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Probabilistically Checkable Arguments for all NP
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| Conference: | EUROCRYPT 2024 |
| Abstract: | A probabilistically checkable argument ($\mathsf{PCA}$) is a computational relaxation of $\mathsf{PCP}$s, where soundness is guaranteed to hold only for false proofs generated by a computationally bounded adversary. The advantage of $\mathsf{PCA}$s is that they are able to overcome the limitations of $\mathsf{PCP}$s. A \emph{succinct} $\mathsf{PCA}$ has a proof length that is polynomial in the witness length (and is independent of the non-deterministic verification time), which is impossible for $\mathsf{PCP}$s, under standard complexity assumptions. Bronfman and Rothblum (ITCS 2022) constructed succinct $\mathsf{PCA}$s for $\mathsf{NC}$ that are publicly-verifiable and have constant query complexity under the sub-exponential hardness of $\mathsf{LWE}$. We construct a publicly-verifiable succinct $\mathsf{PCA}$ with constant query complexity for all $\mathsf{NP}$ in the adaptive security setting. Our $\mathsf{PCA}$ scheme offers several improvements compared to the Bronfman and Rothblum construction: (1) it applies to all problems in $\mathsf{NP}$, (2) it achieves adaptive security, and (3) it can be realized under any of the following assumptions: the \emph{polynomial} hardness of $\mathsf{LWE}$; $O(1)$-$\mathsf{LIN}$; or sub-exponential $\mathsf{DDH}$. Moreover, our $\mathsf{PCA}$ scheme has a \emph{succinct prover}, which means that for any $\mathsf{NP}$ relation that can be verified in time $T$ and space $S$, the proof can be generated in time $O_{\lambda,m}(T\cdot\mathrm{polylog}(T))$ and space $O_{\lambda,m}(S\cdot\mathrm{polylog}(T))$. Here, ${O}_{\lambda,m}$ accounts for polynomial factors in the security parameter and in the size of the witness. En route, we construct a new \emph{complexity-preserving} $\mathsf{RAM~Delegation}$ scheme that is used in our $\mathsf{PCA}$ construction and may be of independent interest. |
BibTeX
@inproceedings{eurocrypt-2024-33920,
title={Probabilistically Checkable Arguments for all NP},
publisher={Springer-Verlag},
doi={10.1007/978-3-031-58734-4_12},
author={Shany Ben-David},
year=2024
}