A New Dynamic S-Box-Based Microfluidic Technique

In the current era, the field of image encryption has seen notable advancements. However traditional methods still face challenges that limit their effectiveness. While these methods work well for some types of data, they fail to address the complexities presented by image data, such as high redundancy and large file sizes [1-4]. These limitations can be observed in many aspects, for example, Insufficient Complexity; where the simplicity and predictability of their maps make them vulnerable to some types of attacks. Lack of Scalability; where traditional methods face difficulties when dealing with high-resolution images due to the load and time required for encrypting sized files. Security for Sensitive Applications; where the existing encryption methods often fail to meet the security requirements in critical fields, like military and medical imaging where security is paramount. Ensuring the security of the system is one of the most crucial aspects of any cryptographic primitive. Therefore, the challenge is to find an approach that could share unique characteristics with them and overcome such limitations. Due to their properties that meet the cryptography requirements, such as complex behavior, a large distribution, and higher ergodicity, the chaos theory is extremely significant in cryptographic systems [5-8].

Since this discovery, several investigators have presented many encryption systems based on highly performed chaotic systems. For example, Hua et al. [9] proposed a new 2D Logistic-Sine-Coupling Map-based encryption image technique (2D-LSCM). Al-Saidi et al. [10] adopted new 2D maps to be used for the construction of a new image encryption technique (2D-LICM). Roy et al. [11] investigated colour image encryption algorithm processes which employed the polarization dynamics synchronization in a free-running vertical-cavity surface-emitting laser (VCSEL). Farhan et al. [12] presented a novel chaotic system possessing the peculiar ability to move both inside and outside of a cylinder periodically. In the same year, Ali et al. [6] proposed an encryption method based on a new chaotic map called 2D-HLCM. Additionally, in 2021 Alwan et al. [13] introduced a new chaotic encryption method called 2D-LCHM. In their 2023 study, Ndassi et al. [7] developed an innovative cryptosystem based on compression. This system uniquely blends a high-dimensional chaotic system with a Dynamic S-Box, and utilizes 2D compress sensing for image encryption. The encryption process incorporates a secret key generated through the SHA-256 function. Additionally, the system features a key-dependent Mordell elliptic curve-based Dynamic S-Box for substituting the compressed image. Moreover, Alwan et al. [8] introduced a new encryption algorithm based on an nD-hyperchaotic system derived from the Lorenz system.

This paper introduces a new image encryption method that overcomes limitations in the aforementioned previous methods. This is achieved by combining a 7D chaotic system with a dynamic mechanism to generate new S-boxes utilizing microfluidic technology. This integration does not increase the complexity and unpredictability of the encryption process, it also ensures the scalability and robustness of the algorithm, which makes it suitable for high-resolution images. The dynamic nature of the S-boxes generated using these new techniques provides a higher level of security that meets the requirements of sensitive applications and represents an advancement in the field of image encryption.

The algorithms of image encryption are divided into two categories. One treats a digital image as a bitstream and encrypts the image using traditional techniques. The other category uses current techniques like chaos, wavelet transforms, and so on. The performance of the algorithms that are based on chaotic maps is good [5].

S-boxes play a role, in image encryption because of the connection between neighbouring pixels, in images. If not properly encrypted this correlation makes images available to attacks. By using S-boxes we can minimize this correlation and enhance the security of the encrypted image. This section introduces a new S-box and strings letters and mixture them via the microfluidic technique. However, this S-box is adopted to generate keys for the image encryption algorithm.

3.1 Design of a new S-box

S-boxes play a crucial role in providing the strength, reliability, and security of image encryption methods. This is achieved due to its nonlinearity improves confusion and diffusion and offers protection against different types of cryptographic attacks. Microfluidic technology (MF) offers unique advantages in controlling and manipulating fluids at a micro-scale, where surface forces such as capillary action and electrokinetic effects dominate [20]. These principles enable the precise generation of complex cryptographic elements, making microfluidics a valuable tool in enhancing the security and efficiency of encryption systems. By understanding and leveraging these forces, microfluidic devices can produce highly secure, dynamic cryptographic components that are difficult to predict [21]. MF can be used to mix fluids that represent different chaotic sequences such as system (1) in a highly controlled environment. The chaotic nature of the system, combined with the micro-scale precision of fluid manipulation, results in the generation of dynamic and highly unpredictable cryptographic elements such as S-box [21, 22].

