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Reversible Data Hiding in Encrypted Images based on MSB Prediction and Huffman Coding

Youzhi Xiang, Zhaoxia Yin, Xinpeng Zhang

arXiv:1812.09499v1cs.MM

TL;DR

RDHEI must embed secret data without exposing image content while permitting error-free extraction and lossless restoration. This paper proposes a Huffman-coding labeling method that predicts MSBs, encrypts the image with a stream cipher, and uses vacated space for additional data. The reported results are higher embedding capacity than state-of-the-art methods, with separable extraction and recovery.

  • Problem

    RDHEI seeks to embed secret information in encrypted images while protecting the original content and enabling error-free extraction and lossless image restoration.

  • Method

    The proposed HVLCL-RDHEI method adaptively predicts and Huffman-labels MSBs, embeds the label map into a stream-cipher-encrypted image, and uses reserved room for secret data.

  • Results

    The method reports greatly improved embedding capacity compared with previous or state-of-the-art methods while separating data extraction from image recovery and preserving both losslessly.

  • Takeaways & Limitations

    Huffman coding labeling provides a high-capacity RDHEI approach with separable data extraction and image recovery.

Abstract

from arXiv · show

With the development of cloud storage and privacy protection, reversible data hiding in encrypted images (RDHEI) has attracted increasing attention as a technology that can embed additional data in the encryption domain. In general, an RDHEI method embeds secret data in an encrypted image while ensuring that the embedded data can be extracted error-free and the original image can be restored lossless. In this paper, A high-capacity RDHEI algorithm is proposed. At first, the Most Significant Bits (MSB) of each pixel was predicted adaptively and marked by Huffman coding in the original image. Then, the image was encrypted by a stream cipher method. At last, the vacated space can be used to embed additional data. Experimental results show that our method achieved higher embedding capacity while comparing with the state-of-the-art methods.

1 School of Computer Science and Technology, Anhui University

RDHEI protects image content while embedding secret information in encrypted images, addressing privacy concerns and the limited capacity and errors of existing approaches. The proposed HVLCL-RDHEI method uses Huffman coding labeling and reports higher capacity with separable, lossless recovery.

  • Motivation: RDHEI embeds secret information into encrypted images so data hiding does not expose the original image content.The content-owner encrypts the image, the data-hider embeds information without obtaining the original image, and authorized receivers obtain data or image content according to their keys.
  • Existing approaches: Existing RDHEI methods are divided into vacating room after encryption and reserving room before encryption.VRAE modifies the encrypted image after encryption, whereas RRBE exploits spatial correlation before encryption to reserve embedding room.
  • Related methods: Several separable methods use compression, prediction errors, estimation errors, or wet-paper coding to reserve room while supporting separate extraction and recovery.The cited approaches include compressed encrypted-image LSBs, prediction-error methods, distributed-source coding, and multi-layer wet-paper coding.
  • Limitations: VRAE methods may have relatively low embedding capacity and errors during secret-data extraction or image restoration.Earlier methods also linked capacity to block size, and some made data extraction and image restoration inseparable.
  • Proposed method: The proposed HVLCL-RDHEI method is designed as a high-capacity and separable approach based on Huffman coding labeling.Its reported pipeline includes labeling the original image, embedding the label map into the encrypted image, obtaining reserved room from that map, and embedding secret data.
  • Reported results: The method reports greatly improved embedding capacity, separable extraction and recovery, and lossless extracted data and restored images.The conclusion likewise reports higher capacity than advanced algorithms and separation of data extraction from image recovery.

II. Related Works

In encrypted-domain RDH, visual quality is less central than in plaintext RDH, allowing MSBs to record a label map for image restoration. Related methods use one or two MSBs and parametric binary-tree labeling.

