On treewidth, separators and Yao’s garbling

Kamath Hosdurg C, Klein K, Pietrzak KZ. 2021. On treewidth, separators and Yao’s garbling. 19th International Conference. TCC: Theory of Cryptography, LNCS, vol. 13043, 486–517.


Conference Paper | Published | English

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Department
Series Title
LNCS
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 SO(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(δwlog(S)) , δ being the fan-out of the circuit. The design of the strategy relies on separators, a graph-theoretic notion with connections to circuit complexity. with only a SO(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(δwlog(S)) , δ being the fan-out of the circuit. The design of the strategy relies on separators, a graph-theoretic notion with connections to circuit complexity.
Publishing Year
Date Published
2021-11-04
Proceedings Title
19th International Conference
Acknowledgement
We are grateful to Daniel Wichs for helpful discussions on the landscape of adaptive security of Yao’s garbling. We would also like to thank Crypto 2021 and TCC 2021 reviewers for their detailed review and suggestions, which helped improve presentation considerably.
Volume
13043
Page
486-517
Conference
TCC: Theory of Cryptography
Conference Location
Raleigh, NC, United States
Conference Date
2021-11-08 – 2021-11-11
ISSN
eISSN
IST-REx-ID

Cite this

Kamath Hosdurg C, Klein K, Pietrzak KZ. On treewidth, separators and Yao’s garbling. In: 19th International Conference. Vol 13043. Springer Nature; 2021:486-517. doi:10.1007/978-3-030-90453-1_17
Kamath Hosdurg, C., Klein, K., & Pietrzak, K. Z. (2021). On treewidth, separators and Yao’s garbling. In 19th International Conference (Vol. 13043, pp. 486–517). Raleigh, NC, United States: Springer Nature. https://doi.org/10.1007/978-3-030-90453-1_17
Kamath Hosdurg, Chethan, Karen Klein, and Krzysztof Z Pietrzak. “On Treewidth, Separators and Yao’s Garbling.” In 19th International Conference, 13043:486–517. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-90453-1_17.
C. Kamath Hosdurg, K. Klein, and K. Z. Pietrzak, “On treewidth, separators and Yao’s garbling,” in 19th International Conference, Raleigh, NC, United States, 2021, vol. 13043, pp. 486–517.
Kamath Hosdurg C, Klein K, Pietrzak KZ. 2021. On treewidth, separators and Yao’s garbling. 19th International Conference. TCC: Theory of Cryptography, LNCS, vol. 13043, 486–517.
Kamath Hosdurg, Chethan, et al. “On Treewidth, Separators and Yao’s Garbling.” 19th International Conference, vol. 13043, Springer Nature, 2021, pp. 486–517, doi:10.1007/978-3-030-90453-1_17.
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