In this work, a new Dynamic S-Box is unique due to its integration with advanced MF and the use of a 7D hyperchaotic system is designed. This combination allows for the real-time generation of highly adaptive and unpredictable S-boxes, significantly enhancing security by introducing dynamic variability with each encryption process. The MF ensures precise control and mixing of chaotic sequences, which is difficult to achieve with conventional methods, thereby providing a superior defense against cryptographic attacks. Figure 4 shows the flowchart of the S-box generation steps.

This section introduced a procedure to generate a new S-box based on system (1) and MF. Figure 3 shows this procedure.

3.1.1 Generate random sequence based on system (1)

To generate random sequence based on system (1). First step is set initial state and parameters of system (1) with set iterations and time, after that, we implement the system generates seven randoms chaotic sequences, these steps illustrated in Algorithm 1.

3.1.2 Microfluidic mixer to generate S-box

In this phase, we generated an S-box based on system (1), and a string of letters, then mixed them via the microfluidic mixer; as shown in Algorithm 2 and Table 1.

Table 1 shows a sample of 10×10 S-box generated via microfluidic technique with the hexadecimal number. The size of the S-box can be changed according to the size of the image to be encrypted.

The utilization of the microfluidic technique offers numerous benefits compared to traditional methods in the generation of S-boxes for encryption purposes. The utilization of the microfluidic technique provides a dynamic generation and precise control, integration with chaotic maps. It is an excellent choice for enhancing the encryption algorithm's security due to its efficiency and scalability.

4.png

Figure 4. Flowchart of S-box generation steps

Table 1. Sample of S-box generated via a microfluidic technique of size 10×10

Also, the dynamic nature of the S-boxes generated by microfluidics makes it challenging for cryptanalysis resistance to attacks. Attackers cannot rely on precalculated tables or traditional methods of analyzing cryptographic systems, as the properties of the S-boxes change in an unpredictable manner with each encryption instance. Microfluidic techniques have a wide range of applications for data encryption, not just limited to images. This adaptability makes this technique valuable in various fields that require strong encryption, such as telecommunications, data storage and secure transmissions.

3.2 S-box performance metrics

At this stage of our work, we need to test our proposed algorithm using well-known analysis frameworks in the scientific community to ensure the effectiveness of our S-box. For example, we will evaluate its performance based on nonlinearity, the Avalanche Effect (AE), and the Output Bit Independence Criterion (BIC) to demonstrate the effectiveness of the proposed S-box design.

1. Nonlinearity

One of the tests to measure the efficiency of an S-box is nonlinearity, which is defined as the minimum Hamming distance between the S-box function and the set of all affine functions [22], it can be mathematically defined as:

$S_{(f)}(\omega)=\sum_{\omega \in G F\left(2^n\right)}(-1)^{f(x) \oplus x \cdot \omega}$     (9)

where, the dot product between $x$ and $\omega$ is defined by

$x \cdot \omega=x_1 \cdot \omega_1 \oplus x_2 \cdot \omega_2 \oplus \ldots x_n \cdot \omega_n$

Thus, the nonlinearity is calculated by

$N_f=2^{n-1}\left(1-2^{-n} \max _{\omega \in G F\left(2^n\right)}\left|S_{(f)}(\omega)\right|\right)$     (10)

The nonlinearity of the proposed S-box and some previous methods are shown in Table 2.

Table 2. The nonlinearity of some S-boxes

2. Avalanche effect (AE)

The AE measures how much the output changes when a single input bit is flipped. The general idea, where a flipping one bit of the input sequence has the effect of changing about half of the bits in the output [23]. Table 3 shows the AE of the proposed S-box and some previous methods.