  • Domain differences: Plaintext RDH commonly modifies LSBs to preserve visual quality, whereas encrypted-domain RDH does not require high visual quality.This distinction motivates using more significant bits for marking in encrypted images.
  • MSB labeling: MSBs can be used as marked bits to record a label map for image restoration in encrypted images.The paper identifies MSB marking as a basis for high-capacity encrypted-domain data hiding.
  • Related methods: Puteaux et al. proposed EPE-HCRDH, which uses MSB predictive detection to generate a label map.The approach is described as a high-capacity reversible data hiding method with embedded prediction errors.
  • Related methods: Puyang et al. proposed Two-MSB-RDHEI, which uses two MSBs to mark pixels.The method was introduced to improve embedding ability relative to the preceding approach.
  • Related methods: Yi et al. proposed PBTL-RDHEI, a parametric binary tree labeling scheme for RDHEI.The passage identifies the method but does not report a specific quantitative result.

A. EPE-HCRDH

EPE-HCRDH detects MSB prediction errors, encrypts the image, embeds a label map through MSB replacement, and hides data in error-free blocks. Key ownership determines whether receivers extract data, recover the image, or perform both.

  • MSB prediction error detection: EPE-HCRDH predicts each current pixel from preceding pixels and marks prediction errors before encryption.The predictor uses left and top pixels, while the inverse pixel value helps compare prediction differences.
  • Image encryption and pixel marking: The image is encrypted by XORing each pixel with pseudo-random bytes generated from encryption key Ke.The label map is then embedded into the encrypted image by MSB replacement.
  • Image encryption and pixel marking: Label-map embedding is performed in blocks of eight pixels to reduce errors during data extraction and image recovery.If a block contains an error pixel, neighboring blocks are flagged by replacing their MSBs with “1”.
  • Data hiding: Secret data encrypted with data-hiding key Kw replaces the MSB of each pixel in an error-free block.The resulting marked encrypted image contains the secret information in the substituted MSBs.
  • Data extraction and image recovery: A receiver with Kw extracts the secret message, whereas a receiver with Ke decrypts and recovers the image.A receiver holding both keys can perform data extraction and image recovery at the same time.
  • Data extraction and image recovery: The recovered image has seven LSBs matching the original, while MSBs are restored using prediction-error detection.The method states that the restored image is the same as the original image.

B. Two-MSB-RDHEI

Two-MSB-RDHEI extends MSB labeling by comparing the two most significant bits of each pixel with a MED prediction. It marks blocks, hides two message streams in correct blocks, and supports key-dependent extraction and lossless recovery.

  • Prediction error detection: Two-MSB-RDHEI uses a median edge detection predictor based on three neighboring pixels.The current pixel and predicted value are compared through their two-MSB representations.
  • Prediction error detection: A pixel is labeled “0” when its two MSBs equal the predictor’s two MSBs; otherwise it is labeled “1” as an error pixel.The label indicates whether the current pixel can be treated as prediction-error-free.
  • Image encryption: The original image is encrypted by bitwise XOR with a pseudo-random sequence generated by encryption key Ke.This produces the encrypted image used by subsequent preprocessing and data hiding.
  • Preprocessing: Pixels are grouped into four-pixel blocks, with MSBs cleared in error-free blocks and neighboring blocks flagged around error blocks.Error blocks remain unchanged, while adjacent blocks receive flags to highlight prediction errors.
  • Data hiding: Two secret messages are embedded by replacing the two MSBs of pixels in correct blocks.The message is encrypted with data-hiding key Kw before embedding.
  • Data extraction and image recovery: Receivers use marked-block conditions and available keys to extract encrypted data or restore the original image.With Ke, the first two MSBs are predicted in correct blocks, while error blocks remain unchanged; the resulting image is reported identical to the original.

C. PBTL-RDHEI

PBTL-RDHEI labels encrypted-image pixels using parameters α and β, groups pixels by prediction-related differences, and reserves label-dependent space for reversible data embedding, extraction, and recovery.

