### On Treewidth, Separators and Yao's Garbling

Chethan Kamath, Karen Klein, and Krzysztof Pietrzak

##### 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.

Available format(s)
Category
Foundations
Publication info
Preprint. Minor revision.
Keywords
Contact author(s)
ckamath @ protonmail com
kklein @ ist ac at
pietrzak @ ist ac at
History
Short URL
https://ia.cr/2021/926

CC BY

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},
note = {\url{https://eprint.iacr.org/2021/926}},
url = {https://eprint.iacr.org/2021/926}
}

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