Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article presents a very interesting piece of work. I appreciated the subtle sarcasm embedded in several phrases — particularly the remark that "perfect secrecy is perfectly useless..." 

This version appears to be a reviewed update of an earlier submission posted on arXiv (https://arxiv.org/pdf/2404.07022). While the topic is engaging, I found parts of the text somewhat difficult to follow.

The Introduction is generally well-written, although there is inconsistency in the notation used for the key. After line 67, the uppercase K becomes lowercase k, and this change propagates through the rest of the text.

Lines 106 to 121 appear to be identical to lines 609 to 712, which may be an editorial oversight.

Line 121 states "in additoin" should say "in addition"

In Section 3, I suggest a reformulation. The introduction to Lehmer codes and factoroids felt somewhat cumbersome. In particular, line 178 states that the Lehmer code 3 0 0 0 is obtained from 1 2 3 0, but according to my calculations, this code corresponds instead to the permutation 3 0 1 2. This discrepancy appears to contradict the earlier statement in line 172 referencing a "cyclic permutation."

In line 265, the text reads: "We start with a non-binary trijection." I assume this is meant to say "non-degenerate trijection," as indicated by the subsection title. If that is the case, a definition or clarification of non-degeneracy would be helpful here, since the term was not introduced earlier when trijections were first discussed (e.g., in line 55).

In Proposition 1, the notation reintroduces variables p,k,c, with c=EK(Rm(p)) as defined in line 42. However, it now states that 0 \leq p,k,c < r, and introduces the expression c = \pi^k[k], with \pi as an arbitrary cyclic permutation. This raises confusion: is the K in the encryption function the same as the k in this proposition?

In Proposition 2, are the components p_i, k_i, c_i​ meant to represent the Lehmer components of p,k,c respectively, as defined by the encryption scheme? At this point, I find it difficult to continue parsing the details, as much of the logic appears unclear without further explanation. I would encourage the author to consider revising the text in light of these comments to facilitate better comprehension. A clearer presentation would allow readers like myself to continue the evaluation more effectively.

The manuscript is indeed promising. However, I would also have appreciated references to, or comparisons with, other permutation-based encryption methods. For example, Proposition 2 evokes structural similarities with AES or DES. To assess this connection, though, a clearer exposition of the proposed scheme is necessary.

Given the time constraints for this review, I will pause here and request clarification from the author.

Sincerely,

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In paper Author presents a construction of a One Time Pad with unique feature based on the inherent diffusive properties and a redundancy injection mechanism. In general paper clearly shows the construction mentioned and discusses its correctness. Section 3 presents a one-time pad in a nondegenerate manner. Especially Proposition 2 with recurrence which expresses the Lehmer component of plaintext, ciphertext and key. Significant role plays the section 4 where Author recall that the problem whether the Moriarty’s attack strategy can be based on the valid ciphertext that he has intercepted. On this fact the enhanced variant called Non-Degenerate One-Time Pad is introduced. Additional discussion is presented in sections 4.3 and 4.4. Section 5 presents Pseudo Foata Injection and its robustness.

Generally, the paper already at the introduction points out which results stand for the main contribution and presence of strict mathematical analysis i.e. proposition and theorems with proofs outline precisely the results presented by Author.  It allows analysis of obtained results by the other readers interested in further developing of similar method or performing similar analysis.

Paper generally is well written although Figure 4 mentions the red line, but the second line on the plot is orange. 

colors at Figure 4 should be corrected

Author Response

The only comment that requires action is about the colour in Figure 4. The mistake will be corrected.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I thank the author for the provided clarifications. In my humble opinion, this work represents a remarkable piece of research. My remaining suggestions pertain primarily to some minor issues within the manuscript itself: Firstly, consistency is recommended for the acronym representing the 'Non-degenerate One-Time Pad' across all instances (lines 263, 296, 413, 431, 579, 618, 625, 716, 727, 752, 764, 768, and 773); the instance on line 625 may potentially be a typographical error. Secondly, the reference section should be clearly demarcated with an appropriate heading, such as 'References' or 'Bibliography', to distinguish it from the Conclusion section.

Author Response

All done as requested. Many thanks for the review.