  • PBTL: PBTL divides pixels into G1 and G2, marking G2 with β zero bits and categorizing G1 into nα subcategories for α-bit labels.The parameters satisfy 1 ≤ α, β ≤ 7, and pixels in different subcategories receive different α-bit binary codes.
  • Image Encryption: Image encryption first partitions the grayscale image into s×s blocks, permutes them with Ke, and uniformly modifies pixels using pseudorandom values generated from Ke.The image contains k = mn/s^2 non-overlapping blocks, with s ≥ 2.
  • Pixel Grouping: Pixel grouping selects one reference pixel per block, reserves one special pixel for α and β, and classifies remaining pixels as embeddable or non-embeddable by their blockwise differences.The difference for current pixel Ei is computed relative to its corresponding reference pixel Eiref.
  • Pixel Labeling and Data Hiding: PBTL marks only embeddable and non-embeddable pixels, while preserving reference and special pixels and storing required original bits as auxiliary information.For embeddable pixels, the remaining 8-α bits become available for secret-data replacement.
  • Data Extraction and Image Recovery: The receiver extracts data from the remaining bits of embeddable pixels, restores auxiliary bits, decrypts blocks with Ke, and recovers the original image.The extracted secret data is decrypted with Kw before image restoration is completed.

III. Proposed Methods

The proposed HVLCL-RDHEI method targets higher embedding capacity while preserving correct data extraction and lossless image recovery by using multi-MSB substitution with Huffman coding labeling.

  • Proposed Method: HVLCL-RDHEI uses multi-MSB substitution with Huffman coding labeling to increase embedded capacity while retaining correct extraction and lossless recovery.The framework separates content-owner, data-hider, and receiver roles.
  • Framework: The content owner calculates a label map, after which the data-hider extracts that map from the encrypted image and embeds secret information according to each pixel’s label.The receiver subsequently extracts the data and recovers the image based on the embedded labeling information.

A. Label Map Generation

Label-map generation predicts each pixel with the MED predictor, compares pixel and prediction bits from MSB to LSB, and assigns a label based on their matching prefix. The label determines how many leading bits are recoverable and therefore how many bits can be embedded.

  • Bit Comparison: The method converts each pixel and its prediction into 8-bit sequences and compares corresponding bits sequentially from the first MSB to the last LSB.The resulting bit sequences are denoted xk(i,j) and pxk(i,j), for k = 1,2,…,8.
  • Prediction: The MED predictor estimates each current pixel from three neighboring pixels, while the first row and first column serve as unmarked reference pixels.The predictor context is defined for pixels with 1 < i ≤ m and 1 < j ≤ n.
  • Label Assignment: A pixel label t ranges from 0 to 8 and equals the maximum number of leading bits shared by the pixel and its predicted value.The label is determined from the first position where the two binary sequences differ.
  • Embedding Capacity: A label t enables embedding of t+1 bits because the first t MSBs match the prediction and the next MSB can be recovered by negating the corresponding predicted bit.This rule uses the predicted value to reconstruct the leading portion of the original pixel.
  • Example: For x = 156 and px = 150, the first four bits match, producing label 4 and allowing 5 bits to be embedded.The label map is obtained by scanning all pixels after applying this rule.

B. Image Encryption

The method encrypts each pixel with a key-generated pseudo-random matrix and bitwise XOR, then records a predicted-label map using variable-length Huffman coding. This compressed label information is embedded into the encrypted image to create space for secret data.

  • Image encryption: Each pixel is converted into an 8-bit binary sequence and encrypted by bitwise XOR with a key-generated pseudo-random sequence.The encrypted pixels form the encrypted image Ie.
  • Label-map coding: Huffman coding compresses the label map and thereby increases the payload available for embedding.The label map is converted into a binary sequence together with its coding rule and length as auxiliary information.
  • Embedding preparation: The label map and auxiliary information are embedded into the encrypted image through multiple MSB substitution.Reference pixels store part of the auxiliary information, while the remaining information and reference pixels occupy labeled encrypted pixels.
  • Embedding preparation: Reference rows and columns are reserved so the auxiliary information can later be extracted and the original image completely reconstructed.The approach requires setting multiple rows and columns as reference pixels in some rough images.

D. Data Hiding

The data-hiding process recovers the label map from the marked encrypted image and places encrypted secret data into the remaining reserved space. With both keys, the recipient can extract the secret data and restore the original image reversibly.

