
It is becoming increasingly apparent that businesses must consider the impact they have on the environment and society while pursuing profit maximization. As a result, there is a growing need to incorporate sustainable frameworks into business decision-making. By focusing on sustainable performance at the firm level, we addressed a significant gap in understanding how environmental and social Sustainable Development Goals (SDGs) impact bottom-line performance and the crucial role that effective country governance plays in implementing sustainability at the organization level. In 2015, the United Nations established Sustainable Development Goals (SDGs), where firms are encouraged to practice in the strategic operation of their businesses. In addition, country governance can play a significant role in adopting sustainable practices and policies that can impact bottom-line performance. In this study, we examined the relationship between environmental and social Sustainable Development Goals (SDGs) practices, country governance, and firms' financial performance from 2017 to 2021. The sample data set consisted of top-listed firms in the finance, manufacturing, and technology industries of 100 companies from 17 countries in developed and developing and emerging economies. We utilized content analysis to account for the qualitative aspects of how firms implement social and environmental SDGs. Ten environmental SDGs and eight social SDGs were incorporated in this study as a means of measuring sustainable development goals' impact on a firm's financial performance. We adopted return on assets (ROA) to measure the firm's financial performance. We adopted government effectiveness and regulatory quality to moderate the relationship between social and environmental sustainability practices and firm performance. The panel regression method was exercised to find out the relationship between environmental and social SDGs' impact on financial performance. In addition, we measured the interaction effect between environmental and social SDGs and country governance on firms' performance. We also deployed two-stage least squares (2SLS) regression estimation to mitigate endogeneity concerns. We found that environmental SDGs had a positive and significant impact on firms' financial performance. The coefficient of social SDGs on firm performance was negative and statistically significant. We observed that the coefficient of interaction terms between environmental SDGs and country governance was positive and statistically significant. Moreover, the coefficient interaction terms between social SDGs and country governance were positive and statistically significant, lessening the negative impact of social SDGs on firm financial performance. Finally, we also performed a robustness test on our analysis based on the firm's average capital and average assets. The findings almost held the same.
Citation: Sabuj Saha, Ahmed Rizvan Hasan, Kazi Rezwanul Islam, Md Asraful Islam Priom. Sustainable Development Goals (SDGs) practices and firms' financial performance: Moderating role of country governance[J]. Green Finance, 2024, 6(1): 162-198. doi: 10.3934/GF.2024007
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It is becoming increasingly apparent that businesses must consider the impact they have on the environment and society while pursuing profit maximization. As a result, there is a growing need to incorporate sustainable frameworks into business decision-making. By focusing on sustainable performance at the firm level, we addressed a significant gap in understanding how environmental and social Sustainable Development Goals (SDGs) impact bottom-line performance and the crucial role that effective country governance plays in implementing sustainability at the organization level. In 2015, the United Nations established Sustainable Development Goals (SDGs), where firms are encouraged to practice in the strategic operation of their businesses. In addition, country governance can play a significant role in adopting sustainable practices and policies that can impact bottom-line performance. In this study, we examined the relationship between environmental and social Sustainable Development Goals (SDGs) practices, country governance, and firms' financial performance from 2017 to 2021. The sample data set consisted of top-listed firms in the finance, manufacturing, and technology industries of 100 companies from 17 countries in developed and developing and emerging economies. We utilized content analysis to account for the qualitative aspects of how firms implement social and environmental SDGs. Ten environmental SDGs and eight social SDGs were incorporated in this study as a means of measuring sustainable development goals' impact on a firm's financial performance. We adopted return on assets (ROA) to measure the firm's financial performance. We adopted government effectiveness and regulatory quality to moderate the relationship between social and environmental sustainability practices and firm performance. The panel regression method was exercised to find out the relationship between environmental and social SDGs' impact on financial performance. In addition, we measured the interaction effect between environmental and social SDGs and country governance on firms' performance. We also deployed two-stage least squares (2SLS) regression estimation to mitigate endogeneity concerns. We found that environmental SDGs had a positive and significant impact on firms' financial performance. The coefficient of social SDGs on firm performance was negative and statistically significant. We observed that the coefficient of interaction terms between environmental SDGs and country governance was positive and statistically significant. Moreover, the coefficient interaction terms between social SDGs and country governance were positive and statistically significant, lessening the negative impact of social SDGs on firm financial performance. Finally, we also performed a robustness test on our analysis based on the firm's average capital and average assets. The findings almost held the same.
Over the last few decades, the number of organizations and individuals working on the web has increased remarkably. Because of the widespread availability of data and information in every field, which is accessible to everyone, serious issues such as unauthorized access to confidential information have cropped up. As a result of this massive quantity of work and traffic, the risks of valuable data theft have significantly increased, and preventing these situations is a challenging task. Various researchers in their respective fields have worked to secure data by employing various cryptographic, watermarking, and stenographic schemes. Cryptography is a technique that restricts access to original information to the sender and recipient only [1]. It contains algorithms to block potential unauthorized access. Cryptographic algorithms are mathematical tools that helps in protection of data. The cryptography has two main types, symmetric and asymmetric cryptography. A symmetric cryptography [2] involves the procedures requires sole key to encrypt and decrypt the related content, while the algorithm in asymmetric cryptography contains two different keys for the process of encryption and decryption [3]. The symmetric cipher is further classified into two types: stream cipher and block cipher. The stream cipher modifies the original information bit-by-bit or byte-by-byte while the block cipher does so in blocks involving several bits or bytes simultaneously [4]. Data Encryption Standard (DES), GOST, Advanced Encryption Standard (AES), BLOWFISH, etc., are the well-known block ciphers. The substitution box (S-box) is a pertinent non-linear ingredient in block cipher that plays a very decisive role in encrypting the plaintext [5]. An n×n S-box is a Boolean function f:Zn2⟶Zn2 which maps an input of n bits to an n bits output. It generates perplexity and responsible for the complex relationship between actual and encrypted contents [6]. Therefore, it is not an overstatement to state that the security level of a block cipher can be determined by analyzing the performance of S-box.
Considering the importance of the S-box in the security of cryptosystems, designing complex mathematical techniques to construct robust S-boxes has become a goal of cryptographers. The scientists working in this field are primarily interested in improving the performance of block ciphers. For this purpose, thousands of studies have been conducted and published in leading journals in recent years. A novel approach of S-box creation is introduced in [7]. The authors developed their proposed S-box using a chaotic system and fitness function. Javeed et al. [8] developed an effective framework for generating strong S-boxes relying on chaotic maps and symmetric groups. The authors designed an initial S-box with the help of chaotic dynamical system. Then the final proposed S-box is obtained by applying a permutation of S256. In [9] a specific type of graphs based the concepts of group theory were employed to develop a new S-box. Multiple performance evaluation metrics validate the resilience of the suggested S-box.
