Separable Reversible Data Hiding Based on Integer Mapping and Multi-MSB Prediction for Encrypted 3D Mesh Models

Feng Wang; Na Xu; Zhaoxia Yin

REVIEW 6 major objections 5 minor 22 references

Separable Reversible Data Hiding Based on Integer Mapping and Multi-MSB Prediction for Encrypted 3D Mesh Models

T0 review · 6 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A reversible data-hiding scheme for encrypted 3D meshes embeds up to 18.12 bits per vertex and recovers the quantized original exactly, with zero extraction error.

desk verdict First separable multi-MSB RDH-ED for 3D meshes with a genuinely new vertex-partition idea, but the printed equations do not support the lossless-recovery claim as written. read the letter →

arxiv 1908.02473 v2 pith:OTUUYSR2 submitted 2019-08-07 cs.MM

Zhaoxia Yin , Na Xu , Feng Wang This is my paper · ORCID

classification cs.MM

keywords reversibledatahidingencrypteddomain3DmeshmodelsMulti-MSBpredictionringintegermappingseparablerecoveryembeddingcapacity

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes a reversible data-hiding method that operates directly on encrypted 3D mesh models, an extension of a technique that has mostly been developed for images. The core idea is to map the mesh's floating-point vertex coordinates to fixed-width integers, encrypt the resulting bitstream, and then embed the hidden message by overwriting the upper (most significant) bits of carefully chosen vertices. Because the upper bits of a vertex's coordinates can be predicted from the coordinates of its topological neighbors, the message can be extracted without error while the quantized original geometry is reconstructed exactly. On four standard test meshes the reported embedding rates reach 13.66 to 18.12 bits per vertex, compared with 0.34 to 6.00 for earlier encrypted-mesh schemes, and the paper reports zero data-extraction error on all tested models, including dense meshes.

What carries the argument

The load-bearing object is the Multi-MSB prediction rule operating over topological rings. After integer mapping $\bar{v}_{i,j} = \lfloor v_{i,j} \times 10^m \rfloor$ (Eq. 1) fixes each coordinate to an $l$-bit integer, the sender counts, from MSB down to LSB, whether the majority of an embedded vertex's neighboring reference vertices share the same bit value; the length $L$ is the largest prefix of bits for which this holds on all axes. Data embedding replaces those $n \leq L$ MSBs of the embedded vertex's coordinates with payload bits (Eq. 7), and recovery uses the same ring-prediction to regenerate them. This converts spatial smoothness of the mesh geometry into a bit-substitution channel that survives stream-cipher encryption.

What would settle it

Run the proposed preprocessing with m=4 on a mesh that contains a vertex coordinate of 7.0, for example a cube of side 7. The mapped integer is 70000, which is larger than $2^{16}-1$, the 16-bit length that Eq. (3) assigns for m=4; Eq. (7) then truncates the coordinate's high bits, and no ring-prediction can restore the original value, contradicting the paper's zero-error and exact-recovery claims.

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Extended reading notes

Core claim

The central claim is that the most significant bits of mesh vertex coordinates carry reliable, encryption-invariant redundancy that can be harvested for reversible data hiding. The method splits vertices into an "embedded" set and a "reference" set, computes, for each embedded vertex, the maximum number of MSBs that can be guessed by a majority vote over the corresponding bits of its adjacent reference vertices, and then encrypts the whole mesh with a stream cipher. Payload bits are substituted into those predictable MSBs, and the data-hiding key alone reads them back from the ciphertext without any reference to the original geometry. A recipient with only the encryption key predicts the removed MSBs from the surrounding vertices and recovers the integer-mapped mesh exactly, which the paper calls "perfectly" recovering the original mesh; the original floating-point coordinates are recovered to the precision m chosen in the integer-mapping step.

Load-bearing premise

The scheme assumes all vertex coordinates are smaller than 1 in absolute value so that the integer-mapping step in Eq. (1) always produces values that fit the bit-length table in Eq. (3); meshes with larger coordinates would overflow that bit-length assignment and break both embedding and recovery.

