Enhanced Efficiency and Security in LSB2 Steganography: Burst Embedding and Private Key Integration

One commonly employed method in data steganography is the LSB technique. This approach embeds information into a cover image by allocating 8 pixels from the cover image to accommodate one character (byte) from the concealed message [30-34]. In the case of RGB colour images, which utilise a 24-bit colour encoding, the LSB from each of the red, green, and blue components can be utilised to host binary bits from the clandestine message. A depiction of this method, using three pixels of a 24-colour image consuming 9 bytes of memory, with the covert message represented as 01000001, can be observed in Figure 4. Alterations to this bit have been shown not to compromise the integrity of the cover image and are imperceptible to the human eye.

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Figure 4. Implementation of the LSB method

The LSB method introduces minor pixel adjustments, which might involve no change, an addition of 1 to the pixel value, or a subtraction of 1. Such modifications result in a low Mean Square Error (MSE) value and a high Peak Signal-to-Noise Ratio (PSNR) value. Thus, any changes in the image introduced by this method are not discernible to human vision.

The capacity limit for the LSB method is determined by dividing the image size by 8. Notably, the security level offered by the LSB technique is considered low, although enhancements in security can be achieved by integrating a reference, which serves as a PK. When using the LSB technique for data steganography, it is ensured that the clandestine message is embedded into the cover image byte by byte. A portion of the cover image, equivalent in size to the message size multiplied by 8, must be earmarked to accommodate the concealed message, meaning the capacity of the LSB technique is defined as the cover image size divided by 8.

In embedding messages using the LSB method, the LSBs of sequential holding bytes store the concealed message bits. The initial byte of the message is followed by the second byte, and so forth. This process is further illustrated in Figure 5, where the stego colour image is interpreted as an array of RGB pixel values columns. Here, the LSBs of the columns are supplanted by the binary values of the ASCII representations of hidden messages, such as '5fk'.

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Figure 5. Message byte concealment using the LSB technique

Building upon the foundational principles of the LSB method, the LSB2 technique in data steganography has been introduced. This enhanced method reserves 4 bytes from the cover image to accommodate a single character from the concealed message, doubling the capacity compared to its predecessor [35-38]. Consequently, the character bits of the concealed message are stored in the two LSBs of the cover image, as depicted in Figure 6. The maximum capacity of this approach is determined by dividing the image size by 4.

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Figure 6. Data hiding using the LSB2 method

Variations in the byte values of the cover image, subsequent to the data hiding process, have been observed to range between -3 to +3. Notably, such alterations remain imperceptible to the human eye. The classical LSB2 method, as documented in study [19], carries out data hiding and extraction by executing a sequence of logical operations. This approach embeds the concealed message byte-by-byte into consecutive bytes of the cover image.

Two illustrative examples further elucidating the treatment of each byte from the concealed message can be observed in Tables 2 to 5.

Table 2. Methodology of data concealment: Example 1

Table 3. Data extraction procedure: Example 1

Table 4. Methodology of data concealment: Example 2

Table 5. Data extraction procedure: Example 2

Example 1:

The objective was to conceal the character ‘A’, which possesses a decimal value denoted as a1=65. Its binary equivalent has been determined to be: 01000001. When presented with covering bytes represented as [b= [217 200 120 190]], the complement of 252 was found to be 3. The intricacies of the hiding process, executed via MATLAB functions, can be discerned in Table 2.

Subsequent to the data hiding process, data extraction can be undertaken. By leveraging a series of logical operations via MATLAB functions, the extraction process was realised, as depicted in Table 3.

Example 2:

With an aim to hide the character represented by the decimal a1=223, its binary form was identified as 11011111. Given the covering bytes b=[217,200,120,190], the complement of 3 was established to be 252. The hiding process, once again facilitated through MATLAB functions, is showcased in Table 4.

The subsequent stage involves the extraction of the embedded data. Delving into MATLAB functions, the extraction procedure was executed, the details of which are illustrated in Table 5.

In evaluating image quality, two crucial metrics are commonly employed: the PSNR and the MSE. The PSNR metric is described as the ratio between the maximum conceivable power of a signal and the corrupting noise's power which impinges upon the integrity of its representation. Essentially, this metric facilitates a qualitative assessment between a reference image and a cover image embedded with concealed data. Conversely, the MSE metric quantifies the mean of the squared discrepancies between the distorted image and its reference counterpart. Notably, a high MSE coupled with a reduced PSNR indicates compromised image quality, whereas an elevated PSNR and a diminished MSE signify optimal quality. It is imperative for an adept data steganography technique to yield a stego image of superior quality, as evidenced by a minimal MSE and a heightened PSNR. The computation of the MSE value is accomplished by aggregating the squared variances of all pixels and subsequently dividing by the total pixel count, as elucidated in Eq. (1). Subsequent to this, PSNR can be derived through Eq. (2):

MSE between x and y, n: message length

$M S E_{S R}=\frac{1}{N} \sum_{j=0}^{n-1}[x(j)-y(j)]^2, N=n$       (1)   

$P S N R_{S R}=10 \times \log _{10} \frac{\left(M A X_j\right)^2}{M S E_{S R}}$         (2)

In the formulae, 'MAX' signifies the pinnacle pixel value, while 'N' denotes the aggregate sample count. The symbols x_j and y_j correspond to the sample values of the original and modified images, respectively.