In [10] Si et al. proposes a method to create a secure S-Box for symmetric cryptography using a 2D enhanced quadratic map, and an algorithm is designed to eliminate vulnerabilities. Experimental results confirm the method's effectiveness. Lambic [11] used usual multiplication and circular shift to generate an innovative discrete-space chaotic map which further employed in the construction of S-box having good security properties. Anees and Ahmed [12] designed a potent S-box by investigating the behavior of van der pol oscillator. Firstly, the author used a numerical technique to obtain the iterative solution of chaotic map. Then the ceiling function is employed to those solution to achieve the task. Liu et al. [13] proposes a strong S-Box construction method using a non-degenerate 3D improved quadratic map. The proposed algorithm satisfies six criteria and eliminates fixed points, reverse fixed points, and short cycles. Results show effectiveness in encrypting color images and verified security. A systematic scheme to evolve a S-box with high non-linearity value is given in [14]. The chaotic map iteration yields a 16×16 matrix on which the genetic technique is applied to obtain the suggested S-box. We recommend to read [15,16,17,18,19,20] for further information on S-box generation methodologies. In [21], a secure image encryption method was introduced. It used a new framework to create chaotic signals with finite computer precision, and includes circular diffusion and local/global scrambling. In [22] the authors introduced a new encryption algorithm for color images using DNA dynamic encoding, self-adapting permutation, and a new 4D hyperchaotic system. Zhou et al. [23] proposes a secure color image cryptosystem using deep learning to train hyper-chaotic signals, which are then applied to increase the system's security. Liu et al. [24] developed a secure color image encryption algorithm using a conservative chaotic system without attractors. They employed techniques such as plane element rearrangement, dynamic selection row-column cross scrambling, and cross-plane diffusion to enhance the encryption's security and mixing. The study [25] proposed a 2D hyperchaotic map to generate S-boxes and combine them to create a secure image encryption algorithm that passed NIST and TestU01 tests and resists common attacks. In [26], a new n-dimensional conservative chaos was designed to address security issues with encryption algorithms based on dissipative chaos. A new image encryption system using true random numbers and chaotic systems has been proposed in [27]. The method is found to be more secure and resistant to classical attacks compared to existing models.
The study presents a novel method for constructing robust S-boxes for use in block ciphers. The following factors were considered during the creation of the S-box:
i. The generated S-box must be cryptographically robust and comply with the mandatory information security standards.
ii. The S-box must exhibit a sufficient level of confusion and complexity, while the method used to construct it remains simple and computationally efficient.
iii. The S-box should demonstrate good performance when evaluated using modern cryptographic performance assessment parameters.
iv. The S-box must meet the requirements for suitability in multimedia image encryption, as determined through a thorough evaluation of its cryptographic properties and performance under relevant metrics.
The following paragraph summarizes the main contributions and proposed scheme of this article.
By utilizing the action of the modular group on a Galois field of order 1024, GF(210)={0,κ1,κ2,κ4,…,κ1023} a coset graph is constructed. The vertices of the coset graph are utilized in a specific manner to generate a random sequence of the elements in GF(210)∗={κ1,κ5,κ9,…,κ1021}, which is presented in a 16×16 matrix. Then, a bijective mapping from the group GF(210)∗ to GF(28) yields an initial S-box that exhibits reasonable security. A new notion named "matrix transformer" which transforms a matrix into another matrix has been introduced. By applying a specific matrix transformer to the initial S-box, we obtain a proposed S-box with almost optimal features. Furthermore, a series of well-established analyses are carried out to establish the potential effectiveness of the proposed S-boxes for image encryption in the context of multimedia encryption.
The arrangement of the remaining content of this paper is as follows: The purpose of Section 2 is to discuss the newly developed matrix transformer and modular group-based coset graphs over finite fields. Using the concepts described in Section 2 as a foundation, we propose our S-box design scheme in Section 3. Assessing the algebraic robustness of the constructed S-box is the focus of Section 4. This section also includes a comparison with some recently developed S-boxes. Sections 5–7 are devoted to examining the suitability of constructed S-box for image protection. We reveal the concluding remark in Section 8.
In this section, we will discuss some fundamental concepts that are required to comprehend the proposed S-box construction scheme.
The modular group M is an infinite non-cyclic group of linear transformations. It is generated by x and y such that (s)x=−1s and (s)y=s−1s. The finite presentation of M is ⟨x,y:x2=y3=1⟩. Let p be a prime number and n∈N. Then GF(pn) denote a Galois field of order pn, it is well known that M cannot act directly on GF(pn) as (0)x=−10∉GF(pn), so the action of M is possible if ∞ is adjoined with GF(pn), that is M acts on GF(pn)∪{∞}. The graphical interpretation of the action of M is described with the help of coset graphs [28,29,30,31]. As (s)y3=s, so y has cycles of length three which are represented by triangles whose vertices are elements of GF(pn)∪{∞} are permuted counter-clockwise by y. Moreover, since (s)x2=s, therefore an undirected line connecting a pair of vertices of the triangles is drawn to represent x. The heavy dots are used to denote fixed points of x and y, if they exist. For the better understanding of readers, here we describe the action of M on GF(23)∪{∞} and draw the corresponding coset graph. We apply (s)x=−1s and (s)y=s−1s on each element of GF(23)∪{∞} and obtain permutation representations of x and y. For example, (1)x=−11≡22 and (22)x=−122≡1 mean a cycle (1,22) of x. Moreover, (2)y=12≡12, (12)y=1112≡22 and (22)y=2122≡2 give rise to a cycle (2,12,22) of y. In a similar way, all other cycles of x and y can be computed and we have the following permutation representations of x and y.
x:(0,∞)(22,1)(11,2)(15,3)(17,4)(9,5)(19,6)(13,7)(20,8)(16,10)(21,12)(18,14); |
y:(1,0,∞)(2,12,22)(11,3,16)(15,4,18)(17,5,10)(9,6,20)(19,7,14)(13,8,21). |
The permutation representation of y consists of 8 cycles. Consequently, the resulting coset graph has eight triangles. The graphical version of the cycle (1,0,∞) in y is a triangle with the vertices 1,0 and ∞ permuted counter-clockwise by y. In a similar way, we can draw and label all triangles. The permutation representation of x contains 12 transpositions which correspond to12 undirected lines joining all 24 vertices of 8 triangles. For instance, (1,22) means the vertices 1 and 22 are connected through an undirected line. Similarly, the remaining vertices can be joined with each other through x and the following coset graph is emerged (See Figure 1).
