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Paper: Efficient Fully Secure Computation via Distributed Zero-Knowledge Proofs

Authors:
Elette Boyle
Niv Gilboa
Yuval Ishai
Ariel Nof
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DOI: 10.1007/978-3-030-64840-4_9
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Abstract: Secure computation protocols enable mutually distrusting parties to compute a function of their private inputs while revealing nothing but the output. Protocols with {\em full security} (also known as {\em guaranteed output delivery}) in particular protect against denial-of-service attacks, guaranteeing that honest parties receive a correct output. This feature can be realized in the presence of an honest majority, and significant research effort has gone toward attaining full security with good asymptotic and concrete efficiency. We present a fully secure protocol for {\em any constant} number of parties $n$ and $t<n/2$ corruptions that achieves full security with the {\em same amortized communication} as for semi-honest security: $\frac{3t}{2t+1}|C| + o(|C|)$ $R$-elements per party ($\approx 1.5$ $R$-elements), for a circuit with $|C|$ multiplication gates over either a finite field $R=\FF$ or over the ring $R=\Z_{2^k}$. Our techniques include new methods for utilizing the distributed zero-knowledge proofs of Boneh {\em et al.} (CRYPTO 2019) for both distributed verifiers {\em and} provers. As a secondary contribution, we show that similar techniques can be used to compile the best known honest-majority protocols for an arbitrary (super-constant) number of semi-honest parties into ones that achieve {\em security with abort} against malicious parties, with sublinear additive cost. We present an efficient protocol for {\em any constant} number of parties $n$, with full security against $t<n/2$ corrupted parties, that makes a black-box use of a pseudorandom generator. Our protocol evaluates an arithmetic circuit $C$ over a finite ring $R$ (either a finite field or $R=\Z_{2^k}$) with communication complexity of $\frac{3t}{2t+1}S + o(S)$ $R$-elements per party, where $S$ is the number of multiplication gates in $C$ (namely, $<1.5$ elements per party per gate). This matches the best known protocols for the semi-honest model up to the sublinear additive term. For a small number of parties $n$, this improves over a recent protocol of Goyal {\em et al.} (Crypto 2020) by a constant factor for circuits over large fields, and by at least an $\Omega(\log n)$ factor for Boolean circuits or circuits over rings. Our protocol provides new methods for applying the distributed zero-knowledge proofs of Boneh {\em et al.}~(Crypto 2019), which only require logarithmic communication, for compiling semi-honest protocols into fully secure ones in the more challenging case of $t>1$ corrupted parties. %Similarly to the recent fully secure 3-party protocol of Boyle {\em et al.} (CCS 2019), our protocol builds on the sublinear-communication distributed zero-knowledge proofs of Boneh {\em et al.} (Crypto 2019) to compile any ``natural'' semi-honest protocol into a fully secure protocol. However, applying this tool with $t>1$ corrupted parties introduces several nontrivial challenges that we overcome in this work. Our protocol relies on {\em replicated secret sharing} to minimize communication and simplify the mechanism for achieving full security. This results in computational cost that scales exponentially with $n$. Our main protocol builds on a new honest-majority protocol for verifying the correctness of multiplication triples by making a {\em general} use of distributed zero-knowledge proofs. While the protocol only achieves the weaker notion of {\em security with abort}, it applies to any linear secret-sharing scheme and provides a conceptually simpler, more general, and more efficient alternative to previous protocols from the literature. In particular, it can be combined with the Fiat-Shamir heuristic to simultaneously achieve logarithmic communication complexity and constant round complexity.
Video from ASIACRYPT 2020
BibTeX
@article{asiacrypt-2020-30731,
  title={Efficient Fully Secure Computation via Distributed Zero-Knowledge Proofs},
  booktitle={Advances in Cryptology - ASIACRYPT 2020},
  publisher={Springer},
  doi={10.1007/978-3-030-64840-4_9},
  author={Elette Boyle and Niv Gilboa and Yuval Ishai and Ariel Nof},
  year=2020
}