DiFastBit: Transaction Differentiation Scheme to Avoid Double-Spending for Fast Bitcoin Payments

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. Some abbreviations are used without expatiation, such as HBR etc.

2. The notations in Eq(1) should be explained. 

3. Simulation results showing the probability of preventing double spending should be provided. 

 

Comments on the Quality of English Language

1. The presentation should be improved， some grammar errors exist in this manuscript. 

 

Author Response

We would like to thank the reviewer for their valuable comments on the manuscript mathematics-3107245, as well as the suggestions for improvements. By following the feedback, we have significantly enhanced the quality of the manuscript.

 

The response is provided in the attached PDF document.

Best regards,

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for DiFastBit: distributed transaction scheme. Excellent team work. I recommend some of the following:

1. References more than ten years old ... of 2012, [6] 2013, [8] 2014 [3] can be updated or avoided !

2. In Table 1 comparison can be elaborated fast payments with model characteristics and features !  

Comments for author File: Comments.pdf

Author Response

We would like to thank the reviewer for their valuable comments on the manuscript mathematics-3107245, as well as the suggestions for improvements. By following the feedback, we have significantly enhanced the quality of the manuscript.

 

The response is provided in the attached PDF document.

Best regards,

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper suggests a new transaction differentiation scheme, dubbed DiFastBit to mitigate the double-spending issue in fast Bitcoin payments. This model of Bitcoin as a distributed system and an example set or sequence is used to restate Eve, Mallory et al's requirements for their successful double-spending attack using Karame's Lamport-Happened-before relation. They come up with DiFastBit scheme which is ultimately a merchant layer, and this provides extra incentive as to why fast payments should be different from normal secure payment by modifying the transaction structures. Authors give formal proofs and also provide practical relevance of their approach.

It tackles an important problem of fast payment scenario in Bitcoin, and presents a new idea with transaction classification together with add-on merchant layer.

The authors present a distributed systems model of Bitcoin, and restate Karame's requirements with the Happened-Before Relation from Lamport to enrich their write-up.

Or should it contain formal proofs of the correctness and integrity of the DiFastBit scheme, because without them all other claims about accuracy have no more credibility than they?

It also does not include specific technical details required to implement the DiFastBit scheme, such as transaction types and creation/verification algorithms for fast-payment operations. This includes an explanation of how the neural networks are structured, what they find and in some cases dont find (both chosen strategies will return results) as well as more specific parameters implemented during training.

This paper does not conduct an empirical study of the DiFastBit scheme to know how it behaves in a real bitcoin network or by simulation. It would have been nice for the paper to find practical experimental validation of the scheme and make its case considerably stronger.

The paper would also have benefited from a deeper comparison against existing double-spending prevention schemes, noting the specific advantages of DiFastBit compared with all previous work.

The clarity and presentation of the paper could be better. Certain sections are a little redundant, and the prose at large could be more direct

 

 

Author Response

We would like to thank the reviewer for their valuable comments on the manuscript mathematics-3107245, as well as the suggestions for improvements. By following the feedback, we have significantly enhanced the quality of the manuscript.

 

The response is provided in the attached PDF document.

Best regards

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Summary:

Bitcoin payment system has recently attracted widespread adoption. Transaction verification in the Bitcoin network is a slow process making it challenging to apply for fast transaction applications. A major problem associated with the Bitcoin network is the double spending problem. To avoid this, all nodes in the Bitcoin network should have a consensus about a transaction. This is a slow process; however, to detect the double spending problem, Karame has introduced three requirements. The first is to flood the transactions, and the second is to deploy active listeners for the transactions. Third is to connect to random nodes and reject such connections to prevent the isolation of nodes. Adopting these requirements for fast transactions using bitcoin is a fruitful solution to detect double spending problems. Though the Bitcoin coin network is an asynchronous network, imposing temporal constraints can help verifiers to ensure the order of transactions. This work utilizes Lamport’s happen before relationships for imposing timing constraints. Then, it contributes sufficient theorem and formalism as contributions.

While the formalism of the proposal is sound and intriguing, this work put forward three lammata based on temporal constraints as the sufficient conditions for thwarting the double spending attacks. The formulated lemmata are proved using the contradiction method with supportive figures and arguments. However, this work requires further improvement. Please find the detailed comments.

Minor:

1)     The abstract introduces Karame’s requirements without referencing it.

2)     Figure A3 on page 25 must be moved to the appropriate place.

Major:

1)     In line 452, Theorem 1 should be formulated other way around. Stating sufficient components resulting in DSS rather than saying conclusion (DSS) has certain premises.

2)     Abbreviations should be moved at the beginning.

3)     Proofs of lemmata 1,2 and 3 need clear information about what is premise, what is contradiction and what is conclusion. Present explanation begs conclusion as the explanation is insufficient. Especially, in lemma 1, how P AND (NOT Q) resulting in a tautology is missing as sufficient explanation is given only for an explanation for NOT Q resulting in some conclusion. The same is applicable for lemmata 2 and 3.

4)     Formal verification of the three lemmata could be done using the Tamarin tool to confirm the correctness of the lemmata.

 

5)     DifastBit needs at least minimal experimentation.

Comments for author File: Comments.pdf

Author Response

We would like to thank the reviewer for their valuable comments on the manuscript mathematics-3107245, as well as the suggestions for improvements. By following the feedback, we have significantly enhanced the quality of the manuscript.

 

The response is provided in the attached PDF document.

Best regards

Author Response File: Author Response.pdf

Round 2

Reviewer 4 Report

Comments and Suggestions for Authors

In my opinion, the article is ready for publication. If it requires further revision, it is not to be re-reviewed from my side.