Abstract
The recently proposed YOSO model is a groundbreaking approach to MPC, executable on a public blockchain, circumventing adaptive player corruption by hiding the corruption targets until they are worthless. Players are selected unpredictably from a large pool to perform MPC subtasks, in which each selected player sends a single message (and reveals their identity). While YOSO MPC has attractive asymptotic complexity, unfortunately, it is concretely prohibitively expensive due to the cost of its building blocks.
We propose a modification to the YOSO model that preserves resilience to adaptive server corruption, but allows for much more efficient protocols. In SCALES (Small Clients And Larger Ephemeral Servers) only the servers facilitating the MPC computation are ephemeral (unpredictably selected and “speak once”). Input providers (clients) publish problem instance and collect the output, but do not otherwise participate in computation \(\text {SCALES}\) offers attractive features, and improves over YOSO in outsourcing MPC to a large pool of servers under adaptive corruption.
We build \(\text {SCALES}\) from Rerandomizable Garbling Schemes (RGS). RGS is a contribution of independent interest with additional applications.
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Notes
- 1.
The final output of the protocol can easily be made private - known only to the clients. This is done by computing a function that gives an encryption of the desired output under the client’s key.
- 2.
We define this notion as a symmetric key primitive which suffices for our purposes. Nevertheless, the instantiation we give uses a public key encryption scheme [BHHO08].
- 3.
Note that \(\mathcal {B} _d\) has been specified as an input to \(\textsf{Aggregate}\), but \(\textsf{Aggregate}\) is required to only use a part of \(\mathcal {B} _d\) which is independent of k.
- 4.
For simplicity we define KMHE as a private key primitive (where encryption is carried out using the secret key). Nevertheless, the definition can be naturally extended to a public key setting as well.
- 5.
We assume that the evaluator identifies the valid output label by adding a fixed suffix to the plaintext as suggested originally in [LP09].
- 6.
As different transformations are applied to the keys used for encrypting the different input labels, and only on the key domain, it suffices to use KMHE.
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Acknowledgments
We thank Shai Halevi for discussions including feedback regarding the gap in [GHV10]. Anasuya Acharya and Carmit Hazay are supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office, and by ISF grant No. 1316/18. Vladimir Kolesnikov was supported in part by NSF award #1909769, by a Facebook research award, a Cisco research award, and by Georgia Tech’s IISP cybersecurity seed funding (CSF) award. Manoj Prabhakaran is supported by a Ramanujan Fellowship of the Department of Science and Technology, India. Carmit Hazay and Manoj Prabhakaran are also supported by the Algorand Centres of Excellence programme managed by Algorand Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of Algorand Foundation.
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Acharya, A., Hazay, C., Kolesnikov, V., Prabhakaran, M. (2022). SCALES. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13748. Springer, Cham. https://doi.org/10.1007/978-3-031-22365-5_18
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