Abstract
Starting with the work of Rivest et al. in 1996, timed assumptions have found many applications in cryptography, building e.g. the foundation of the blockchain technology. They also have been used in the context of classical MPC, e.g. to enable fairness. We follow this line of research to obtain composable general MPC in the plain model.
This approach comes with a major advantage regarding environmental friendliness, a property coined by Canetti et al. (FOCS 2013). Informally, this means that our constructions do not “hurt” game-based security properties of protocols that hold against polynomial-time adversaries when executed alone.
As an additional property, our constructions can be plugged into any UC-secure protocol without loss of security.
Towards proving the security of our constructions, we introduce a variant of the UC security notion that captures timed cryptographic assumptions. Combining standard timed commitment schemes and standard polynomial-time hardness assumptions, we construct a composable commitment scheme in the plain model. As this construction is constant-round and black-box, we obtain the first fully environmentally friendly composable constant-round black-box general MPC protocol in the plain model from standard (timed) assumptions.
For the full version [BMM21], see https://eprint.iacr.org/2021/843.
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Notes
- 1.
Newer versions of the UC framework such as UC2020 explicitly allow multiple work tapes, allowing the emulation of other Turing machines with only additive overhead.
- 2.
In order to capture the setting where \(\ell (\kappa )\) is constant but e.g. the reduction overhead depends on \(\kappa \), we parameterize \(\ell '\) with both values.
- 3.
When considering an appropriate encoding, the definition can be extended to e.g. group elements.
- 4.
We assume unique timer IDs within a protocol throughout this paper.
- 5.
This is even more plausible when using cryptographic assumptions that are believed to be hard even for parallel adversaries.
- 6.
In contrast to stand-alone experiments where \(\mathtt {timer}\) messages are not parameterized with the timed security parameter, we have chosen to do so in the TLUC setting because the mechanism should be agnostic of the currently executed protocol and its timed security parameter.
- 7.
A UC protocol \(\pi \) that UC-realizes an ideal functionality \(\mathcal {F} \) may of course send \(\mathtt {timer}\) messages. However, as UC emulation also considers environments that handle these messages arbitrarily, the security of \(\pi \) cannot rely on them.
- 8.
\(\mathcal {F} _{\mathrm {MCOM}}\) and the multi-session extension \(\hat{\mathcal {F}}_{\mathrm {COM}}\) of \(\mathcal {F} _{\mathrm {COM}}\) are equivalent [CR03].
- 9.
Informally, a functionality \(\mathcal {F}\) is well-formed if its behavior is independent of which parties are corrupted [Can+02].
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Acknowledgements
Jeremias Mechler, Jörn Müller-Quade: This work was supported by funding from the topic Engineering Secure Systems of the Helmholtz Association (HGF) and by KASTEL Security Research Labs.
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Broadnax, B., Mechler, J., Müller-Quade, J. (2021). Environmentally Friendly Composable Multi-party Computation in the Plain Model from Standard (Timed) Assumptions. In: Nissim, K., Waters, B. (eds) Theory of Cryptography. TCC 2021. Lecture Notes in Computer Science(), vol 13042. Springer, Cham. https://doi.org/10.1007/978-3-030-90459-3_25
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