Editorial extensions

If this is right

Encrypted 3D content can be annotated or watermarked by an untrusted data hider without the hider ever seeing the plaintext geometry.
Payload capacities on the order of 14–19 bits per vertex are high enough to embed meaningful metadata, such as provenance, integrity hashes, or access-control tags, inside ciphertext for large meshes.
Zero extraction error eliminates the error-correcting overhead that earlier LSB-based encrypted-mesh methods needed, so the recovered payload is directly usable.
Separability of extraction and recovery means a cloud service can provide data management on encrypted models, while only the model owner can recover the geometry, a division of trust that matches privacy-preserving storage workflows.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same majority-vote MSB prediction could be applied to ordered point clouds or to meshes with a spatial-index-based neighbor definition, not only to triangular faces; the paper's experiments stop at standard triangle meshes.
The scheme fixes one embedding length L for the whole mesh, so a single vertex with a poorly predictable MSB caps the payload for every embedded vertex; an adaptive per-vertex length selection would likely push the average rate closer to the per-mesh maximum.
The "perfect recovery" guarantee is relative to the integer-mapped, precision-m quantized mesh, not to the original floating-point coordinates; the choice of m is therefore a real lossy parameter hidden inside the reversible pipeline.
The bit-length table in Eq. (3) is derived from a normalization assumption that coordinates lie in (-1,1); for meshes in other ranges the bit length must be recomputed, and the paper's capacity figures cannot be assumed to transfer.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new thing here is applying Puteaux–Puech style multi-MSB prediction to 3D mesh topology, via an embedded/reference vertex partition, with separable data extraction and mesh recovery. That is a real combination not in the prior art, and the measured rates (up to 18.12 bpv on Elephant) would be a meaningful step up from the two existing encrypted-mesh schemes. The paper is worth reading for that idea alone.

The soft spots are serious and they are all in the formal core. Eq. (6) reconstructs the encrypted integer as a sum of bits each weighted by 10^m, which returns a count of ones, not the binary integer from Eq. (4). Eq. (7) uses mod 2^{l-(n+1)} for n-MSB substitution, which keeps l-n-1 low bits instead of l-n, silently discarding a bit that is not stored anywhere. Eq. (8) extracts the top-k bits as an integer, not the k-th bit. These are exactly the load-bearing operations for the paper's central claim of perfect recovery and error-free extraction. As printed, the algorithm does not work. My strong suspicion is that these are typesetting slips rather than deep flaws: the prose and the worked example describe the intended mechanism clearly, and the fix for each equation is obvious. But the preprint does not currently support its headline claims.

There are also smaller issues: Table III swaps the Mushroom and Mannequin capacity numbers relative to Table II (16.72/13.66 vs 13.66/16.20), the SNR definition in Eq. (13) is non-standard, and the preprocessing quietly assumes every coordinate satisfies |v|<1, which is not true of many real meshes—a normalization step is needed and not described. The experiments themselves look like real measurements, not fitted to a target, so I do not see circularity.

The paper deserves a serious referee, not a desk reject. The niche is small, but the contribution is a plausible first separable encrypted-mesh RDH scheme with real capacity gains. I would send it to review with an expectation of major revision: fix the equations, reconcile the tables, state the coordinate-range assumption, and re-run to confirm the numbers. If the authors fix the formal parts, this is likely publishable. For now, treat the specific capacity and lossless claims as unverified.

Referee Report

6 major / 5 minor

Summary. The paper proposes a separable reversible data hiding in encrypted domain (RDH-ED) method for 3D meshes. Vertex coordinates are scaled to integers, vertices are split into an 'embedded' set and a 'reference' set, prediction-error-free embedded vertices are identified, the mesh is encrypted with a stream cipher, and additional data are embedded by substituting the n most significant bits (MSBs) of encrypted coordinates. Three recipient cases are considered: data extraction with only the data-hiding key, mesh recovery with only the encryption key, and joint extraction/recovery with both keys. The paper reports embedding rates up to 18.12 bpv on the Elephant mesh, zero extraction error, and claims higher embedding capacity and better recovered-mesh quality than prior methods [20], [21].

