Abstract
Structured random strings (SRSs) and correlated randomness are important for many cryptographic protocols. In settings where interaction is expensive, it is desirable to obtain such randomness in as few rounds of communication as possible; ideally, simply by exchanging one reusable round of messages which can be considered public keys.
In this paper, we describe how to generate any SRS or correlated randomness in such a single round of communication, using, among other things, indistinguishability obfuscation. We introduce what we call a distributed sampler, which enables \(n\) parties to sample a single public value (SRS) from any distribution. We construct a semi-malicious distributed sampler in the plain model, and use it to build a semi-malicious public-key PCF (Boyle et al., FOCS 2020) in the plain model. A public-key PCF can be thought of as a distributed correlation sampler; instead of producing a public SRS, it gives each party a private random value (where the values satisfy some correlation).
We introduce a general technique called an anti-rusher which compiles any one-round protocol with semi-malicious security without inputs to a similar one-round protocol with active security by making use of a programmable random oracle. This gets us actively secure distributed samplers and public-key PCFs in the random oracle model.
Finally, we explore some tradeoffs. Our first PCF construction is limited to reverse-sampleable correlations (where the random outputs of honest parties must be simulatable given the random outputs of corrupt parties); we additionally show a different construction without this limitation, but which does not allow parties to hold secret parameters of the correlation. We also describe how to avoid the use of a random oracle at the cost of relying on sub-exponentially secure indistinguishability obfuscation.
Supported by the Independent Research Fund Denmark (DFF) under project number 0165-00107B (C3PO), the European Research Council (ERC) under the European Unions’s Horizon 2020 research and innovation programme under grant agreement No 803096 (SPEC), and a starting grant from Aarhus University Research Foundation.
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Notes
- 1.
This requirement is inherent; otherwise, an adversary would be able to take the message an honest party sent, and recompute the function with that party’s input while varying the other inputs. NIMPC does allow similar recomputation attacks, but only with all honest party inputs fixed, which a PKI can be used to enforce.
- 2.
By sub-exponential security, we mean that no PPT adversary cannot break the security of that primitive with probability better than \(2^{-\mathrm {\lambda }^c}\) for a constant c.
- 3.
Note that formally, in the presence of malicious adversaries, preprocessing garbled circuits in this way requires the garbling scheme to be adaptively secure [BHR12].
- 4.
In the examples above, reverse-samplability is possible for pseudorandom secret-sharing, but not for garbled circuits, since we should not be able to find valid input wire labels when given only a garbled circuit.
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Abram, D., Scholl, P., Yakoubov, S. (2022). Distributed (Correlation) Samplers: How to Remove a Trusted Dealer in One Round. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13275. Springer, Cham. https://doi.org/10.1007/978-3-031-06944-4_27
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