  • Auxiliary-information extraction: The receiver extracts the HVLCL rule and auxiliary-information length from reference pixels before recovering the label map.The tag value determines how many leading MSBs contain auxiliary information in each current pixel.
  • Secret-data embedding: Secret data is encrypted with the data-hiding key Kw before it is embedded in the remaining reserved pixels.The remaining space is identified after auxiliary information and the label map are recovered.
  • Image recovery: The recovery process predicts each pixel with the MED predictor and reconstructs its original MSBs from the tag value and predicted bits.For tag value 8, the original pixel equals its predicted value.
  • Image recovery: The original image is reconstructed by restoring remaining pixels after the predicted MSB relationships are recovered.The restored pixels support reconstruction of the remaining image content.
  • Access conditions: Only a recipient with both Kw and Ke can reversibly extract the secret data and restore the original image.With Kw alone, the secret data can be obtained but the original image cannot be reconstructed.

IV. Experimental Results and Discussion

Experiments evaluate capacity, reversibility, and security on standard test images and three datasets using embedding rate, PSNR, and SSIM. The proposed method achieves high capacity while preserving error-free extraction and lossless image recovery.

  • Evaluation setup: The evaluation uses six standard test images and the BOSSBase, BOWS-2, and UCID datasets.Embedding rate, PSNR, and SSIM measure capacity and reversibility.
  • Capacity analysis: 1470568 bits is the total embedding capacity calculated for the Lena image.The capacity is derived from the label-specific embedding amounts.
  • Capacity analysis: 677264 bits is the net payload before subtracting the 32-bit coding-rule field and 20-bit auxiliary-length field for Lena.The auxiliary information occupies 793304 bits.
  • Test-image results: 2.583 bpp is the embedding rate reported for the marked encrypted Lena image.The receiver reconstructs the image with PSNR approaching +∞ and SSIM equal to 1.
  • Dataset results: Average embedding rates are 3.361 bpp for BOSSBase, 3.246 bpp for BOWS-2, and 2.688 bpp for UCID.Across the datasets, data extraction is error-free and reconstructed images have PSNR close to +∞ and SSIM equal to 1.

B. Comparison with State-of-the-arts

The proposed HVLCL-RDHEI method is compared with EPE-HCRDH, Two-MSB-RDHEI, and PBTL-RDHEI across test images and three datasets. It generally achieves higher embedding capacity, including on the rough Baboon image.

  • The comparison evaluates HVLCL-RDHEI against EPE-HCRDH, Two-MSB-RDHEI, and PBTL-RDHEI using ER (bpp).Experiments use six test images and images from BOSSBase, BOWS-2, and UCID.
  • EPE-HCRDH embeds no more than 1 bpp because it replaces one MSB per embeddable pixel.
  • Two-MSB-RDHEI and PBTL-RDHEI generally improve ER by embedding multiple bits per embeddable pixel, but both perform worse on Baboon.PBTL-RDHEI reaches only 0.462 bpp on Baboon, while Two-MSB-RDHEI can also fall below EPE-HCRDH there because of fewer usable pixels and incorrectly marked pixels.
  • 3.361 bpp is the average ER achieved by HVLCL-RDHEI on BOSSBase, exceeding EPE-HCRDH, Two-MSB-RDHEI, and PBTL-RDHEI values of 0.966, 1.447, and 1.957 bpp.
  • 3.246 bpp and 2.688 bpp are the average ERs achieved by HVLCL-RDHEI on BOWS-2 and UCID, respectively.
  • Across 500 randomly selected images from the three datasets, HVLCL-RDHEI generally has higher ER, with only a small number of images showing lower embedding rates.The lower rates are attributed to unsmooth images requiring more auxiliary information.

V. Conclusion

The conclusion presents HVLCL labeling as the basis for reserving embedding space in encrypted images while supporting data extraction and image recovery. Experiments report substantially improved embedding capacity, while future work targets stronger entropy compression.

  • The proposed HVLCL scheme marks each original-image pixel using Huffman coding labeling and compresses the label map to free embedding space.
  • The embedded label map determines reserved room for secret data in the encrypted image and supports data extraction and image recovery during decryption.
  • The method reports greatly improved embedding capacity compared with state-of-the-art algorithms while achieving separable data extraction and image restoration.
  • The total embedding capacity is determined after each pixel receives a tag value based on its predicted value.
  • Future work will focus on lossless entropy-coder compression to compress marker information further and increase net embedding capacity.
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