Limits on the Adaptive Security of Yao’s Garbling

Kamath Hosdurg C, Klein K, Pietrzak KZ, Wichs D. 2021. Limits on the Adaptive Security of Yao’s Garbling. 41st Annual International Cryptology Conference, Part II . CRYPTO: Annual International Cryptology Conference, LCNS, vol. 12826, 486–515.


Conference Paper | Published | English
Department
Series Title
LCNS
Abstract
Yao’s garbling scheme is one of the most fundamental cryptographic constructions. Lindell and Pinkas (Journal of Cryptograhy 2009) gave a formal proof of security in the selective setting where the adversary chooses the challenge inputs before seeing the garbled circuit assuming secure symmetric-key encryption (and hence one-way functions). This was followed by results, both positive and negative, concerning its security in the, stronger, adaptive setting. Applebaum et al. (Crypto 2013) showed that it cannot satisfy adaptive security as is, due to a simple incompressibility argument. Jafargholi and Wichs (TCC 2017) considered a natural adaptation of Yao’s scheme (where the output mapping is sent in the online phase, together with the garbled input) that circumvents this negative result, and proved that it is adaptively secure, at least for shallow circuits. In particular, they showed that for the class of circuits of depth δ , the loss in security is at most exponential in δ . The above results all concern the simulation-based notion of security. In this work, we show that the upper bound of Jafargholi and Wichs is basically optimal in a strong sense. As our main result, we show that there exists a family of Boolean circuits, one for each depth δ∈N , such that any black-box reduction proving the adaptive indistinguishability of the natural adaptation of Yao’s scheme from any symmetric-key encryption has to lose a factor that is exponential in δ√ . Since indistinguishability is a weaker notion than simulation, our bound also applies to adaptive simulation. To establish our results, we build on the recent approach of Kamath et al. (Eprint 2021), which uses pebbling lower bounds in conjunction with oracle separations to prove fine-grained lower bounds on loss in cryptographic security.
Publishing Year
Date Published
2021-08-11
Proceedings Title
41st Annual International Cryptology Conference, Part II
Acknowledgement
We would like to thank the anonymous reviewers of Crypto’21 whose detailed comments helped us considerably improve the presentation of the paper.
Volume
12826
Page
486-515
Conference
CRYPTO: Annual International Cryptology Conference
Conference Location
Virtual
Conference Date
2021-08-16 – 2021-08-20
IST-REx-ID

Cite this

Kamath Hosdurg C, Klein K, Pietrzak KZ, Wichs D. Limits on the Adaptive Security of Yao’s Garbling. In: 41st Annual International Cryptology Conference, Part II . Vol 12826. Cham: Springer Nature; 2021:486-515. doi:10.1007/978-3-030-84245-1_17
Kamath Hosdurg, C., Klein, K., Pietrzak, K. Z., & Wichs, D. (2021). Limits on the Adaptive Security of Yao’s Garbling. In 41st Annual International Cryptology Conference, Part II (Vol. 12826, pp. 486–515). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-84245-1_17
Kamath Hosdurg, Chethan, Karen Klein, Krzysztof Z Pietrzak, and Daniel Wichs. “Limits on the Adaptive Security of Yao’s Garbling.” In 41st Annual International Cryptology Conference, Part II , 12826:486–515. Cham: Springer Nature, 2021. https://doi.org/10.1007/978-3-030-84245-1_17.
C. Kamath Hosdurg, K. Klein, K. Z. Pietrzak, and D. Wichs, “Limits on the Adaptive Security of Yao’s Garbling,” in 41st Annual International Cryptology Conference, Part II , Virtual, 2021, vol. 12826, pp. 486–515.
Kamath Hosdurg C, Klein K, Pietrzak KZ, Wichs D. 2021. Limits on the Adaptive Security of Yao’s Garbling. 41st Annual International Cryptology Conference, Part II . CRYPTO: Annual International Cryptology Conference, LCNS, vol. 12826, 486–515.
Kamath Hosdurg, Chethan, et al. “Limits on the Adaptive Security of Yao’s Garbling.” 41st Annual International Cryptology Conference, Part II , vol. 12826, Springer Nature, 2021, pp. 486–515, doi:10.1007/978-3-030-84245-1_17.
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