Paper 2021/926 Original: eprint.iacr.org/2021/926 ↗
On Treewidth, Separators and Yao's Garbling
Abstract
We show that Yao’s garbling scheme is adaptively indistinguishable for the class of Boolean circuits of size S and treewidth w with only a S^O(w) loss in security. For instance, circuits with constant treewidth are as a result adaptively indistinguishable with only a polynomial loss. This (partially) complements a negative result of Applebaum et al. (Crypto 2013), which showed (assuming one-way functions) that Yao’s garbling scheme cannot be adaptively simulatable. As main technical contributions, we introduce a new pebble game that abstracts out our security reduction and then present a pebbling strategy for this game where the number of pebbles used is roughly O(d w log(S)), d being the fan-out of the circuit. The design of the strategy relies on separators, a graph-theoretic notion with connections to circuit complexity.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2021-07-09: last updated
- 2021-07-09: published
- Short URL
- https://ia.cr/2021/926
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2021/926,
author = {Chethan Kamath and Karen Klein and Krzysztof Pietrzak},
title = {On Treewidth, Separators and Yao's Garbling},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/926},
year = {2021},
url = {https://eprint.iacr.org/2021/926}
}