In the next subsection, we have introduced a new notion namely matrix transformer to generate a strong S-box from an initial S-box.
Suppose M is a square matrix of order n. Let us define the position of the elements of M as follows;
kth element = mth element of ⌈kn⌉th row
where m={n if n divides mk mod (n) otherwise, and ⌈kn⌉ means ceiling of ⌈kn⌉.
For example, in a 3×3 matrix, we have 1st element means 1st element of 1st row, 2nd element means 2nd element of 1st row, 3rd element means 3rd element of 1st row, 4th element means 1st element of 2nd row and so on.
Definition 2.1. A square matrix A of order n with entries from {1,2,3,…,n2} is called matrix transformer of square matrix M of order n if the action of A on M evolves a new matrix M' of order n in the following way; t∈{1,2,3,…,n2} is the ith element of the matrix transformer A⟺ tth element of M' is equal to ith element of M.
Example 2.1. Consider M=(fdgcaiehb) and A=(397862415). Then the action of of A on M generates M'=(hifebagcd).
In this section, we propose our S-box construction method based on the concepts describe in the previous section.
The proposed S-box generation scheme involves coset graph of the modular group M on GF(210)∪{∞}. So, in the 1st phase, we have to construct the Galois field GF(210). It is well-known that a primitive irreducible polynomial of degree 10 over Z2 is required to compute all the elements of GF(210) [32]. For that purpose, we choose p(κ)=κ10+κ7+1 and obtain GF(210)={0,κ1,κ2,κ3,…,κ1023=1}. In Table 1, we present some of the elements of GF(210) along with their binary and decimal form.
Binary form | Decimal | 𝐺𝐹 (210) | Binary form | Decimal | 𝐺𝐹(210) | Binary form | Decimal | 𝐺𝐹(210) | Binary form | Decimal | 𝐺𝐹(210) |
0000000000 | 0 | 0 | 0000000001 | 1 | 1 | 0000000010 | 2 | κ1 | 0000000100 | 4 | κ2 |
0000001000 | 8 | κ3 | 0000010000 | 16 | κ4 | 0000100000 | 32 | κ5 | 0001000000 | 64 | κ6 |
0010000000 | 128 | κ7 | 0100000000 | 256 | κ8 | 1000000000 | 512 | κ9 | 0010000001 | 129 | κ10 |
0100000010 | 258 | κ11 | 1000000100 | 516 | κ12 | 0010001001 | 137 | κ13 | 0100010010 | 274 | κ14 |
1000100100 | 548 | κ15 | 0011001001 | 201 | κ16 | 0110010010 | 402 | κ17 | 1100100100 | 804 | κ18 |
1011001001 | 713 | κ19 | 0100010011 | 275 | κ20 | 1000100110 | 550 | κ21 | 0011001101 | 205 | κ22 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
1010111011 | 699 | κ311 | 0111110111 | 503 | κ312 | 1111101110 | 1006 | κ313 | 1101011101 | 861 | κ314 |
1000111011 | 571 | κ315 | 0011110111 | 247 | κ316 | 0111101110 | 494 | κ317 | 1111011100 | 988 | κ318 |
1100111001 | 825 | κ319 | 1011110011 | 755 | κ320 | 0101100111 | 359 | κ321 | 1011001110 | 718 | κ322 |
0100011101 | 285 | κ323 | 1000111010 | 570 | κ324 | 0011110101 | 245 | κ325 | 0111101010 | 490 | κ326 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
0100110000 | 304 | κ1007 | 1001100000 | 608 | κ1008 | 0001000001 | 65 | κ1009 | 0010000010 | 130 | κ1010 |
0100000100 | 260 | κ1011 | 1000001000 | 520 | κ1012 | 0010010001 | 145 | κ1013 | 0100100010 | 290 | κ1014 |
1001000100 | 580 | κ1015 | 0000001001 | 9 | κ1016 | 0000010010 | 18 | κ1017 | 0000100100 | 36 | κ1018 |
0001001000 | 72 | κ1019 | 0010010000 | 144 | κ1020 | 0100100000 | 288 | κ1021 | 1001000000 | 576 | κ1022 |
To draw the coset graph of M on GF(210)∪∞, we firstly apply the generators (s)x=−1s and (s)y=s−1s of M on all elements of GF(210)∪∞toget permutation representations of x and y. For instance, (κ1)x=−1κ1=1κ1=κ1023κ1=κ1022 and (κ1022)x=−1κ1022=1κ1022=κ1023κ1022=κ1 yield a cycle (κ1,κ126) of x. Moreover, (κ1)y=κ1−1κ1=κ947κ1=κ946, (κ946)y=κ946−1κ946=κ1022κ946=κ76 and (κ76)y=κ76−1κ76=κ77κ76=κ1, generate a (κ1,κ946,κ76)of y.
Similarly, the remaining cycles of x and y can be found and some of them are presented below;
x:(0,∞)(1)(κ1,κ1022)(κ2,κ1021)(κ3,κ1020)(κ4,κ1019)(κ5,κ1018)(κ6,κ1017)(κ7,κ1016)(κ8,κ1015) |
(κ9,κ1014)…(κ507,κ516)(κ508,κ515)(κ509,κ514)(κ510,κ513)(κ511,κ512); |
y:(κ1,κ946,κ76)(κ2,κ869,κ152)(κ3,κ1013,κ7)(κ4,κ715,κ304)(κ5,κ510,κ508)(κ6,κ1003,κ14) |
(κ8,κ407,κ608)…(κ650,κ713,κ683)(κ652,κ656,κ738)(κ654,κ695,κ697)(0,∞,1)(κ341)(κ682). |
Both permutations of x and y produced a disconnected coset graph which contains 172 number of patches. It is important to note that out of these 172 patches, 170 are of the same type, denoted by η1,η2,η3,…,η170. The other two patches are denoted by η171 and η172. We denote this coset graph by D and D=η1∪η2∪η3∪⋯∪η170∪η171∪η172 The Figures 2–4 represent η1,η171 and η172 respectively.
Step I: We first construct a square matrix of order 16 using vertices of coset graph in a specific way.