Another pivotal statistic for gauging steganographic algorithm quality is the correlation coefficient (CC) between a pair of images. This metric provides insights into the interdependence between the grey values of the respective images. Evaluating the CC furnishes an understanding of the correlation magnitude between two images. Notably, coefficients within the |1–0.7| range indicate robust correlation, suggesting significant similarity between source and encrypted file samples. A medium correlation is inferred from values within the |0.7–0.3| span, whereas coefficients within the |0.3–0| bracket signify weak correlation. The calculation of the CC is delineated in Eq. (3):

$C C_{x y}=\frac{\operatorname{cov}(x, y)}{\sqrt{D(x)} \sqrt{D(y)}}$,               (3)

where,

$\begin{gathered}D(x)=\frac{1}{N} \sum_{i=1}^N\left(x_i-\overline{\mathrm{x}}\right)^2, \\ D(y)=\frac{1}{N} \sum_{i=1}^N\left(y_i-\bar{y}\right)^2, \\ \operatorname{cov}(x, y)=\sum_{i=1}^N\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right),\end{gathered}$

In the above equations, 'N' represents the cumulative sample number. Symbols x­_j and y_j indicate the sample values of the cover and stego entities, respectively. The symbols x¯ and y¯ represent the mean sample values. Lastly, 'cov(x, y)' embodies the covariance between the two datasets.

The robustness of data steganography algorithms is often gauged through the Number of Sample Change Rate (NSCR), a test crafted to assess algorithmic quality. Primarily, this test is devised to juxtapose the sample values of the covering and stego images, subsequently delineating the percentage variance. NSCR is mathematically derived using the equation provided as Eq. (4):

$N S C R=\frac{\sum_{i=1}^N D_i}{N} \times 100 \%$,         (4)

where,

$D_i\left\{\begin{array}{l}1, x_i \neq y_i \\ 0, \text { Otherwise }\end{array}\right.$

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Figure 10. Histogram of covering image

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Figure 11. Histogram of LSB stego image

Table 6. Quality parameters - A comparison between covering and stego images (LSB method)

Table 7. Speed parameters associated with the LSB method

A series of messages was examined using the LSB method of data steganography. The histogram of the covering image is depicted in Figure 10, while Figure 11 showcases the stego image histograms, encapsulating a message of 10,000 characters.

Subsequent measurements and calculations focused on assessing quality and speed parameters. The derived results are illustrated in Tables 6 and 7.

Based on the data extracted from Table 6, it is discerned that the LSB method conformed to stipulated quality benchmarks. Irrespective of the embedded message's length, the stego image consistently approximated the covering image. Moreover, the LSB method exhibited commendable speed parameters, with an average concealment duration of 0.3889 seconds and an average extraction duration amounting to 1.0709 seconds.

In a parallel assessment, messages were evaluated using the conventional LSB2 data steganography method. The ensuing quality and speed metrics for this method are presented in Tables 8 and 9. Furthermore, Figure 12 displays the stego image, containing a 10,000 character message, accompanied by its RGB histograms.

From the insights gleaned from Table 8, the LSB2 method was identified as meeting the prescribed quality specifications. Analogous to the LSB method, the stego image mirrored the covering image, independent of the message length (be it short or extensive). As depicted in Table 9, the LSB2 steganography method advanced its speed metrics, marking a decline in both the concealment (0.0675 seconds on average) and extraction (0.0176 seconds on average) intervals.

Upon subjecting the same messages to the classical ULSB2 data steganography method, Tables 10 and 11 were formulated, illustrating the quality and speed parameters pertinent to this technique. Concurrently, Figure 13 unveils the stego image encapsulating a 10,000-character message, complemented by its RGB histograms.

As per the insights drawn from Table 10, it was determined that the ULSB2 method met the designated quality criteria. For every message, irrespective of its length, the stego image exhibited a striking resemblance to the corresponding covering image.

In terms of speed metrics, the ULSB2 method showcased commendable efficiency, registering an average concealment duration of 0.0655 seconds and an average extraction time (ET) of 0.0161 seconds.

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Figure 12. Histogram of LSB2 stego image

Table 8. Quality parameters - A comparison using the LSB2 method

Table 9. Speed parameters associated with the LSB2 method

Table 10. Quality metrics - contrasting covering and stego images (ULSB2 method)

Table 11. Speed Metrics concerning the ULSB2 method

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Figure 13. Histogram of ULSB2 stego image ULSB2

Upon examination of the data in Table 10, it was ascertained that the ULSB2 method adhered to stringent quality standards. In every instance, regardless of the hidden message's length, the stego image bore remarkable similarity to its corresponding covering image. The ULSB2 method also manifested superior speed parameters, registering an average concealment duration of 0.0655 seconds and an average extraction duration of 0.0161 seconds.

The speed metrics obtained underscored the proficiency of the proposed ULSB2 method, notably in both hiding times (HT) and ET, as illuminated in Figures 14 and 15. A notable augmentation in data concealment and extraction speeds for the proposed method is articulated in Tables 12 and 13.

From the collated results, an inference was drawn underscoring that methods LSB, LSB2, and ULSB2 aligned with the designated quality standards, delivering robust quality metric values. The derived PSNR values for these triadic data steganography methods, as depicted in Figure 16, met the acceptable threshold.

The speed enhancement attributable to the proposed method, particularly in concealment duration (HT), is chronicled in Table 12. This enhancement, or speedup, was computed by contrasting the average concealment time across methods against the average time exhibited by ULSB2. Similarly, the escalation in extraction speed is elaborated upon in Table 13, where the metric is derived by equating the average ET across the spectrum of methods against the ULSB2 benchmark.

Table 12. Speedup assessment vis-a-vis ULSB2 (HT)

Table 13. Speedup assessment vis-a-vis ULSB2 (ET)

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Figure 14. Comparative analysis of HTs

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Figure 15. Comparative analysis of ETs

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Figure 16. PSNR comparative analysis