Abstract
We revisit the problem of reusable non-interactive secure computation (NISC). A standard NISC protocol for a sender-receiver functionality f enables the receiver to encrypt its input x such that any sender, on input y, can send back a message revealing only f(x, y). Security should hold even when either party can be malicious. A reusable NISC protocol has the additional feature that the receiver’s message can be safely reused for computing multiple outputs \(f(x,y_i)\). Here security should hold even when a malicious sender can learn partial information about the honest receiver’s outputs in each session.
We present the first reusable NISC protocol for general functions f that only makes a black-box use of any two-message oblivious transfer protocol, along with a random oracle. All previous reusable NISC protocols either made a non-black-box use of cryptographic primitives (Cachin et al. ICALP 2002) or alternatively required a stronger arithmetic variant of oblivious transfer and were restricted to f in \(\textsf{NC}^1\) or similar classes (Chase et al. Crypto 2019). Our result is obtained via a general compiler from standard NISC to reusable NISC that makes use of special type of honest-majority protocols for secure multiparty computation.
Finally, we extend the above main result to reusable two-sided NISC, in which two parties can encrypt their inputs in the first round and then reveal different functions of their inputs in multiple sessions. This extension either requires an additional (black-box) use of additively homomorphic commitment or alternatively requires the parties to maintain a state between sessions.
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Notes
- 1.
Since a pseudorandom generator can be constructed from an OT protocol in a black-box way, OT alone suffices.
- 2.
In fact, our result applies to a more general notion of two-sided NISC that strictly generalizes both the above notion and standard (one-sided) NISC.
- 3.
In the actual definition, we consider a more general situation where the adversary can learn some partial information about the output, such as whether the receiver aborts. This makes reusable security nontrivial even for functionalities such as OLE, where the receiver’s output reveals its input. However, for the sake of this overview, we make the simplifying assumption that the entire receiver output is given to the adversary.
- 4.
OLE is the arithmetic analogue of OT which takes in a field element x from the receiver, and two field elements (a, b) from the sender and outputs \(ax + b\) to the receiver.
- 5.
In reusable receiver security game, we fix the first round message from the honest receiver and the corrupted sender could generate multiple second round messages. We require the joint distribution of the view of the sender and the receiver’s output in each of the sender executions to be indistinguishable to an ideal world where the parties have access to the ideal OLE functionality.
- 6.
We restrict ourselves to the case of a two-message OT protocol as this gives a two-message NISC protocol.
- 7.
The standard Shamir secret sharing using bivariate polynomials satisfies this property.
- 8.
We note that the servers have to additionally re-randomize these shares but we ignore this step to keep the exposition simple.
- 9.
As our main results are in the random oracle model, we can avoid an explicit setup phase that samples the CRS uniformly and instead use the random oracle’s output on some default input as the CRS.
- 10.
We are little imprecise here and this global predicate acts only on a part of the sender’s message and not on the whole message. To be more specific, the sender’s message consists of two parts. We want the first part to satisfy local consistency and the second part to satisfy global consistency.
- 11.
We implicitly assume that all the algorithms take in the unary encoding of the security parameter \(1^\lambda \) as part of their inputs.
- 12.
We implicitly assume that all these algorithms have access to a random oracle and hence, do not include an explicit setup phase. We also assume that all the algorithms take \(1^\lambda \) as an additional input.
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Acknowledgments
Y. Ishai was supported in part by ERC Project NTSC (742754), BSF grant 2018393, ISF grant 2774/20, and a Google Faculty Research Award. D. Khurana was supported in part by DARPA SIEVE award and a gift from Visa Research. A. Sahai was supported in part from a Simons Investigator Award, DARPA SIEVE award, NTT Research, NSF Frontier Award 1413955, BSF grant 2012378, a Xerox Faculty Research Award, a Google Faculty Research Award, and an Okawa Foundation Research Grant. This material is based upon work supported by the Defense Advanced Research Projects Agency through Award HR00112020024. A. Srinivasan was supported in part by a SERB startup grant and Google India Research Award.
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Ishai, Y., Khurana, D., Sahai, A., Srinivasan, A. (2023). Black-Box Reusable NISC with Random Oracles. In: Hazay, C., Stam, M. (eds) Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023. Lecture Notes in Computer Science, vol 14005. Springer, Cham. https://doi.org/10.1007/978-3-031-30617-4_3
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