Paper 2024/599
Probabilistically Checkable Arguments for all NP
Abstract
A probabilistically checkable argument (PCA) is a computational relaxation of PCPs, where soundness is guaranteed to hold only for false proofs generated by a computationally bounded adversary. The advantage of PCAs is that they are able to overcome the limitations of PCPs. A succinct 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 PCPs, under standard complexity assumptions. Bronfman and Rothblum (ITCS 2022) constructed succinct PCAs for NC that are publicly-verifiable and have constant query complexity under the sub-exponential hardness of LWE. We construct a publicly-verifiable succinct PCA with constant query complexity for all NP in the adaptive security setting. Our PCA scheme offers several improvements compared to the Bronfman and Rothblum construction: (1) it applies to all problems in NP, (2) it achieves adaptive security, and (3) it can be realized under any of the following assumptions: the polynomial hardness of LWE; $O(1)$-LIN on bilinear maps; or sub-exponential DDH. Moreover, our PCA scheme has a succinct prover, which means that for any 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 complexity-preserving RAM delegation scheme that is used in our PCA construction and may be of independent interest.
Metadata
- Available format(s)
-
PDF
- Category
- Cryptographic protocols
- Publication info
- Published by the IACR in EUROCRYPT 2024
- Keywords
- PCPsuccinct argumentsinstance compressionRAM delegation
- Contact author(s)
- shany ben-david @ biu ac il
- History
- 2024-05-25: revised
- 2024-04-17: received
- See all versions
- Short URL
- https://ia.cr/2024/599
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/599, author = {Shany Ben-David}, title = {Probabilistically Checkable Arguments for all {NP}}, howpublished = {Cryptology {ePrint} Archive, Paper 2024/599}, year = {2024}, url = {https://eprint.iacr.org/2024/599} }