Table 3. AE values of some S-boxes

3. Bit Independence Criterion (BIC)

The BIC measures how independently the output bits behave when specific input bits are flipped. It checks the independence between pairs of output bits for different input bit changes. The general idea of BIC lies in the flipping of one input bit will cause an independent and unpredictable changes in the output bits. The BIC values should show minimal correlation between the effects on different output bits [23]. Table 4 shows the BIC of our proposed S-box and some other S-boxes from the literature.

Table 4. BIC of the proposed S-box and some other S-boxes

3.3 Encryption part

In this part, three steps (Confusion Pixels, Pixels-permutation, Substitution) are implemented to produce the encrypted image. In our proposed encryption algorithm, we choose some parameters to generate S-boxes using a system (1) with parameters: $a=40, b=60, c=8, d=$ $20, e=0.1, f=77$, and $g=10$, and initial state $x(i)=0.1$. These parameters were chosen to ensure that the chaotic system exhibits strong sensitivity to initial conditions and generates highly unpredictable sequences, essential for secure S-box construction based on its evaluation tests. The system (1) produced by iterating this system is mapped to an $8 \times 8 \mathrm{~S}$-box, with each sequence value normalized and converted into an S-box entry. To add an additional layer of randomness, microfluidic technology is employed to mix and refine the chaotic sequences, resulting in a unique S-box for each encryption session. This S-box is then integrated into the image encryption process at the substitution stage, where it replaces pixel values in the image with their corresponding Sbox values. The continuous adaptation of the S-box for each block of data significantly enhances the security, making the encryption resistant to a variety of cryptographic attacks. They are described as a block diagram in Figure 5.

5.png

Figure 5. The encryption process structure

3.3.1 Confusion process

The process of rearranging the positions of pixels is referred to as confusion. Let us say we have a plain image called I with dimensions m × n where each pixel's value falls within the range of [0, 255]. To change the locations, we create a random matrix that matches the size of the original image. Then we proceed to modify the locations based on this random matrix. The confused pixels of the image can be generated as shown in Algorithm 3. In the decryption part, the confusing image should pass through Algorithm 4 which represents the inverse operations.

3.3.2 Diffusion process

The process of altering the image's values is known as diffusion. Let us say we have an image called I with dimensions m × n, where each pixel has a value ranging in [0, 255]. To modify these values, we apply the XOR operation using an S-box. The diffusion pixels of the image can be generated as shown in Algorithm 5. In the decryption part, we used Algorithm 6 which performed the inverse operations on the diffused image.

3.3.3 Substitution of pixel values

This part of the encryption operation used the S-box to change the values of pixels via substitution values of the image with values of the S-box. The substitution values of image pixels are generated by Algorithm 7. Algorithm 8 is used to perform the inverse operations on the substitution values of the image in the decryption part.

After these three operations (confusion pixels, diffusion Pixels and substitution of Pixel’s values), the cipher image is obtained. The main steps are abstracted in Algorithm 9.

3.4 Decryption process

In general, the decryption operation is the inverse operation of encryption algorithm, which means the last stage of encryption become the first stage in the encryption algorithm. The steps, for decryption are outlined in Figure 6.

6.png

Figure 6. The decryption processes

For evaluating the security of the encryption technique to withstand different attacks for example differential attacks, where these attacks involve making small changes to the original image and observing the resulting differences in the encrypted output. Some performance measures are implemented to show the effectiveness of the proposed technique. The dynamic nature of the generated S-box, which changes with each encryption instance significantly enhance security against both differential and linear cryptanalysis.

