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- W1748404930 abstract "Verifiable Secret Sharing (VSS) is a fundamental primitive used in many distributed cryptographic tasks, such as Multiparty Computation (MPC) and Byzantine Agreement (BA). It is a two phase (sharing, reconstruction) protocol. The VSS and MPC protocols are carried out among n parties, where t out of n parties can be under the influence of a Byzantine (active) adversary, having unbounded computing power. It is well known that protocols for perfectly secure VSS and perfectly secure MPC exist in an asynchronous network iff n ≥ 4t + 1. Hence, we call any perfectly secure VSS (MPC) protocol designed over an asynchronous network with n = 4t + 1 as optimally resilient VSS (MPC) protocol. A secret is d-shared among the parties if there exists a random degree-d polynomial whose constant term is the secret and each honest party possesses a distinct point on the degree-d polynomial. Typically VSS is used as a primary tool to generate t-sharing of secret(s). In this paper, we present an optimally resilient, perfectly secure Asynchronous VSS (AVSS) protocol that can generate d-sharing of a secret for any d, where t ≤ d ≤ 2t. This is the first optimally resilient, perfectly secure AVSS of its kind in the literature. Specifically, our AVSS can generate d-sharing of ℓ ≥ 1 secrets from ${mathbb F}$ concurrently, with a communication cost of ${cal O}(ell n^2 log{|{mathbb F}|})$ bits, where ${mathbb F}$ is a finite field. Communication complexity wise, the best known optimally resilient, perfectly secure AVSS is reported in [2]. The protocol of [2] can generate t-sharing of ℓ secrets concurrently, with the same communication complexity as our AVSS. However, the AVSS of [2] and [4] (the only known optimally resilient perfectly secure AVSS, other than [2]) does not generate d-sharing, for any d > t. Interpreting in a different way, we may also say that our AVSS shares ℓ(d + 1 − t) secrets simultaneously with a communication cost of ${cal O}(ell n^2 log{|{mathbb F}|})$ bits. Putting d = 2t (the maximum value of d), we notice that the amortized cost of sharing a single secret using our AVSS is only ${cal O}(n log{|{mathbb F}|})$ bits. This is a clear improvement over the AVSS of [2] whose amortized cost of sharing a single secret is ${cal O}(n^2 log{|{mathbb F}|})$ bits. As an interesting application of our AVSS, we propose a new optimally resilient, perfectly secure Asynchronous Multiparty Computation (AMPC) protocol that communicates ${cal O}(n^2 log|{mathbb F}|)$ bits per multiplication gate. The best known optimally resilient perfectly secure AMPC is due to [2], which communicates ${cal O}(n^3 log|{mathbb F}|)$ bits per multiplication gate. Thus our AMPC improves the communication complexity of the best known AMPC of [2] by a factor of Ω(n)." @default.
- W1748404930 created "2016-06-24" @default.
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- W1748404930 date "2010-01-01" @default.
- W1748404930 modified "2023-09-26" @default.
- W1748404930 title "Communication Efficient Perfectly Secure VSS and MPC in Asynchronous Networks with Optimal Resilience" @default.
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- W1748404930 doi "https://doi.org/10.1007/978-3-642-12678-9_12" @default.
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