Abstract
We revisit the problem of universally composable (UC) secure multiparty computation in the stateless hardware token model.
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We construct a three round multi-party computation protocol for general functions based on one-way functions where each party sends two tokens to every other party. Relaxing to the two-party case, we also construct a two round protocol based on one-way functions where each party sends a single token to the other party, and at the end of the protocol, both parties learn the output.
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One of the key components in the above constructions is a new two-round oblivious transfer protocol based on one-way functions using only one token, which can be reused an unbounded polynomial number of times.
All prior constructions required either stronger complexity assumptions, or larger number of rounds, or a larger number of tokens.
S. Badrinarayanan—Research supported in part by the IBM PhD Fellowship.
A. Jain—Research supported in part by NSF SaTC grant 1814919 and Darpa Safeware grant W911NF-15-C-0213.
R. Ostrovsky—Research supported in part by NSF-BSF Grant 1619348, DARPA/SPAWAR N66001-15-C-4065, ODNI/IARPA 2019-1902070008 US-Israel BSF grant 2012366, JP Morgan Faculty Award, OKAWA Foundation Research Award, IBM Faculty Research Award, Xerox Faculty Research Award, B. John Garrick Foundation Award, Teradata Research Award, and Lockheed-Martin Corporation Research Award. The views expressed are those of the authors and do not reflect position of the Department of Defense or the U.S. Government.
I. Visconti—Research supported in part by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 780477 (project PRIViLEDGE).
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Notes
- 1.
One-way function is a necessary assumption in the stateless hardware token model since an unbounded adversary can simply “learn” a stateless token [GIS+10].
- 2.
This is the standard model for multiparty computation, where in each round, every party simultaneously broadcasts a message to the other parties. However, a rushing adversary may wait to receive the honest party’s message in any round before deciding its own message.
- 3.
For simplicity, here we assume a non-interactive commitment scheme. In order to use a two-round commitment scheme based on one-way functions, we use the token \({\mathbf T} \) to generate the first commitment message.
- 4.
Such argument systems can be constructed from one-way functions [COPV13].
- 5.
An alternate proof strategy is for the simulator to directly extract the values \(\mathsf {r}_0\) and \(\mathsf {r}_1\) using the extractor of the RWIAOK but we won’t delve further into that.
- 6.
To ease the exposition, we use non-interactive commitments that are based on injective one-way functions. We describe later how the protocol can be modified to use a two-round commitment scheme that relies only on one-way functions without increasing the round complexity of the protocol.
- 7.
To ease the exposition, we use non-interactive commitments that are based on injective one-way functions. We describe later how the protocol can be modified to use a two-round commitment scheme that relies only on one-way functions without increasing the round complexity of the protocol.
- 8.
To ease the exposition, we assume that \({\mathsf x} _k\) and \(\mathsf {r}_k\) are hardwired inside each token. Instead, we can have each party broadcast encrypted signed versions of them which are sent to the respective token along with the other messages.
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Badrinarayanan, S., Jain, A., Ostrovsky, R., Visconti, I. (2019). UC-Secure Multiparty Computation from One-Way Functions Using Stateless Tokens. In: Galbraith, S., Moriai, S. (eds) Advances in Cryptology – ASIACRYPT 2019. ASIACRYPT 2019. Lecture Notes in Computer Science(), vol 11922. Springer, Cham. https://doi.org/10.1007/978-3-030-34621-8_21
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