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Lecture notes in computer science

Efficient Fully Secure Computation via Distributed Zero-Knowledge Proofs

Elette Boyle, Niv Gilboa, Yuval Ishai, Ariel Nof

Published Jan 1, 2020• 46 citations
Publisher
DOI
10.1007/978-3-030-64840-4_9

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Fully Homomorphic Encryption (FHE) enables one to implement low-round and low-communication complexity Multi-Party Computation (MPC) which is secure in the static malicious corruption model. By expanding on an idea presented in the full version of the FHE-based MPC protocol of Smart (IMA, 2023), we show how to completely remove the need for Zero-Knowledge Proofs-of-Knowledge in that protocol. This simplification makes the final security proof of the MPC protocol much simpler, and more modular. The new protocol makes use of an FHE scheme with an encrypted PRF functionality, and in addition to our main result we formalize the security of such encrypted PRFs and prove the construction of Deo et al. (CCS 2025) secure in this model.

IACR Communications in Cryptology•Oct 26, 2026•0 citations
Abstract. Secure multiparty computation (MPC) allows a set of parties to securely evaluate any agreed function of their inputs, even when up to t of the n parties are faulty. Protocols for synchronous networks (where every sent message is assumed to arrive within a constant time) tolerate up to t < n/2 faulty parties, whereas in the more realistic asynchronous setting (with no a priory information on maximal message delay) only security against t < n/3 is possible. Note that even asynchronous Byzantine agreement requires t < n/3. In this paper, we are interested in the minimal synchronicity assumption for achieving security against t < n/2. It turns out that the bottleneck of asynchronous MPC is the distribution of the inputs: Once the inputs are correctly distributed, any deterministic function can be computed over a fully asynchronous network with t < n/2. Furthermore, we show that the inputs can be verifiably distributed with t < n/2, if a single round of synchronous broadcast is available. Composing the above, we obtain the first MPC protocol that achieves security against t < n/2 without assuming a fully synchronous network. Actually our protocol guarantees security against any faulty minority in an almost asynchronous network, i.e. in a network with one single round of synchronous broadcast (followed by a fully asynchronous communication). Furthermore our protocol takes inputs of all parties (in a fully asynchronous network only inputs of n−t parties can be guaranteed), and so achieves everything that is possible in synchronous networks (but impossible in fully asynchronous networks) at the price of just one synchronous broadcast round. As tools for our protocol we introduce the notions of almost non-interactive verifiable secret-sharing and almost non-interactive zero-knowledge proof of knowledge, which are of independent interest as they can serve as efficient replacements for fully non-interactive verifiable secret-sharing and fully non-interactive zero-knowledge proof of knowledge.
Distributed networks remarkably enhance the convenience of network connectivity. How to achieve efficient cooperative computation while preserving data privacy is a challenge in the scenario of distributed networks. Secure computation, as the key technology of information security and privacy protection in the distributed networks, attracts more and more attention. In the paper, we develop the protocols of secure two-party computation in the presence of malicious adversaries which are constructed with homomorphic probabilistic cryptosystem, and propose four honest-verifier zero-knowledge proof protocols to detect two cheating behaviours of the malicious adversary. The proposed protocols are more targeted than the existing work. The analysis shows that the proposed protocols are complete, sound and zero-knowledge. As an application, we show how to use our protocols in a secure two-party protocol to detect cheating, which can make it secure in the presence of malicious adversaries.
Fully Homomorphic Encryption (FHE) enables one to implement low-round and low-communication complexity Multi-Party Computation (MPC) which is secure in the static malicious corruption model. By expanding on an idea presented in the full version of the FHE-based MPC protocol of Smart (IMA, 2023), we show how to completely remove the need for Zero-Knowledge Proofs-of-Knowledge in that protocol. This simplification makes the final security proof of the MPC protocol much simpler, and more modular. The new protocol makes use of an FHE scheme with an encrypted PRF functionality, and in addition to our main result we formalize the security of such encrypted PRFs and prove the construction of Deo et al. (CCS 2025) secure in this model.