Paper 2023/1284
Improving logarithmic derivative lookups using GKR
Abstract
In this informal note, we instantiate the Goldwasser-Kalai-Rothblum (GKR) protocol to prove fractional sumchecks as present in lookup arguments based on logarithmic derivatives, with the following impact on the prover cost of logUp (IACR eprint 2022/1530): When looking up $M\geq 1$ columns in a (for the sake of simplicity) single column table, the prover has to commit only to a single extra column, i.e. the multiplicities of the table entries. In order to carry over the GKR fractional sumcheck to the univariate setting, we furthermore introduce a simple, yet (as far as we know) novel transformation for turning a univariate polynomial commitment scheme into a multilinear one. The transformation complements existing approaches and might be of independent interest for its elegant way to prove arbitrary powers of the lexicographic shift over the Boolean hypercube.
Note: Further typos corrected.
Metadata
- Available format(s)
-
PDF
- Category
- Cryptographic protocols
- Publication info
- Preprint.
- Keywords
- lookup argumentsGKRmultilinear commitment scheme
- Contact author(s)
-
spapini @ starkware co
uhaboeck @ polygon technology - History
- 2023-09-18: last of 2 revisions
- 2023-08-27: received
- See all versions
- Short URL
- https://ia.cr/2023/1284
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2023/1284,
author = {Shahar Papini and Ulrich Haböck},
title = {Improving logarithmic derivative lookups using {GKR}},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/1284},
year = {2023},
url = {https://eprint.iacr.org/2023/1284}
}