Consider a patch η1 containing κ1 as vertex from the coset graph D. The application of xyxy−1x on κ1 carries us to κ77 by following the route κ1x→κ1022y→κ947x→κ76y−1→κ946x→κ77 (see Figure 2). So, in this way, we generate a sequence κ1,κ1022,κ947,κ76,κ946,κ77 of vertices. Consider a sub-sequence {κi:i≡1 mod (4)}=κ1,κ77} of this sequence and place κ1 and κ77 at 1st and 2nd position of the first row respectively. Thereafter, we find the vertex from D−{η1} having the smallest power of κ, that is, κ2. Let us denote the copy from D−{η1} containing κ2 by η2. Note that if κ2 would been exhausted in η1 , then η2 is a copy from D−{Γ1} containing κ3 . Generate a sequence of the vertices of the type κi:i≡1 mod (4), present in η2, in a similar way as done in the case of η1. Write this sequence at the 1st row after κ77 by maintaining the order of sequence. After that, we chose a copy from d−{η1,η2} possessing a vertex κm, where m is the least positive integer. In a similar way, continue to select the copies ηi and write vertices of the type κi such that i≡1 mod (4) in the matrix until all copies ηi are used. So, a square matrix of 256 distinct entries from GF(210)∗={κ1,κ5,κ9,…,κ1021} is generated (see Table 2).
κ1 | κ77 | κ1021 | κ869 | κ1013 | κ5 | κ513 | κ1017 | κ1009 | κ9 | κ189 | κ13 | κ301 | κ709 | κ353 | κ193 |
κ209 | κ17 | κ729 | κ1005 | κ393 | κ21 | κ305 | κ1001 | κ645 | κ937 | κ25 | κ385 | κ997 | κ421 | κ817 | κ29 |
κ537 | κ457 | κ993 | κ317 | κ265 | κ637 | κ605 | κ33 | κ989 | κ401 | κ909 | κ149 | κ237 | κ273 | κ37 | κ161 |
κ985 | κ473 | κ545 | κ41 | κ849 | κ981 | κ413 | κ45 | κ977 | κ897 | κ673 | κ397 | κ49 | κ225 | κ749 | κ973 |
κ253 | κ109 | κ965 | κ181 | κ233 | κ53 | κ481 | κ969 | κ665 | κ213 | κ865 | κ57 | κ437 | κ529 | κ345 | κ737 |
κ449 | κ389 | κ61 | κ917 | κ961 | κ493 | κ65 | κ621 | κ957 | κ297 | κ945 | κ145 | κ153 | κ221 | κ69 | κ953 |
κ725 | κ261 | κ549 | κ477 | κ73 | κ949 | κ701 | κ405 | κ81 | κ177 | κ765 | κ941 | κ593 | κ785 | κ321 | κ113 |
κ197 | κ85 | κ349 | κ589 | κ489 | κ577 | κ89 | κ893 | κ933 | κ761 | κ93 | κ657 | κ929 | κ229 | κ721 | κ97 |
κ925 | κ573 | κ165 | κ417 | κ517 | κ101 | κ789 | κ133 | κ921 | κ805 | κ601 | κ525 | κ661 | κ557 | κ105 | κ837 |
κ269 | κ913 | κ597 | κ169 | κ705 | κ117 | κ461 | κ445 | κ905 | κ333 | κ553 | κ125 | κ245 | κ121 | κ357 | κ901 |
κ689 | κ257 | κ521 | κ649 | κ129 | κ561 | κ429 | κ889 | κ733 | κ329 | κ829 | κ717 | κ581 | κ137 | κ885 | κ873 |
κ141 | κ881 | κ501 | κ541 | κ877 | κ777 | κ853 | κ325 | κ157 | κ361 | κ505 | κ569 | κ613 | κ861 | κ669 | κ857 |
κ381 | κ797 | κ629 | κ173 | κ313 | κ845 | κ585 | κ841 | κ425 | κ465 | κ741 | κ185 | κ377 | κ565 | κ833 | κ609 |
κ825 | κ693 | κ201 | κ745 | κ821 | κ757 | κ205 | κ813 | κ441 | κ249 | κ809 | κ485 | κ409 | κ625 | κ217 | κ337 |
κ469 | κ801 | κ685 | κ793 | κ617 | κ773 | κ533 | κ241 | κ681 | κ781 | κ309 | κ497 | κ293 | κ769 | κ509 | κ433 |
κ633 | κ653 | κ753 | κ365 | κ277 | κ281 | κ453 | κ289 | κ285 | κ677 | κ641 | κ713 | κ373 | κ697 | κ369 | κ381 |
We can generate 3 more tables simply by replacing the type of vertices in step I, from κi:i≡1 mod (4) to κi:i≡0 mod (4), κi:i≡2 mod (4) and κi:i≡3 mod (4) .
Step II: The outcome of Step I yields a 16×16 matrix of distinct element from GF(210)∗={κ1,κ5,κ9,…,κ1021}. To bring all the element in the range of 0 to 255, we define a mapping f:GF(210)∗⟶GF(28) by f(κn)=βn−14. Note the Galois GF(28) is generated by primitive irreducible polynomial β8+β6+β5+β3+1. Table 3 shows some of the elements of GF(28) and their binary and decimal form.
Binary form | Decimal | 𝐺𝐹 (28) | Binary form | Decimal | 𝐺𝐹 (28) | Binary form | Decimal | 𝐺𝐹 (28) | Binary form | Decimal | 𝐺𝐹 (28) |
00000000 | 0 | 0 | 00000001 | 1 | 1 | 00000010 | 2 | β1 | 00000100 | 4 | β2 |
00001000 | 8 | β3 | 00010000 | 16 | β4 | 00100000 | 32 | β5 | 01000000 | 64 | β6 |
10000000 | 128 | β7 | 01101001 | 105 | β8 | 11010010 | 210 | β9 | 11001101 | 205 | β10 |
11110011 | 243 | β11 | 10001111 | 143 | β12 | 01110111 | 119 | β13 | 11101110 | 238 | β14 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
10101100 | 172 | β163 | 00110001 | 49 | β164 | 01100010 | 98 | β165 | 11000100 | 196 | β166 |
11100001 | 225 | β167 | 10101011 | 171 | β168 | 00111111 | 63 | β169 | 01111110 | 126 | β170 |
11111100 | 252 | β171 | 10010001 | 145 | β172 | 01001011 | 75 | β173 | 10010110 | 150 | β174 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
11010111 | 215 | β243 | 11000111 | 199 | β244 | 11100111 | 231 | β245 | 10100111 | 167 | β246 |
00100111 | 39 | β247 | 01001110 | 78 | β248 | 10011100 | 156 | β249 | 01010001 | 81 | β250 |
10100010 | 162 | β251 | 00101101 | 45 | β252 | 01011010 | 90 | β253 | 10110100 | 180 | β254 |
In this manner, we have designed our initial S-box (See Table 4). We have examined its cryptographic strength via some well-known performance evaluation criteria and found that it provides adequate security for transmitting sensitive information. To increase its security even further, let us proceed to step III.
