Welcome to the resource topic for 2015/1250
Title:
Adaptively Secure Garbled Circuits from One-Way Functions
Authors: Brett Hemenway, Zahra Jafargholi, Rafail Ostrovsky, Alessandra Scafuro, Daniel Wichs
Abstract:A garbling scheme is used to garble a circuit C and an input x in a way that reveals the output C(x) but hides everything else. In many settings, the circuit can be garbled off-line without strict efficiency constraints, but the input must be garbled very efficiently on-line, with much lower complexity than evaluating the circuit. Yao’s scheme has essentially optimal on-line complexity, but only achieves selective security, where the adversary must choose the input x prior to seeing the garbled circuit. It has remained an open problem to achieve adaptive security, where the adversary can choose x after seeing the garbled circuit, while preserving on-line efficiency. In this work, we modify Yao’s scheme in a way that allows us to prove adaptive security under one-way functions. As our main instantiation, we get a scheme where the on-line complexity is only proportional to the width w of the circuit, which corresponds to the space complexity of the computation, but is independent of the circuit’s depth d. Alternately, we can also get an instantiation where the on-line complexity is only proportional to the input/output size and the depth d of the circuit but independent of its width w, albeit in this case we incur a 2^{O(d)} security loss in our reduction. More broadly, we relate the on-line complexity of adaptively secure garbling schemes in our framework to a certain type of pebble complexity of the circuit. As our main tool, of independent interest, we develop a new notion of somewhere equivocal encryption, which allows us to efficiently equivocate on a small subset of the message bits.
ePrint: https://eprint.iacr.org/2015/1250
Talk: https://www.youtube.com/watch?v=jVkhVhG6z-E
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