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

Round 1

Reviewer 1 Report

Review of the paper titled "Probability models of distributed proof generation for zk-SNARK-based blockchains".  

Summary of the paper: The authors investigate two models of distributed proof production for ZK-SNARKs-based sidechains using the Latus consensus protocol, simulating the proof generation process using discrete Markov chains. The first model corresponds to the more straightforward approach, in which each proof is built separately. When the proofs are grouped in a perfect binary tree, the second model analyzes a more challenging problem. Because the proofs from the upper level of the tree can only be produced after the evidence from the preceding levels have been constructed, this set of proofs has natural partial order. The recurrent formulas for the expectation and variance of the number of steps are obtained for the first model. The authors show that expectation reliance on two parameters - the number of provers $n$ and the number of leaves $m$ - may be reduced asymptotically to a function $h$ of a single parameter $n/m$ and characterize this function. The second model is a generalization of the first to the case of a partially ordered set. The authors conclude our research with numerical results on the number of transactions that should be included in the current block by blockforger. The recommended amount of transactions is determined by network factors like time slot length, number of proverbs, proof generation time, and so forth.

  Opinion: On the scientific plan, the paper is very strong, with solid results and proofs, and a plethora of well commented examples. The research perspectives and applications of this work are awesome. This is a very nice paper on the topic of probability models. On the writing plan, I am not so enthusiastic; there are a lot of grammar and punctuation problems. Also, several typos are detected. In conclusion, I suggest a deep revision on the writing side, before publication. When it is done, this work deserves publication in a very nice journal such as Mathematics.  

Author Response

Thank you for your review. We've processed all reviews, changes are marked with the different color of the text. We'll proceed with English editing provided by MDPI after approval by all reviewers'.

Reviewer 2 Report

The proposed manuscript needs some minor improvements:

1) The comparison with the related works in the conclusion could be deeper.(A better comparison with competing solutions is really recommended.)
 By the way, the conclusion itself is quite brief.

2) Furthermore, authors should still consider the format of the images.

3) The paper length is borderline to keep the reader's attention.

Author Response

Thank you for your review. We've processed all reviews, changes are marked with the different color of the text. We'll proceed with English editing provided by MDPI after approval by all reviewers'.

Reviewer 3 Report

The paper was in good form, I just have some minor comments 

1- the result should present in abstract

2- it’s English needs to improve

3- comparison need to present better in comparison section

Author Response

Thank you for your review. We've processed all reviews. We'll proceed with English editing provided by MDPI after approval by all reviewers'.