An Alternative Diffie-Hellman Protocol

Round 1

Reviewer 1 Report

Manuscript is very interesting but before further proceedings require some important aspects to address.

the attached commented PDF contains of those.

Comments for author File: Comments.pdf

Author Response

Detailed Response to Reviewers

 

Manuscript ID: cryptography-663370

Title: An alternative Diffie-Hellman protocol

Journal: Cryptography.

 

Dear Reviewer 1,

 

I would like to thank you for your comments and recommendations. I have tried to include all the suggestions in this new version of the paper. I have also tried to answer all your recommendations point by point. In this document, my answers are marked in red.

 

In the revised manuscript, the required changes are also marked in red.

 

If there are any or some of your comments which I misinterpreted or misunderstood, please comment more precisely which change you are suggesting. I really appreciate the feedback I can get. Thank you for all the consideration!

 

Yours sincerely,

Eric Järpe

 

 

Reviewers/Editor comments:

 

Reviewer 1:

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1. English language and style: Moderate English changes required

 

Author: The manuscript has, as a last step after other changes were made, been grammar- and spell-checked by means of the software cloud service Grammarly (https://app.grammarly.com).

Also, the sentence “Then all security the depends on M1FP and the secrecy of $a$ and $b$.” was updated to “Then all security depends on M1FP and the secrecy of $a$ and $b$.”

 

2. Does the introduction provide sufficient background and include all relevant references? Can be improved.

 

Author: Subsection 1.1 Related literature with some recent progress relating to post-quantum solutions and to key exchange methods was added.

 

3. Is the research design appropriate? Must be improved.

 

Author: The presentation in section “4. Attacks and countermeasures” was much changed. Most importantly an algorithm defining the Naïve attack has been included.

 

4. Are the methods adequately described? Can be improved.

 

Author: The proofs of statements about computation complexity (Theorems 2 and 3) are stated and proved in the Appendix.

 

5. Are the results clearly presented? Must be improved.

 

Author: The presentation of the results in the text and the reasoning is done relating to these Theorems in the Appendix. This change has been done to subsection “2.1 The core function”, to section “4. Attacks and countermeasures” and to subsection “4.2 Computation complexity”.

Another change is that the numbers used in the Example in section “5. An example” was extended to include more digits of accuracy in order to make the presentation authentic; For sending a message consisting of N digits, the numbers $a’$ and $b’$ transferred between Alice and Bob really need to be 2N+1 to be guaranteed successful key generation. Now the keys $a’$ and $b’$ do indeed consist of 61 digits for transferring the 30 digits message.

 

6. Are the conclusions supported by the results? Can be improved

 

Author: The conclusions are that:

- the protocol is quantum computer resilient (supported by the fact that M1FP is not solved by any existing quantum computer algorithms)

- there is a possibility for an unknown number of digits in the floating point number used in case of Version 1 of the protocol (i.e. if the initial transcendental number is secret)

- only one number needs to be public in case of Version 2 of the protocol (as opposed to both the order N of the field and the generator g) in case of Diffie-Hellman.

7. Enhance the list with recent strong literature.

 

Author: 10 extra bibliographical references were added of which 2 are from 2019, 2 are from 2018, 1 is from 2017, 3 are after 2000 and 2 are before 2000.

These are one main exception from making all changes in red: I was not able to put the literature entries added in red since these were generated by bibtex, not written by myself. However, for the record, the newly added entries are the ones numbered 2, 5 – 12, 17

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Cryptographic protocol design is an important and difficult process. Formal proof techniques are needed to make this process acceptable. The proof presented in the study is not convincing enough.

The advantages of the proposed method should be demonstrated experimentally and theoretically. In particular, references are inadequate. The study is expected to express the authenticity of the proposal presented in more persuasive methods.

Author Response

Detailed Response to Reviewers

 

Manuscript ID: cryptography-663370

Title: An alternative Diffie-Hellman protocol

Journal: Cryptography.

 

Dear Reviewer 2,

 

I would like to thank you for your comments and recommendations. I have tried to include all the suggestions in this new version of the paper. I have also tried to answer all your recommendations point by point. In this document, my answers are marked in red.

 

In the revised manuscript, the required changes are also marked in red.

 

If there are any or some of your comments which I misinterpreted or misunderstood, please comment more precisely which change you are suggesting. I really appreciate the feedback I can get. Thank you for all the consideration!

 

Yours sincerely,

Eric Järpe

 

Reviewers/Editor comments:

 

 

Reviewer 2:

꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊꞊

 

1. English language and style: English language and style are fine/minor spell check required.

 

Author: The manuscript has, as the last step after other changes were made, been grammar- and spell-checked by means of the software cloud service Grammarly (https://app.grammarly.com).

 

2. Does the introduction provide sufficient background and include all relevant references? Must be improved.

 

Author: Subsection 1.1 Related literature with some recent progress relating to post-quantum solutions and to key exchange methods was added.

 

3. Is the research design appropriate? Must be improved.

 

Author: The presentation in section “4. Attacks and countermeasures” was much changed. Most importantly an algorithm defining the Naïve attack has been included.

 

4. Are the methods adequately described? Must be improved.

 

Author: The proofs of statements about computation complexity (Theorems 2 and 3) are stated and proved in the Appendix.

 

5. Are the results clearly presented? Must be improved.

 

Author: The presentation of the results in the text and the reasoning is done relating to these Theorems in the Appendix. This change has been done to subsection “2.1 The core function”, to section “4. Attacks and countermeasures” and to subsection “4.2 Computation complexity”.

Another change is that the numbers used in the Example in section “5. An example” were extended to include more digits of accuracy in order to make the presentation authentic; For sending a message consisting of N digits, the numbers $a’$ and $b’$ transferred between Alice and Bob really need to be 2N+1 to be guaranteed successful key generation. Now the keys $a’$ and $b’$ do indeed consist of 61 digits for transferring the 30 digits message.

 

6. Are the conclusions supported by the results? Must be improved

 

Author: The conclusions are that:

- the protocol is quantum computer resilient (supported by the fact that M1FP is not solved by any existing quantum computer algorithms)

- there is a possibility for an unknown number of digits in the floating point number used in case of Version 1 of the protocol (i.e. if the initial transcendental number is secret)

- only one number needs to be public in case of Version 2 of the protocol (as opposed to both the order N of the field and the generator g) in case of Diffie-Hellman.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Very nicely answered and have updated the manuscript

Just double check the complete manuscript to avoid language mistakes and typos

Reviewer 2 Report

Revised version can be accepted