Significance. If correct, the scheme would be a useful extension of MSB-prediction-based RDH-ED from images to 3D meshes, with an attractive separable design and high reported capacities. The paper has some strengths: capacity figures appear to be measured rather than fitted, dense-mesh results are reported, and the comparison with prior work is explicitly attempted. However, the central embedding and recovery equations as written are internally inconsistent, the preprocessing is only specified for a narrow coordinate range with no signed-integer handling, and the reported comparison tables are mutually inconsistent. These issues strike at the paper's main claims of reversibility, error-free extraction, and improved performance, so the contributions cannot be accepted in their current form.

major comments (6)

[Section II.C, Eq. (6)] Equation (6) defines E_{i,j} = sum_{u=0}^{l-1} e_{i,j,u} × 10^m, which weights every bit identically and therefore reconstructs neither the binary integer from Eq. (4) nor the encrypted coordinate. The bit positions must be weighted by powers of 2 (2^u), not by 10^m. As written, Eq. (6) returns 10^m times the number of 1-bits, so the subsequent XOR decryption in Eq. (9) and the modular arithmetic in Eq. (7) operate on the wrong quantity. This invalidates the encryption-to-embedding-to-recovery pipeline.
[Section II.D, Eq. (7)] Equation (7) writes v'' = s1·2^{l-1} + ... + sn·2^{l-n} + v' mod 2^{l-(n+1)}. For n-MSB substitution, the untouched lower part of v' should be v' mod 2^{l-n}; the printed modulus 2^{l-(n+1)} discards bit position l-n-1, which is not stored anywhere, making exact recovery of the original coordinate impossible. The expression is also undefined for n=l, since the exponent becomes -1. This is a load-bearing defect in the reversibility claim because the lost bit is not recoverable by any subsequent prediction step.
[Section II.E, Eq. (8)] Equation (8), s_k = v''/2^{l-k}, does not extract the k-th embedded bit. If division is integer division, the right-hand side gives the k-bit value formed by the top k MSBs; if it is real division, the result is generally non-integer. No floor, rounding, or modulo operation is specified, so the extraction rule does not correctly recover the individual bits s_k. Error-free extraction is therefore not established by the stated formula.
[Section II.A, Eqs. (1)-(4)] The preprocessing assumes each vertex coordinate satisfies |v_{i,j}| < 1 and states that the integer value is between 0 and 2^m, but the paper's own example uses negative coordinates: v = (-0.202018, -0.0740184, 0.288808) with m=4, giving integer coordinates (-2020, -7400, 2888). This contradicts Eq. (1), since floor(-0.202018 × 10^4) = floor(-2020.18) = -2021, not -2020, and negative integers are outside the stated range [0, 2^m]. No normalization or signed-integer representation is specified for Eq. (4)'s bit decomposition, so the entire integer mapping is undefined for the negative coordinates that are common in real 3D meshes.
[Section III.A and Table III] The text in Section III.A reports maximum embedding rates of 16.72 bpv for Mushroom and 13.66 bpv for Mannequin, which matches Table II. Table III, however, lists 13.66 bpv for Muchroom and 16.20 bpv for Mannequin. These swapped or inconsistent values undermine the comparison with [20] and [21] and the paper's headline capacity claims.
[Section III.B, Eq. (13)] The SNR formula in Eq. (13) is non-standard: the numerator is the power of the original coordinates about their mean, while the denominator is the power of the modified coordinates about the original mean. The standard SNR uses the introduced error (e.g., sum (g_i - v_i)^2) in the denominator. As written, the metric conflates signal power with noise power and can be artificially inflated by a uniform offset or scaling. Since SNR is used as a quality comparison in Table III and Fig. 6, this definition needs to be justified or replaced.

minor comments (5)