24 | 41 | 1 | 180 | 2 | 140 | 113 | 52 | 32 | 4 | 190 | 42 | 125 | 102 | 90 | 60 |
8 | 128 | 205 | 45 | 253 | 16 | 250 | 86 | 162 | 109 | 17 | 115 | 244 | 81 | 217 | 64 |
238 | 48 | 101 | 57 | 156 | 59 | 148 | 78 | 35 | 105 | 122 | 98 | 100 | 39 | 210 | 182 |
104 | 167 | 50 | 239 | 46 | 231 | 38 | 13 | 243 | 221 | 213 | 97 | 72 | 132 | 199 | 143 |
248 | 164 | 83 | 215 | 119 | 55 | 214 | 223 | 219 | 181 | 177 | 200 | 3 | 135 | 224 | 235 |
111 | 216 | 6 | 54 | 80 | 99 | 108 | 241 | 12 | 73 | 30 | 94 | 27 | 76 | 149 | 185 |
96 | 232 | 87 | 129 | 192 | 195 | 67 | 116 | 240 | 166 | 233 | 188 | 254 | 23 | 69 | 58 |
7 | 187 | 133 | 51 | 203 | 63 | 212 | 29 | 68 | 31 | 153 | 186 | 62 | 74 | 93 | 79 |
124 | 157 | 28 | 173 | 154 | 141 | 77 | 14 | 92 | 146 | 171 | 91 | 229 | 137 | 144 | 85 |
5 | 155 | 193 | 10 | 82 | 36 | 20 | 168 | 174 | 230 | 18 | 121 | 21 | 40 | 71 | 249 |
227 | 130 | 196 | 9 | 252 | 61 | 176 | 134 | 201 | 160 | 178 | 43 | 88 | 117 | 107 | 44 |
22 | 208 | 11 | 150 | 33 | 19 | 66 | 236 | 114 | 246 | 112 | 202 | 118 | 152 | 34 | 194 |
138 | 251 | 197 | 169 | 237 | 26 | 145 | 158 | 56 | 179 | 95 | 15 | 255 | 161 | 159 | 106 |
234 | 120 | 220 | 198 | 110 | 222 | 147 | 183 | 142 | 218 | 123 | 191 | 228 | 131 | 139 | 151 |
245 | 165 | 89 | 163 | 209 | 189 | 206 | 65 | 47 | 225 | 175 | 103 | 53 | 247 | 207 | 75 |
211 | 136 | 226 | 25 | 170 | 242 | 70 | 184 | 126 | 84 | 172 | 49 | 37 | 127 | 204 | 0 |
Step III: Since an S-box is a square matrix of order 16. Therefore, the newly defined notion "matrix transformer" (see Section 2.2) can be used on initial S-box to enhance the security level. For this purpose, we tried several matrix transformers on our initial S-box by using MATLAB program and found that the matrix transformer displayed in Table 5 is the most suitable. The application of this matrix transformer on our initial S-box gives rise an S-box (See Table 6) with very high NL value 111. We call it our proposed S-box. An algorithm illustrating the process of using matrix transformers on the initial S-box is presented in Figure 5, while a flowchart can be found in Figure 6 to facilitate comprehension.
102 | 62 | 108 | 235 | 184 | 163 | 44 | 240 | 53 | 89 | 70 | 150 | 160 | 155 | 220 | 164 |
191 | 172 | 135 | 79 | 174 | 109 | 12 | 201 | 144 | 251 | 133 | 186 | 134 | 71 | 228 | 147 |
96 | 14 | 50 | 114 | 65 | 32 | 106 | 120 | 255 | 218 | 94 | 177 | 136 | 233 | 115 | 219 |
226 | 250 | 211 | 176 | 68 | 230 | 6 | 199 | 156 | 61 | 9 | 165 | 26 | 196 | 139 | 41 |
1 | 22 | 209 | 125 | 215 | 180 | 63 | 113 | 193 | 192 | 241 | 43 | 17 | 127 | 20 | 67 |
169 | 208 | 256 | 198 | 33 | 28 | 243 | 54 | 234 | 45 | 247 | 101 | 73 | 202 | 252 | 248 |
246 | 154 | 207 | 78 | 19 | 3 | 232 | 236 | 224 | 131 | 59 | 31 | 171 | 39 | 238 | 34 |
40 | 24 | 142 | 72 | 83 | 217 | 103 | 82 | 187 | 52 | 210 | 23 | 7 | 205 | 124 | 123 |
64 | 110 | 170 | 153 | 57 | 112 | 253 | 189 | 56 | 229 | 188 | 60 | 86 | 42 | 36 | 121 |
30 | 140 | 76 | 168 | 122 | 141 | 97 | 152 | 146 | 137 | 27 | 16 | 162 | 195 | 145 | 25 |
221 | 105 | 111 | 69 | 81 | 13 | 194 | 15 | 107 | 48 | 249 | 119 | 8 | 74 | 254 | 35 |
117 | 128 | 173 | 2 | 18 | 242 | 90 | 84 | 167 | 116 | 143 | 132 | 11 | 26 | 99 | 46 |
138 | 88 | 190 | 77 | 104 | 231 | 200 | 204 | 151 | 197 | 178 | 158 | 183 | 213 | 87 | 222 |
55 | 58 | 92 | 161 | 37 | 95 | 100 | 166 | 157 | 85 | 148 | 245 | 91 | 179 | 181 | 4 |
75 | 214 | 38 | 98 | 212 | 149 | 5 | 130 | 244 | 175 | 21 | 203 | 51 | 227 | 182 | 66 |
185 | 225 | 47 | 10 | 129 | 206 | 118 | 49 | 80 | 223 | 216 | 237 | 239 | 126 | 93 | 159 |
248 | 150 | 195 | 151 | 206 | 38 | 62 | 88 | 213 | 25 | 118 | 250 | 61 | 48 | 134 | 121 |
3 | 33 | 192 | 224 | 175 | 164 | 186 | 187 | 249 | 152 | 18 | 99 | 72 | 5 | 188 | 59 |
80 | 58 | 44 | 144 | 110 | 89 | 23 | 7 | 143 | 137 | 200 | 113 | 73 | 194 | 226 | 160 |
184 | 101 | 53 | 31 | 32 | 241 | 234 | 92 | 154 | 120 | 233 | 91 | 221 | 41 | 214 | 124 |
156 | 75 | 235 | 46 | 9 | 190 | 81 | 51 | 27 | 117 | 245 | 193 | 169 | 129 | 45 | 126 |
252 | 29 | 203 | 236 | 218 | 229 | 159 | 251 | 4 | 66 | 228 | 220 | 204 | 122 | 222 | 238 |
20 | 163 | 34 | 147 | 94 | 24 | 212 | 237 | 130 | 148 | 201 | 1 | 16 | 157 | 196 | 141 |
223 | 57 | 210 | 246 | 22 | 70 | 43 | 78 | 85 | 82 | 79 | 93 | 215 | 127 | 135 | 208 |
170 | 65 | 166 | 202 | 17 | 244 | 205 | 100 | 230 | 138 | 199 | 155 | 36 | 133 | 112 | 162 |
71 | 174 | 64 | 123 | 189 | 42 | 56 | 168 | 173 | 232 | 102 | 243 | 142 | 15 | 0 | 125 |
198 | 21 | 140 | 60 | 97 | 183 | 114 | 10 | 111 | 28 | 254 | 128 | 11 | 253 | 225 | 239 |
98 | 95 | 131 | 55 | 139 | 207 | 255 | 2 | 211 | 115 | 68 | 171 | 14 | 197 | 8 | 181 |
219 | 176 | 40 | 132 | 179 | 54 | 13 | 145 | 86 | 76 | 103 | 158 | 74 | 242 | 87 | 216 |
83 | 153 | 50 | 209 | 161 | 165 | 119 | 172 | 63 | 105 | 182 | 90 | 227 | 106 | 84 | 240 |
136 | 104 | 247 | 217 | 146 | 231 | 26 | 67 | 39 | 12 | 180 | 116 | 49 | 69 | 37 | 52 |
177 | 19 | 108 | 47 | 191 | 96 | 30 | 185 | 178 | 167 | 109 | 149 | 77 | 107 | 35 | 6 |
This section contains performance evaluation of the suggested S-box through different state of the art metrics such as the nonlinearity test, differential uniformity, bit independence criterion, strict avalanche criterion and linear approximation probability. We see that the outcome scores of our S-box obtained via these analyses are nearly equals to the ideal ones, demonstrating the effectiveness and capability of the proposed scheme. The analyses applied on our S-box are detailed below.
