International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Paper: Limits on the Adaptive Security of Yao’s Garbling

Authors:
Chethan Kamath , Unaffilated
Karen Klein , IST Austria
Krzysztof Pietrzak , IST Austria
Daniel Wichs , Northeastern University
Download:
Search ePrint
Search Google
Presentation: Slides
Conference: CRYPTO 2021
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 assuming secure symmetric-key encryption (and hence one-way functions). This was fol- lowed 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. Jafagholi and Wichs (TCC 2017) considered a natural adaptation of Yao’s scheme 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 d, the loss in security is at most exponential in d. 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 more or less optimal in a strong sense. As our main result, we show that there exists a family of Boolean circuits, one for each depth d ∈ N, such that any black-box reduction proving the adaptive indistinguishability- security of the natural adaptation of Yao’s scheme from any symmetric-key encryption has to lose a factor that is sub-exponential in d. 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
Video from CRYPTO 2021
BibTeX
@inproceedings{crypto-2021-31221,
  title={Limits on the Adaptive Security of Yao’s Garbling},
  publisher={Springer-Verlag},
  author={Chethan Kamath and Karen Klein and Krzysztof Pietrzak and Daniel Wichs},
  year=2021
}