Probability Models of Distributed Proof Generation for zk-SNARK-Based Blockchains

Bespalov, Yuri; Garoffolo, Alberto; Kovalchuk, Lyudmila; Nelasa, Hanna; Oliynykov, Roman

doi:10.3390/math9233016

Cited by 11 publications

(8 citation statements)

References 26 publications

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“…For the generation of a single block considered in [18], the block forger initially selects the number of levels of a perfect binary tree that will be included into a block. In [18] (table 1), we find what number of provers is needed to build the perfect binary tree with = 4, 5, 6, 7, 8, 9 levels during n st = 9 steps with probability 0.95.…”

Section: Discussionmentioning

confidence: 99%

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Models for Generation of Proof Forest in zk-SNARK Based Sidechains

et al. 2023

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Sidechains are among the most promising scalability and extended functionality solutions for blockchains. Application of zero knowledge techniques (Latus, Mina) allows for reaching high level security and general throughput, though it brings new challenges on keeping decentralization where significant effort is required for robust computation of zk-proofs. We consider a simultaneous decentralized creation of various zk-proof trees that form proof-trees sequences in sidechains in the model that combines behavior of provers, both deterministic (mutually consistent) or stochastic (independent) and types of proof trees. We define the concept of efficiency of such process, introduce its quantity measure and recommend parameters for tree creation. In deterministic cases, the sequences of published trees are ultimately periodic and ensure the highest possible efficiency (no collisions in proof creation). In stochastic cases, we obtain a universal measure of prover efficiencies given by the explicit formula in one case or calculated by a simulation model in another case. The optimal number of allowed provers’ positions for a step can be set for various sidechain parameters, such as number of provers, number of time steps within one block, etc. Benefits and restrictions for utilization of non-perfect binary proof trees are also explicitly presented.

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Section: Discussionmentioning

confidence: 99%

“…Our previous papers [18][19][20] considered only issues related to a single block creation. We used probabilistic and game-theoretic approaches to answer the questions on the optimal choice of SC parameters (e.g., a recommended number of transactions per block and a recommended value of incentives chosen).…”

Section: Introductionmentioning

confidence: 99%

Models for Generation of Proof Forest in zk-SNARK Based Sidechains

et al. 2023

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“…They reduce the amount of data transferred between platforms; however, the validation of ZK proofs can be resource-intensive for smart contracts. This includes both mathematical computations and additional algorithmic segments needed for proofing [32]. If the platform verifier tools lack built-in decoding algorithms for a specific ZK solution, then that algorithm must be developed using the platform development kit, and the resulting smart contracts might require significant resources, leading to higher fees.…”

Section: Zero-knowledge Flowmentioning

confidence: 99%

Cross-Chain Bridges: A Potential Solution to Standardising Distributed Ledger Technology in Payment Systems

Zilnieks,

Erins

2023

ITMS

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Despite standardisation initiatives, the modern financial landscape continues to be characterised by heterogeneous payment systems. This issue persists even with the emergence of distributed ledger technology in the market. Independent groups of developers are producing their own permissioned blockchain solutions without clear directions for standardisation that could be associated to the lack of a clear position from central banks and regulatory organisations regarding these technologies. The unresolved problem of transaction finality in distributed ledgers adds to the difficulty of reconciling separate distributed platforms. One potential solution is the implementation of cross-chain bridges, which can establish connections between platforms and potentially enable seamless experiences for end users and applications. The paper discusses the advantages and issues associated with these bridges.

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“…Moreover, research regarding how zk-SNARKs can contribute to blockchains scalability is being conducted [42], with the research focused on distributed proof generation making use of recursive zk-SNARKs.…”

Section: Related Workmentioning

confidence: 99%

FORT: Right-Proving and Attribute-Blinding Self-Sovereign Authentication

2022

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Nowadays, there are a plethora of services that are provided and paid for online, such as video streaming subscriptions, car-share, vehicle parking, purchasing tickets for events, etc. Online services usually issue tokens that are directly related to the identities of their users after they sign up to a platform; users need to authenticate themselves by using the same credentials each time they use the service. Likewise, when using in-person services, such as going to a concert, after paying for this service, the user usually receives a ticket, which proves that he/she has the right to use that service. In both scenarios, the main concerns surround the centralization of these systems and that they do not ensure customers’ privacy. The involved service providers are trusted third parties—authorities that offer services and handle private data about users. In this paper, we designed and implemented FORT, a decentralized system that allows customers to prove their rights to use specific services (either online or in-person) without revealing sensitive information. To achieve decentralization, we proposed a solution where all of the data are handled by a blockchain. We describe and uniquely identify users’ rights using non-fungible tokens (NFTs), and possession of these rights is demonstrated by using zero-knowledge proofs—cryptographic primitives that allow us to guarantee customers’ privacy. Furthermore, we provide benchmarks of FORT, which show that our protocol is efficient enough to be used in devices with low computing resources, such as smartphones or smartwatches, which are devices commonly used in our use case scenario.

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Probability Models of Distributed Proof Generation for zk-SNARK-Based Blockchains

Cited by 11 publications

References 26 publications

Models for Generation of Proof Forest in zk-SNARK Based Sidechains

Models for Generation of Proof Forest in zk-SNARK Based Sidechains

Cross-Chain Bridges: A Potential Solution to Standardising Distributed Ledger Technology in Payment Systems

FORT: Right-Proving and Attribute-Blinding Self-Sovereign Authentication

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