Quantum MPC from random oracle requires Omega of circuit size communication
Original title: On the (Quantum) Communication Complexity of Secure MPC from a Random Oracle
New lower bounds show random oracle cannot reduce online communication in information-theoretic MPC and that quantum-accessible oracles with classical communication yield no savings.
Information-theoretic MPC protocols achieve specific online communication bounds with preprocessing or honest majority. These bounds are tight for inner products. A new Omega of circuit size lower bound holds even in the random oracle model for preprocessing MPC. An Omega of circuit size lower bound applies to honest-majority MPC relative to a random oracle. Quantum communication protocols cannot reduce communication compared to classical counterparts. A two-party protocol with quantum communication and post-quantum one-way functions achieves poly of lambda and log of circuit size communication.
- Lower bound for preprocessing MPC matches information-theoretic bound
- New construction for degree-2 polynomials matches honest-majority bound
- Quantum protocols offer no communication advantage
- Blackbox protocols with o of circuit size quantum communication require Omega of cryptographic operations
From the original article
1 min read at arxiv.orgInformation-theoretic MPC among $n$ parties with $t$ corruptions can securely evaluate a circuit $C$ with $O(|C| \cdot t/(n-t))$ online communication in the preprocessing model and $O(|C| \cdot t/(n-2t))$ communication in the honest majority setting. Damgård, Larsen and Nielsen (CRYPTO 2019) showed that both communication bounds are tight for inner products.
By Alexander Hoover · arxiv.org
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