5.1 Analysis of key sensitivity performance

The Mean Absolute Error (MAE) serves as a technique for measuring the disparity between two continuous variables. In the context of image encryption, it functions to ascertain the dissimilarity between two images: the original (plain) image and the encrypted (ciphered) image. The MAE is computed using the following formula:

$M A E=\frac{1}{\text { row } \times \operatorname{col}} \sum_{i=0}^{\text {row }-1} \sum_{j=0}^{\text {col- }-1}\left|P_{i, j}-C_{i, j}\right|$

where the row and col represent the dimensions of the images, referring to the number of rows and columns, respectively of the image. While the $P_{i, j}$ refer to the value of the pixel at the location i -th row and j -th column of the plain image, while $C_{i, j}$ refer to the value of the pixel at the location i-th row and j-th column of the ciphered image. A higher MAE value indicates a significant difference between the plain and cipher images, signifying a favourable outcome for encryption as it suggests that the encrypted image bears little resemblance to the original, making decryption more challenging. Mean Squared Error (MSE) provides a measure of dissimilarity between two images by calculating the average of the squared differences between corresponding pixels:

$M S E=\frac{1}{\text { row } \times \operatorname{col}} \sum_{i=0}^{\text {row }-1} \sum_{j=0}^{\text {col- } 1}\left(P_{i, j}-C_{i, j}\right)^2$

The analysis of pixel differences between the plain and cipher images is presented in Table 8.

Table 8. Difference analysis of pixels between plain image and cipher image

5.2 Number of Pixels Change Rate (NPCR)

The NPCR, or the Number of Pixel Changes Rate, quantifies the percentage of pixel positions where two encrypted images exhibit differences. In simpler terms, it gauges the extent of pixel alterations when a single pixel in the original image changes. If $C_1(i, j)$ and $C_2(i, j)$ represent two encrypted images, the NPCR is given by the formula:

$N P C R=\frac{1}{\text { row } \times \operatorname{col}} \sum_{i, j} x(i, j)$

where, rows and cols are the dimensions (height and width) of the images. The function $x(i, j)$ equals 0 if the pixel values at position $(i, j)$ in both encrypted images are identical, and 1 if they differ, specifically defined as 0 if $C_1(i, j)=C_2(i, j)$ and 1 if $C_1(i, j) \neq C_2(i, j)$. A higher NPCR value means that a significant number of pixels have changed between the two encrypted images, indicating that the encryption algorithm is highly sensitive to minor modifications in the input image. Essentially, NPCR evaluates the robustness of the encryption scheme against differential attacks by analyzing how the encrypted image responds to small changes in the original image.

5.3 Unified Average Intensity Change Intensity (UACI)

The UACl is a metric evaluating encryption algorithm sensitivity by measuring the average intensity difference between two encrypted images. It is defined as;

$\mathrm{UACI}=\frac{1}{\text { row } \times \operatorname{col}} \sum_{i=0}^{\text {row-1 }} \sum_{j=0}^{\text {col-1 }}\left|\frac{C_1(i, j)-C_2(i, j)}{255}\right|$

The biggest values of UACl refer to significant intensity differences, which means the encryption scheme introduces substantial changes even with minor alterations to the input image. To assess the encryption scheme's sensitivity through NPCR or UACl, begin by encrypting the original image $(P)$ to create $\mathrm{C}_1$. Introduce a random alteration to a single pixel in $P$, and subsequently encrypt this modified image to generate $C_2$. Calculate NPCR or UACl using the specified formulas, and then compare the resulting cipher images, $C_1$ and $C_2$. The experimental findings of these evaluations are presented in Table 9 and Table 10.

Table 9. Analysis of NPCR test between plain and cipher images in comparison to Ref. [27]

Table 10. Analysis of UACI test between plain and cipher images in comparison to Ref. [27]

Table 11. GLCM analysis

Plain Image	ID	E	Cots	MaxD	Hog
biao_1.png	85302	0.025671	4851.43	6.4510×105	0.261361
biao_2.png	83745	0.025171	4836.14	6.427×105	0.260281
biao_3.png	83256	0.025035	4843.54	6.4206×105	0.261711
biao_4.png	83254	0.026032	4842.54	6.4206×105	0.261651

5.4 Analysis of Gray‑Level Co-Occurrence Matrix

In this test, we will highlight the performance of the proposed encryption algorithm based on the Gray Level Co-occurrence Matrix (GLCM) test, which is a description of some characteristics such as Irregular deviation (ID) contrast (Cots), energy (E), and uniformity [9]. Each one of them can be defined as the following:

5.4.1 Irregular deviation

The Irregular Deviation (ID) quantifies the precise difference between each pixel in the plain image $(I)$ and its corresponding pixel in the encrypted image ( $C$ ). ID is then calculated by taking the average of the absolute differences between the histogram $M_H$ and its mean value $m_{D H}$ [27].