Nonlinearity is a key factor to determine the robustness of a substitution box. If an S-box maps input to output linearly, its resistance is very low [33]. A powerful S-box nonlinearly maps input to output. Any S-box with a higher nonlinearity value guarantees more security against cryptanalytic attacks. In the case of Boolean function of the form θ:Fn2⟶F2, The nonlinearity is calculated as
Nθ=2n−1−12[(h∈GF(2)nmax)|Sθ(h)| | (4.1) |
Note that, Sθ(h)=∑g∈GF(2)n(−1)θ(g)⊕g.h represents the Walsh spectrum of θ(g). Table 7 indicates the nonlinearity values of all Boolean functions of the proposed S-box. The average Non-linearity of our S-box is 110.75.
Boolean mapping | θ0 | θ1 | θ2 | θ3 | θ4 | θ5 | θ6 | θ7 | Mean |
NL score | 110 | 112 | 110 | 112 | 110 | 110 | 110 | 112 | 110 |
SAC is another effective tool to judge the security of an S-box. It was proposed by Webster and Tavares [34]. To meet this requirement, the input bit of any cryptosystem must change along with a 50% change in the output bits. The SAC performance of the S-box is determined by the dependency matrix. The perfect SAC score for the best cryptographic confusion is 0.5. Table 8 shows the dependency matrix of SAC values obtain by proposed S-box. The mean SAC value of proposed S-box is 0.5051, which differs slightly from the optimal value. Therefore, the suggested S-box fulfills the SAC criterion.
0.4844 | 0.5469 | 0.4688 | 0.5625 | 0.5312 | 0.5312 | 0.5156 | 0.4844 |
0.4531 | 0.4844 | 0.5469 | 0.5 | 0.5 | 0.4844 | 0.4844 | 0.5625 |
0.5312 | 0.4688 | 0.5312 | 0.5312 | 0.4375 | 0.4688 | 0.5156 | 0.5 |
0.4375 | 0.5 | 0.5469 | 0.5 | 0.5469 | 0.5312 | 0.4844 | 0.5156 |
0.4531 | 0.5625 | 0.5625 | 0.4688 | 0.4688 | 0.5156 | 0.4375 | 0.5312 |
0.5781 | 0.4844 | 0.5312 | 0.5469 | 0.5156 | 0.5 | 0.5156 | 0.5 |
0.5 | 0.4531 | 0.4531 | 0.4219 | 0.5156 | 0.5469 | 0.5312 | 0.4844 |
0.5 | 0.4844 | 0.5312 | 0.5312 | 0.5 | 0.5312 | 0.4375 | 0.5469 |
This test [34] is satisfied if the output bits operate independently, i.e., do not depend on each other. More specifically, no statistical dependencies or patterns should be present in the bits of the output vectors. It is intended to boost output bit autonomy for greater security. An S-box is said to be meet the BIC criterion if it satisfies SAC and possess nonlinearity score for all Boolean mappings. The Tables 9 and 10 depict the dependency matrices for BIC-nonlinearity and BIC-SAC respectively. The results show that the proposed S-box conforms to the required BIC standards.
- | 110 | 110 | 112 | 112 | 110 | 112 | 110 |
110 | - | 108 | 110 | 112 | 112 | 108 | 110 |
110 | 108 | - | 110 | 112 | 110 | 110 | 112 |
112 | 110 | 110 | - | 110 | 110 | 110 | 112 |
112 | 112 | 112 | 110 | - | 110 | 110 | 110 |
110 | 112 | 110 | 110 | 110 | - | 112 | 110 |
112 | 108 | 110 | 110 | 110 | 112 | - | 112 |
110 | 110 | 112 | 112 | 110 | 110 | 112 | - |
- | 0.4805 | 0.5098 | 0.4941 | 0.4902 | 0.498 | 0.5215 | 0.4824 |
0.4805 | - | 0.5195 | 0.5176 | 0.4922 | 0.4922 | 0.4766 | 0.4902 |
0.5098 | 0.5195 | - | 0.5 | 0.4902 | 0.5137 | 0.4922 | 0.498 |
0.4941 | 0.5176 | 0.5 | - | 0.4961 | 0.5117 | 0.5273 | 0.4902 |
0.4902 | 0.4922 | 0.4902 | 0.4961 | - | 0.4922 | 0.5293 | 0.5195 |
0.498 | 0.4922 | 0.5137 | 0.5117 | 0.4922 | - | 0.4707 | 0.4863 |
0.5215 | 0.4766 | 0.4922 | 0.5273 | 0.5293 | 0.4707 | - | 0.4883 |
0.4824 | 0.4902 | 0.498 | 0.4902 | 0.5195 | 0.4863 | 0.4883 | - |
Modern block ciphers are designed to create as much complexity among the bits as possible to protect the privacy of the information and to offer protection against various decryption techniques employed by the cryptanalysts. It is accomplished by S-box. The lower the value of LP, the better the capability of S-box to withstand linear attacks. The LP value of an S-box can be calculated by using the following equation [35];
LP=(Γw,Γw'≠0max|#{w∈K:w.Γw=S(w).Γw'}2n−12| | (4.2) |
where K={0,1,...,2n} and Γw and Γw' are the input mask and output mask respectively . The designed S-box has an LP score of 0.0781.
