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Lecture notes in computer science

Bingo: Adaptivity and Asynchrony in Verifiable Secret Sharing and Distributed Key Generation

Ittai Abraham, Philipp Jovanovic, Mary Maller, Sarah Meiklejohn, Gilad Stern

Published Jan 1, 2023• 34 citations
Publisher
DOI
10.1007/978-3-031-38557-5_2

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Verifiable secret sharing schemes are important in cloud computing environments. Thus a key can be distributed over many servers by threshold secret sharing mechanism. The key is then reconstructed when needed. Secret sharing has also been suggested for sensor networks where the links are liable to be tapped by sending the data in shares which makes the task of the eavesdropper harder. The security in such environments can be made greater by continuous changing of the way the shares are constructed. In the present paper we proposed a verifiable quantum -threshold secret sharing scheme using Lagrange interpolation and two qudit Bell state in -dimensional Hilbert space. As discussed in the second last section of this paper, the proposed scheme is enough secure against the fraud in secret share distribution phase as well as secret reconstruction phase.

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Distributed key generation (DKG) has been studied extensively in the cryptographic literature. However, it has never been examined outside of the synchronous setting, and the known DKG protocols cannot guarantee safety or liveness over the Internet. In this work, we present the first realistic DKG protocol for use over the Internet. We propose a practical system model for the Internet and define an efficient verifiable secret sharing (VSS) scheme in it. We observe the necessity of Byzantine agreement for asynchronous DKG and analyze the difficulty of using a randomized protocol for it. Using our VSS scheme and a leader-based agreement protocol, we then design a provably secure DKG protocol. We also consider and achieve cryptographic properties such as uniform randomness of the shared secret and compare static versus adaptive adversary models. Finally, we implement our DKG protocol, and establish its efficiency and reliability by extensively testing it on the PlanetLab platform. Counter to a general non-scalability perception about asynchronous systems, our experiments demonstrate that our asynchronous DKG protocol scales well with the system size and it is suitable for realizing multiparty computation and threshold cryptography over the Internet.
In this paper, we present the first Asynchronous Distributed Key Generation (ADKG) algorithm which is also the first distributed key generation algorithm that can generate cryptographic keys with a dual (f,2f+1)-threshold (where f is the number of faulty parties). As a result, using our ADKG we remove the trusted setup assumption that the most scalable consensus algorithms make. In order to create a DKG with a dual (f,2f+1)- threshold we first answer in the affirmative the open question posed by Cachin et al. [7] on how to create an Asynchronous Verifiable Secret Sharing (AVSS) protocol with a reconstruction threshold of f+1<k łe 2f+1, which is of independent interest. Our High-threshold-AVSS (HAVSS) uses an asymmetric bivariate polynomial to encode the secret. This enables the reconstruction of the secret only if a set of k nodes contribute while allowing an honest node that did not participate in the sharing phase to recover his share with the help of f+1 honest parties. Once we have HAVSS we can use it to bootstrap scalable partially synchronous consensus protocols, but the question on how to get a DKG in asynchrony remains as we need a way to produce common randomness. The solution comes from a novelEventually Perfect Common Coin (EPCC) abstraction that enables the generation of a common coin from n concurrent HAVSS invocations. EPCC's key property is that it is eventually reliable, as it might fail to agree at most f times (even if invoked a polynomial number of times). UsingEPCC we implement anEventually Efficient Asynchronous Binary Agreement (EEABA) which is optimal when the EPCC agrees and protects safety when EPCC fails. Finally, using EEABA we construct the first ADKG which has the same overhead and expected runtime as the best partially-synchronous DKG (O(n4) words, O(f) rounds). As a corollary of our ADKG, we can also create the first Validated Asynchronous Byzantine Agreement (VABA) that does not need a trusted dealer to setup threshold signatures of degree n-f. Our VABA has an overhead of expected O(n2) words and O(1) time per instance, after an initial O(n4) words and O(f) time bootstrap via ADKG.
Verifiable secret sharing schemes are important in cloud computing environments. Thus a key can be distributed over many servers by threshold secret sharing mechanism. The key is then reconstructed when needed. Secret sharing has also been suggested for sensor networks where the links are liable to be tapped by sending the data in shares which makes the task of the eavesdropper harder. The security in such environments can be made greater by continuous changing of the way the shares are constructed. In the present paper we proposed a verifiable quantum -threshold secret sharing scheme using Lagrange interpolation and two qudit Bell state in -dimensional Hilbert space. As discussed in the second last section of this paper, the proposed scheme is enough secure against the fraud in secret share distribution phase as well as secret reconstruction phase.