In this work, we study the fascinating notion of output-compressing randomized encodings for Turing Machines, in a shared randomness model. In this model, the encoder and decoder have access to a shared random string, and the efficiency requirement is, the size of the encoding must be independent of the running time and output length of the Turing Machine on the given input, while the length of the shared random string is allowed to grow with the length of the output. We show how to construct output-compressing randomized encodings for Turing machines in the shared randomness model, assuming iO for circuits and any assumption in the set {LWE, DDH, N𝑡ℎ Residuosity}.
We then show interesting implications of the above result to basic feasibility questions in the areas of secure multiparty computation (MPC) and indistinguishability obfuscation (iO):
1.Compact MPC for Turing Machines in the Random Oracle Model. In the context of MPC, we consider the following basic feasibility question: does there exist a malicious-secure MPC protocol for Turing Machines whose communication complexity is independent of the running time and output length of the Turing Machine when executed on the combined inputs of all parties? We call such a protocol as a compact MPC protocol. Hubácek and Wichs [HW15] showed via an incompressibility argument, that, even for the restricted setting of circuits, it is impossible to construct a malicious secure two party computation protocol in the plain model where the communication complexity is independent of the output length. In this work, we show how to evade this impossibility by compiling any (non-compact) MPC protocol in the plain model to a compact MPC protocol for Turing Machines in the Random Oracle Model, assuming output-compressing randomized encodings in the shared randomness model.
2. Succinct iO for Turing Machines in the Shared Randomness Model. In all existing constructions of iO for Turing Machines, the size of the obfuscated program grows with a bound on the input length. In this work, we show how to construct an iO scheme for Turing Machines in the shared randomness model where the size of the obfuscated program is independent of a bound on the input length, assuming iO for circuits and any assumption in the set {LWE, DDH, N𝑡ℎ Residuosity}.
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Towards Multiparty Computation Withstanding Coercion of All Parties
Incoercible multi-party computation (Canetti-Gennaro ’96) allows parties to engage in secure computation with the additional guarantee that the public transcript of the computation cannot be used by a coercive outsider to verify representations made by the parties regarding their inputs, outputs, and local random choices. That is, it is guaranteed that the only deductions regarding the truthfulness of such representations, made by an outsider who has witnessed the communication among the parties, are the ones that can be drawn just from the represented inputs and outputs alone. To date, all incoercible secure computation protocols withstand coercion of only a fraction of the parties, or else assume that all parties use an execution environment that makes some crucial parts of their local states physically inaccessible even to themselves.
We consider, for the first time, the setting where all parties are coerced, and the coercer expects to see the entire history of the computation. We allow both protocol participants and external attackers to access a common reference string which is generated once and for all by an uncorruptable trusted party. In this setting we construct:
- A general multi-party function evaluation protocol, for any number of parties, that withstands coercion of all parties, as long as all parties use the prescribed ``faking algorithm'' upon coercion. This holds even if the inputs and outputs represented by coerced parties are globally inconsistent with the evaluated function.
- A general two-party function evaluation protocol that withstands even the %``mixed'' case where some of the coerced parties do follow the prescribed faking algorithm. (For instance, these parties might collude with the coercer and disclose their true local states.) This protocol is limited to functions where the input of at least one of the parties is taken from a small (poly-size) domain. It uses fully deniable encryption with public deniability for one of the parties; when instantiated using the fully deniable encryption of Canetti, Park, and Poburinnaya (Crypto'20), it takes 3 rounds of communication.
Both protocols operate in the common reference string model, and use fully bideniable encryption (Canetti Park and Poburinnaya, Crypto'20) and sub-exponential indistinguishability obfuscation. Finally, we show that protocols with certain communication pattern cannot be incoercible, even in a weaker setting where only some parties are coerced.
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- NSF-PAR ID:
- 10299514
- Date Published:
- Journal Name:
- Theory of Cryptography Conference
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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