Abstract
The paper is devoted to the investigation of the distributed proof generation process, which makes use of recursive zk-SNARKs. Such distributed proof generation, where recursive zk-SNARK-proofs are organized in perfect Mercle trees, was for the first time proposed in Latus consensus protocol for zk-SNARKs-based sidechains. We consider two models of a such proof generation process: the simplified one, where all proofs are independent (like one level of tree), and its natural generation, where proofs are organized in partially ordered set (poset), according to tree structure. Using discrete Markov chains for modeling of corresponding proof generation process, we obtained the recurrent formulas for the expectation and variance of the number of steps needed to generate a certain number of independent proofs by a given number of provers. We asymptotically represent the expectation as a function of the one variable n/m, where n is the number of provers m is the number of proofs (leaves of tree). Using results obtained, we give numerical recommendation about the number of transactions, which should be included in the current block, idepending on the network parameters, such as time slot duration, number of provers, time needed for proof generation, etc.
Highlights
Sidechains (SCs) [1,2,3,4], and some similar tools, such as [5,6] are very suitable and prospective instrument in modern blockchains
In what follows we will consider only SCs based on Latus Consensus Protocol [11], which isa hybrid PoS based on Ouroboros Praos [12], with additional binding to a PoW mainchain (MC)
In Latus consensus, this information contains a series of recursive zk-SNARK-proofs [14,15] that establish decentralized and verifiable cross-chain data transfers
Summary
Sidechains (SCs) [1,2,3,4], and some similar tools, such as [5,6] are very suitable and prospective instrument in modern blockchains. The main feature of the Latus consensus is to reduce the volume of information sent to MC from SC, using a recursive composition of zk-SNARKs, which allows to construct a succinct proof of the correctness for sidechain state transitions for the period of a withdrawal epoch. Such a number depends on the network parameters, such as time slot duration, number of active provers, time needed for prove generation, and so on.
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