On treewidth, separators and Yao's garbling

conference paper On treewidth, separators and Yao's garbling published yes Chethan Kamath Hosdurg author 4BD3F30E-F248-11E8-B48F-1D18A9856A870009-0006-6812-7317 Karen Klein author 3E83A2F8-F248-11E8-B48F-1D18A9856A87 Krzysztof Z Pietrzak author 3E04A7AA-F248-11E8-B48F-1D18A9856A870000-0002-9139-1654 KrPi department TCC: Theory of Cryptography Conference Teaching Old Crypto New Tricks project 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. International Association for Cryptologic Research2021Raleigh, NC, United States eng 19th Theory of Cryptography Conference 2021 https://research-explorer.ista.ac.at/record/10409 https://research-explorer.ista.ac.at/record/10035 C. Kamath Hosdurg, K. Klein, and K. Z. Pietrzak, “On treewidth, separators and Yao’s garbling,” in 19th Theory of Cryptography Conference 2021, Raleigh, NC, United States, 2021. C. Kamath Hosdurg, K. Klein, K.Z. Pietrzak, in:, 19th Theory of Cryptography Conference 2021, International Association for Cryptologic Research, 2021. Kamath Hosdurg C, Klein K, Pietrzak KZ. On treewidth, separators and Yao’s garbling. In: 19th Theory of Cryptography Conference 2021. International Association for Cryptologic Research; 2021. Kamath Hosdurg C, Klein K, Pietrzak KZ. 2021. On treewidth, separators and Yao’s garbling. 19th Theory of Cryptography Conference 2021. TCC: Theory of Cryptography Conference, 2021/926. Kamath Hosdurg, C., Klein, K., & Pietrzak, K. Z. (2021). On treewidth, separators and Yao’s garbling. In 19th Theory of Cryptography Conference 2021. Raleigh, NC, United States: International Association for Cryptologic Research. Kamath Hosdurg, Chethan, Karen Klein, and Krzysztof Z Pietrzak. “On Treewidth, Separators and Yao’s Garbling.” In 19th Theory of Cryptography Conference 2021. International Association for Cryptologic Research, 2021. Kamath Hosdurg, Chethan, et al. “On Treewidth, Separators and Yao’s Garbling.” 19th Theory of Cryptography Conference 2021, 2021/926, International Association for Cryptologic Research, 2021. 100442021-09-24T12:01:34Z2026-07-06T13:15:57Z