06-07T18:00:01Z)
• A Ihara-Bass Formula for Non-Boolean Matrices and Strong Refutations of Random CSPs [4.023424709659175]
  We prove strong refutations of random constraint satisfaction problems with $k$ variables per constraints (k-CSPs) For a random k-CSP instance constructed out of a constraint that is satisfied by a $p$ fraction of assignments, we can efficiently compute a certificate that the optimum satisfies at most a $p+O_k(epsilon)$ fraction of constraints.
  arXiv  Detail & Related papers  (2022-04-20T16:21:21Z)
• DASHA: Distributed Nonconvex Optimization with Communication Compression, Optimal Oracle Complexity, and No Client Synchronization [77.34726150561087]
  We develop and analyze DASHA: a new family of methods for noneps distributed optimization problems. Unlike MARINA, the new methods DASHA, DASHA-MVR send compressed vectors only and never synchronize the nodes, which makes them more practical for learning.
  arXiv  Detail & Related papers  (2022-02-02T20:10:40Z)
• The Curse of Passive Data Collection in Batch Reinforcement Learning [82.6026077420886]
  In high stake applications, active experimentation may be considered too risky and thus data are often collected passively. While in simple cases, such as in bandits, passive and active data collection are similarly effective, the price of passive sampling can be much higher when collecting data from a system with controlled states.
  arXiv  Detail & Related papers  (2021-06-18T07:54:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.