$\left\{\begin{array}{l}H G_{(i)}=\left|I_{(i)}-C_{(i)}\right| \\ I D=\frac{\sum_1^{256}\left|M_{H(i)}-m_{D H}\right|}{M \times N}\end{array}\right.$     (11)

where, $I$ refer to plain image, while $C$ refer to cipher image. Also, $M_H$ refer to the frequency distribution of pixel intensity values that is mean histogram of $H G$, and $m_{D H}$ refer to the mean value of the $I D$.

5.4.2 Maximum deviation

The Maximum Deviation $\left(\operatorname{Max}_D\right)$ metric measures the highest possible difference within the histogram when comparing the $I$ and $C$ images. It takes into account the amplitude values of the histogram at the extreme ends ( 1 and 256 ) and sums up the values from 2 to 255 , can be defined by the $\operatorname{Max}_D$ [27].

$\operatorname{Max}_D=\frac{A M_v(i)+A M_v(256)}{2}+\sum_{i=2}^{255} H(i)$      (12)

where, $A M_v(i)$ is the amplitude value of the $H G$ mentioned in the above Section.

5.4.3 Contrast

Contrast (Cots) is used to measure the difference in brightness or colour that allows an object within an image to be distinguished. In the context of GLCM, it evaluates the degree of variation between pairs of pixels in the image. Cots is then calculated by [27]:

Cots $=\sum|i-j|^2 G(i, j)_{i, j}$      (13)

5.4.4 Energy

Energy (E) in general is a measure of the uniformity or orderliness of an image. where the low value of E refers to the C, which means a high randomness. The formula for calculating energy is [27]:

$E=\sum_{i, j} G(i, j)^2$      (14)

5.4.5 Homogeneity

Homogeneity $(\mathrm{Hog})$ is used to measure the similarity between pixel pairs in an image, typically yielding a result between 0 and 1 . where the low value of this measurement refers to the $C$, which exhibits significant variation between pixel pairs, and this tends to robust encryption and effective concealment of the $P$. The Hog can be calculated as [27]:

$H o g=\sum_{i, j} \frac{G(i, j)}{1+|i-j|}$       (15)

Table 11 presents some results of the GLCM analysis for several enciphered images.

5.5 Analysis of resistance to classical attacks

To maintain basic security requirements for any encryption algorithms, four classical attacks should be discussed. In the chosen plaintext attack, an unauthorized individual introduces forged text without knowing the key but somehow obtains the corresponding ciphertext. Another technique is the chosen-ciphertext attack, in which the attacker creates fake ciphertext and plaintext in order to obtain the relevant data illegally. The difference between ciphertext-only and known-plaintext attacks is that the former only includes obtaining the ciphertext, while the latter only involves obtaining the plaintext. Nonetheless, our cryptosystem is firmly grounded in a very sensitive and stochastic chaotic system, in which even minute modifications to the initial conditions yield completely distinct chaotic sequences. Consequently, we use the pixel average values from the original image to disturb the initial values while setting them. This guarantees that our approach is robust to traditional attacks and has good plaintext sensitivity. Since the selected plaintext assault is thought to be the most aggressive, the other three forms of attacks usually pose little harm to an image encryption system that can withstand it. In this study, the high dependency on the plaintext means that any attempt by the attackers to reconstruct the original messages, after they have obtained the ciphertext through phoney messages, will be unsuccessful. Additionally, the NPCR and UACI values obtained in Section 4.8 further demonstrate that our algorithm is fully resistant to chosen-plaintext attacks. Also, we can see our system efficiency against the entropy-based cryptanalysis because the values of our explement are near 8 (see section 4.3). Therefore, based on our experiment and cryptosystem analysis we can conclude that our scheme of cryptosystem is capable of resisting all four classical attacks.