The resistance of S-box to differential cryptanalysis is investigated by DU [35]. To determine DU, a input differential Δσi is uniquely linked to an output differential Δρi, for all i. For a given S-box, its value can be calculated by using the following equation:
DU=(Δσi≠0,Δρmaxi{σi∈Γ:S(σi)⨁S(σi+Δσi)=Δρi} | (4.3) |
It is necessary to develop an S-box with smaller DU values in order to withstand differential cryptanalysis attacks. The maximum DU score of the proposed S-box is 6 (See Table 11), indicating its ability to counter differential attacks.
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 |
4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 6 | 4 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 6 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | - |
According to the performance study and comparative analysis, our S-box has better cryptographic properties than many recently designed S-boxes based on optimization, chaos and algebraic techniques. The comparison present in Table 12 demonstrates the suggested technique of designing S-boxes outperforms many of the available approaches. Here are our findings:
S-box | Nonlinearity Min Max Average |
SAC | BIC-SAC | BIC-NL | DU | LP | ||
Suggested S-box | 110 | 112 | 110.75 | 0.5051 | 0.4989 | 110.55 | 6 | 0.0781 |
AES [36] | 112 | 112 | 112 | 0.5058 | 0.5046 | 112 | 4 | 0.0625 |
Reference [37] | 106 | 108 | 106.25 | 0.5112 | 0.4975 | 103.93 | 12 | 0.1484 |
Reference [38] | 106 | 110 | 106.5 | 0.5010 | 0.4987 | 103.93 | 10 | 0.125 |
Reference [39] | 106 | 108 | 107 | 0.4949 | 0.5019 | 102.29 | 12 | 0.141 |
Reference [40] | 106 | 110 | 108.5 | 0.4995 | 0.5011 | 103.85 | 10 | 0.109 |
Reference [41] | 108 | 110 | 109.75 | 0.5042 | 0.4987 | 110.6 | 6 | 0.0859 |
Reference [42] | 102 | 110 | 106.5 | 0.4943 | 0.5019 | 103.35 | 12 | 0.1468 |
Reference [43] | 104 | 108 | 105.5 | 0.5065 | 0.5031 | 103.57 | 10 | 0.1328 |
Reference [44] | 104 | 110 | 107 | 0.4993 | 0.5050 | 103.29 | 10 | 0.1328 |
1. The S-box must have a high nonlinear value to resist linear attacks. According to Table 12, the average nonlinearity of our S-box is almost equal to AES, outperforming all other S-boxes show in Table 12. Therefore, there is considerable confusion, which makes the proposed method resistant to all the existing linear cryptanalysis.
2. The prime goal of every S-box designer is to achieve a SAC score close to the optimal value (0.50). From Table 12 demonstrates that the suggested S-box satisfies the requirements of strict avalanche criterion.
3. The reading of BIC-NL and BIC-SAC obtained from the prosed S-box are very encouraging are better than those of most of the S-boxes in Table 12
4. A potent S-box has a smaller DU value. As seen in Table 12, the DU score of the suggested S-box is less than the S-boxes developed in [37,38,39,40,41,42,43,44].
5. A smaller LP score makes an S-box more resistant to linear cryptanalysis. The LP score of our S-box is 0.0781, which is slightly higher than AES but lower than the LP values of all S-boxes in Table 12.
The evaluating the suitability of an S-box to be employed in an encryption process using the majority logic criteria (MLC) is a useful approach [45]. Randomness in the encoded picture is assessed using these five analyses energy, entropy, homogeneity, contrast and correlation.
Homogeneity and energy are utilized to identify the features of the encoded picture. The correlation test assesses the resemblance level between the host and encrypted picture. The lower correlation value implies more distortion caused by encryption. Through contrast, the decrease of brightness of the plaintext image is assessed. The greater the contrast value, the more efficient the encryption procedure. The process of encryption distorts the plaintext, and statistical parameters characterize the resiliency of S-box. The S-box that is formed is utilized to encrypt digital photos. To conduct MLC four 256 × 256 JPEG photos of Cameraman, Pepper, Lena and Baboon are selected. Two steps of substitution using our S-box are performed in the encrypting process. Encryption is accomplished through two steps of S-box substitution. During the 1st phase, the substitution is performed in a forward direction (from the start pixel to the end pixel) and subsequently in an opposite way. All simulations were conducted using the MATLAB programming. The original and encrypted photos are shown in Figure 7. The distorted pictures differ significantly from their corresponding undistorted versions. The level of visual distortion is quite large, since the graphics lack a pattern that promotes security breaches from the host picture. Table 13 shows the findings of all MLC testing performed. Table 14 presents the calculated correlation coefficients for pictures.
Image | Correlation | Entropy | Energy | Homogeneity | Contrast |
Cameraman Host | 0.9227 | 7.0097 | 0.1805 | 0.8952 | 0.5871 |
Cameraman-Enc | 0.0394 | 7.9972 | 0.0149 | 0.3999 | 10.0509 |
Pepper Host | 0.9312 | 7.5326 | 0.1096 | 0.8880 | 0.3849 |
Pepper-Enc | 0.0021 | 7.9972 | 0.0156 | 0.3902 | 10.4802 |
Baboon Host | 0.7983 | 7.2649 | 0.0943 | 0.7820 | 0.6326 |
Baboon-Enc | 0.0071 | 7.9975 | 0.0156 | 0.3945 | 10.3994 |
Lena Host | 0.9024 | 7.4439 | 0.1127 | 0.8622 | 0.4482 |
Lena-Enc | − 0.0379 | 7.9976 | 0.0157 | 0.3822 | 10.8896 |
Image | Cameraman | Pepper | Baboon | Lena | |
Vertical | Plain Image | 0.9745 | 0.9137 | 0.9090 | 0.9321 |
Distorted Image | 0.0310 | − 0.0392 | − 0.0128 | − 0.0117 | |
Horizontal | Plain Image | 0.9610 | 0.9204 | 0.8727 | 0.883 |
Distorted Image | − 0.0026 | − 0.0015 | 0.0039 | − 0.0021 |
The results suggest that the created substitution box is suitable for encryption purposes and are good enough to be used in the systems designed to ensure the reliability and security of sensitive data.
