Cryptology ePrint Archive: Report 2021/926

On Treewidth, Separators and Yao's Garbling

Chethan Kamath and 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.

Category / Keywords: foundations / adaptive security, garbled circuits

Date: received 8 Jul 2021

Contact author: ckamath at protonmail com, kklein at ist ac at, pietrzak at ist ac at

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Version: 20210709:180236 (All versions of this report)

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