[Section III.A and Table II] The text states that Elephant reaches 18.12 bpv when m=5 and n=18, but Table II shows that the value 18.12 appears at n=19 (columns 17, 18, and 19 read 17.29, 17.92, and 18.12, respectively). Please correct the reported operating point.
[Section III.B] The text says 'the recipient with encryption key Ke can prefectly recover the original mesh,' but Case 2 in Section II.E describes the result as a 'high-quality recovered mesh,' not an exact recovery. These statements should be reconciled; exact recovery in Case 2 would require justification beyond MSB prediction.
[Throughout] There are numerous typos and naming inconsistencies: 'atart-of-the-art', 'shouws', 'descibe', 'prefectly', 'Muchroom' vs. 'Mushroom', 'Mannequim' in Fig. 7(a), and 'compasision'. The authors should perform a careful proofreading pass.
[Section II.D, Eq. (7)] The range condition 'l≤k≤n' after Eq. (7) should presumably be '1≤k≤n'; otherwise the summation indices are inconsistent with the usage of s_k as embedded data bits.
[Section II.C, Eq. (4)] The notation 'l≤i≤N' in Eq. (4) should be '1≤i≤N'; as written, the index range excludes the first vertex.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the prediction-error prescreening is a construction step, capacities are measured, and the flagged equation defects are correctness issues, not circular reductions.

full rationale

The claimed derivation chain is self-contained and contains no step in which an output is equal to an input by construction or in which a fitted parameter is renamed as a prediction. The prediction-error pre-detection in Section II.B is a screening step: it identifies vertices whose n-MSBs can be predicted from unmodified reference neighbors, and only those vertices are embedded via Eq. (7). The recovery step in Section II.E.2 applies the same neighbor-majority prediction to those preselected vertices; because the reference set is left unmodified, the recovery claim follows legitimately from the construction rather than circularly. The embedding rates in Table II and Fig. 7 are measured outcomes of the algorithm over a grid of (m,n), not parameters fitted to match the reported bpv values. No load-bearing claim is justified by a self-citation, and no uniqueness theorem is imported from the authors' prior work. The apparent mathematical defects in Section II.C-D (Eq. (6) weights bits by 10^m instead of 2^u, and Eq. (7) uses modulus 2^{l-(n+1)} rather than preserving the lower l-n bits) and the unnormalized-coordinate assumption |v_{i,j}|<1 are serious correctness and validity concerns, but they are not circularity: they concern whether the printed equations implement the stated reversible substitution, not whether any result reduces to its own input.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The paper introduces two hand-chosen operating parameters (m, n) and relies on two domain assumptions about mesh coordinate ranges and smoothness. No circular fitting or invented entities.

free parameters (2)

m (quantization precision) = 4 (quality), 5 (capacity)
Number of decimal places kept by Eq. (1); chosen by hand; headline embedding rates are the maxima over m=2..9.
n (MSB embedding length) = 16, 15, 15, 18 for the four test meshes
Number of most significant bits replaced by data; reported as the value maximizing embedding rate for each mesh.

assumptions (3)

domain assumption All vertex coordinates satisfy |vi,j| < 1 (Section II.A).
Required for the integer mapping of Eq. (1) to stay within the bit length l of Eq. (3).
domain assumption The mesh is sufficiently smooth that majority-vote MSB prediction over neighboring reference vertices is error-free for the chosen n on the selected vertices.
The sender pre-checks this property (Section II.B), but the method's capacity claim depends on it holding for real meshes.
standard math Stream cipher encryption is applied and the encrypted domain preserves the algebraic structure of the coordinates for XOR-based MSB substitution.
Assumes XOR stream cipher, standard in RDH-ED; no security proof is given (Section II.C).

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Cite this review

Pith. "Pith review of Separable Reversible Data Hiding Based on Integer Mapping and Multi-MSB Prediction for Encrypted 3D Mesh Models." pith.science (2026). https://pith.science/paper/OTUUYSR2

@misc{pith2026190802473,
  author       = {Pith},
  title        = {Pith review of: Separable Reversible Data Hiding Based on Integer Mapping and Multi-MSB Prediction for Encrypted 3D Mesh Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OTUUYSR2}},
  note         = {Machine review of arXiv:1908.02473}
}

read the original abstract

Reversible data hiding in encrypted domain (RDH-ED) has received tremendous attention from the research community because data can be embedded into cover media without exposing it to the third party data hider and the cover media can be losslessly recovered after the extraction of the embedded data. Although, in recent years, extensive studies have been carried out about images based RDH-ED, little attention is paid to RDH-ED in 3D meshes due to its complex data structure and irregular geometry. In this paper, we propose a separable RDH-ED method for 3D meshes based on integer mapping and Multi-MSB (multiplication most significant bit) prediction. The proposed method divides all the vertices of the mesh into the "embedded" set and "reference" set, and maps decimals of the vertex into integers. Then, we calculate the Multi-MSB prediction errors for the vertices of the "embedded" set and a bit-stream encryption technique will be executed. Finally, additional data is embedded by replacing the Multi-MSB of the encrypted vertex coordinates. According to different permissions, recipient can obtain the original plaintext meshes, additional data or both. Experimental results show that the proposed method has higher embedding capacity and higher quality of the recovered meshes compared to the state-of-art methods.

Figures

Figures reproduced from arXiv: 1908.02473 by the authors.

**Figure 2.** Framework of the Proposed Method. A. Pre-processing 3D mesh models are represented in various file formats such as OFF, PLY, OBJ, etc. The 3D mesh is composed of vertices data and faces data. Vertices data include coordinates data of vertices represented as V= {vi ∈ <3 |1≤i≤N} , where the vertex is represented as vi=(vi,x,vi,y,vi,z), and N is the number of vertices. Note that each coordinate vi,j ¡ 1 and j∈{x,y,z}. … view at source ↗

**Figure 3.** Cow Mesh. TABLE I: File format for [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: An example of prediction error detection test on cow mesh. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: Test Meshes: (a) Beetle, (b) Muchroom, (c) Mannequin, (d) Elephant. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: Results of four test meshes on different accuracy [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 8.** Figure 8: shows experimental results, demonstrating the visual [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

**Figure 7.** Figure 7: Test Meshes: (a) Comparison of maximal enbedding rates of test meshes between our method and state-of-the-art [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: Illustrative examples showing the appearance of the mesh of each phase : (a)Original mesh, (b)Encrypted mesh, (c) [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: Dense meshes: (a) Dragon, (b) Armadillo, (c) Happyvrip. [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [20]

IEEE Transactions on Multimedia 20(1), 5567 (2017)

Jiang, R., Zhou, H., Zhang, W., Yu, N.: Reversible data hiding in en- crypted threedimensional mesh models. IEEE Transactions on Multimedia 20(1), 5567 (2017)

work page 2017

[2] [21]

Arabian Journal for Science and Engineering 43(12), 81458157 (2018)

Shah, M., Zhang, W., Hu, H., Zhou, H., Mahmood, T.: Homomorphic encryptionbased reversible data hiding for 3d mesh models. Arabian Journal for Science and Engineering 43(12), 81458157 (2018)

work page 2018

[3] [1]

In: Security and Watermarking of Multimedia Contents IV

Fridrich, J., Goljan, M., Du, R.: Lossless data embedding for all image formats. In: Security and Watermarking of Multimedia Contents IV . vol. 4675, pp. 572583. International Society for Optics and Photonics (2002)

work page 2002

[4] [2]

IEEE transactions on image processing14(2), 253266 (2005)

Celik, M.U., Sharma, G., Tekalp, A.M., Saber, E.: Lossless generalized- lsb data embedding. IEEE transactions on image processing14(2), 253266 (2005)

work page 2005

[5] [3]

IEEE transactions on circuits and systems for video technology 13(8), 890896 (2003)

Tian, J.: Reversible data embedding using a difference expansion. IEEE transactions on circuits and systems for video technology 13(8), 890896 (2003)

work page 2003

[6] [4]

IEEE Transactions on Multimedia 10(8), 15001512 (2008)

Hu, Y ., Lee, H.K., Chen, K., Li, J.: Difference expansion based reversible data hiding using two embedding directions. IEEE Transactions on Multimedia 10(8), 15001512 (2008)

work page 2008

[7] [5]

IEEE transactions on image processing 13(8), 11471156 (2004)

Alattar, A.M.: Reversible watermark using the difference expansion of a generalized integer transform. IEEE transactions on image processing 13(8), 11471156 (2004)

work page 2004

[8] [6]

IEEE Transactions on Information Forensics and Security 10(9), 20162027 (2015)

Li, X., Zhang, W., Gui, X., Yang, B.: Efﬁcient reversible data hiding based on multiple histograms modifcation. IEEE Transactions on Information Forensics and Security 10(9), 20162027 (2015)

work page 2015