The experimental assessments of the proposed image encryption technique are discussed in this section. The 256×256 pixel grayscale photos of Cameraman, Pepper and Baboon are picked for the experiment. Table 15 contains a variety of image quality measurements that have been suggested for use with two rounds of encryption using S-boxes. These methods have been thoroughly discussed. The findings indicate that the recommended S-box is robust enough to survive various attacks.
Test | Cameraman-Enc | Pepper-Enc | Baboon-Enc | Lena-Enc |
MSE | 9212.16 | 8656.41 | 7854.44 | 8414.71 |
MSE [6] | 9079.09 | 8190.01 | 8011.23 | 8239.51 |
MSE [15] | 9189.41 | 8612.09 | 7599.03 | 7930.39 |
MSE [17] | 9187.38 | 8423.61 | 7865.21 | 8274.13 |
PSNR | 8.4723 | 8.8563 | 9.8912 | 8.9912 |
PSNR [6] | 8.1129 | 8.9710 | 8.5539 | 9.1902 |
PSNR [15] | 8.2897 | 8.7091 | 8.1331 | 8.9500 |
PSNR [17] | 8.2891 | 8.3353 | 8.9361 | 8.0032 |
SSIM1 | 0.0009 | 0.0012 | 0.0010 | 0.0011 |
SSIM1 [6] | 0.0013 | 0.0008 | 0.0011 | 0.0012 |
SSIM1 [15] | 0.0010 | 0.0012 | 0.0008 | 0.0014 |
SSIM1 [17] | 0.0009 | 0.0015 | 0.0012 | 0.0013 |
NCC | 0.8633 | 0.8710 | 0.9121 | 0.8803 |
NCC [6] | 0.8537 | 0.8675 | 0.8912 | 0.9016 |
NCC [15] | 0.8733 | 0.8712 | 0.8543 | 0.8461 |
NCC [17] | 0.8640 | 0.87134 | 0.9001 | 0.8692 |
AD | −7.4523 | −4.9812 | −2.3419 | −5.3881 |
AD [6] | −3,4511 | −5.6634 | −1.4529 | −2.3319 |
AD [15] | −6,7819 | −3.8873 | −2.8827 | −4.1198 |
AD [17] | −3.4429 | −4.9821 | −2.3872 | −7.6594 |
SC | 0.8496 | 0.8345 | 0.8456 | 0.8247 |
SC [6] | 0.8455 | 0.8451 | 0.8401 | 0.8342 |
SC [15] | 0.8341 | 0.8489 | 0.8465 | 0.8231 |
SC [17] | 0.8436 | 0.8111 | 0.8265 | 0.8490 |
MD | 240 | 238 | 212 | 234 |
MD [6] | 211 | 231 | 233 | 241 |
MD [15] | 223 | 227 | 227 | 228 |
MD [17] | 234 | 238 | 221 | 219 |
NAE | 0.6358 | 0.6273 | 0.6147 | 0.6384 |
NAE [6] | 0.6455 | 0.5932 | 0.5813 | 0.6459 |
NAE [15] | 0.6040 | 0.6193 | 0.6388 | 0.6026 |
NAE [17] | 0.6219 | 0.6243 | 0.6012 | 0.5856 |
RMSE | 94.6682 | 91.7245 | 84.9561 | 87.9349 |
RMSE [6] | 90.6638 | 92.3402 | 88.3476 | 86.7938 |
RMSE [15] | 93,4428 | 89.7690 | 91.2398 | 87.3947 |
RMSE [17] | 90.4582 | 85.1109 | 84.8934 | 88.1831 |
UQI | 0.0218 | 0.0332 | 0.0314 | 0.0338 |
UQI [6] | 0.0127 | 0.0412 | 0.0279 | 0.0178 |
UQI [15] | 0.0347 | 0.0456 | 0.0127 | 0.0391 |
UQI [17] | 0.0234 | 0.0401 | 0.0298 | 0.0281 |
MI | −1.0292 | −1.0187 | −1.0184 | −1.0281 |
MI [6] | −1.0195 | −1.0490 | −1.0328 | −1.0402 |
MI [15] | −1.0371 | −1.0197 | −1.0294 | −1.0406 |
MI [17] | −1.341 | −1.0198 | −1.0384 | −1.0327 |
During encryption MSE analysis assesses the unpredictability of the encrypted picture [46]. This technique computes the squared difference between the original and distorted picture. It can be computed as follows:
MSE=1U×V∑Uy2=1∑Vy1=1(O(y1,y2)−E(y1,y2))2 | (6.1) |
where U and V represent the dimensions of original O(y1,y2) and distorted E(y1,y2) pictures respectively. For effective encryption methods, the MSE rating must be as high as conceivable [46].
The PSNR test [38] is an ideal criterion for assessing the quality of picture encryption techniques. It estimates how well the original picture matches the ciphertext. PSNR value is calculated using the following formula;
PSNR=10log10V2√MSE | (6.2) |
where V is the amount of variance that was at its highest in the original picture data. It is necessary to have a higher value of PSNR in order to get a superior encoded picture [47].
To determine the average and maximum dissimilarities between the unencrypted O and encrypted E pictures, researchers used the AD and MD test [47]. AD and MD values are determined using the following formulas;
AD=∑Ry2=1∑Sy1=1[O(y1,y2)−E(y1,y2)]R×S | (6.3) |
MD=max|O(y1,y2)−E(y1,y2)| | (6.4) |
MI measures how much information can be retrieved about the original picture from a distorted version of it. Let us denote the joint probability function of O and E by ρ(y1,y2), then the value of MI can be determined by using the formula below;
MI=∑y1∈O∑y2∈Eρ(y1,y2)log2ρ(y1,y2)ρ(y1)ρ(y2) | (6.5) |
The MI value must always be kept to a minimum in a decent encryption system [48].
As stated in reference [49], the UQI method partitions the evaluation of image distortion into three components: luminance, structural comparisons and contrast. The UQI metric for a pair of images O and E can be expressed as follows;
UQ(O,E)=4ρoρEρoE(ρ20−ρ2E)(φ20−φ2E) | (6.6) |
where ρo, ρE represent the mean values of the original and distorted images, respectively, and φo, φE represent the standard deviation of the original and distorted images, respectively.
SSIM is an enhanced version of the UQI designed to assess the similarity between two images. In particular, SSIM evaluates the fidelity of one of the images by assuming that the other image is free from errors. The computation of the SSIM score involves analyzing a pair of windows (R,S) of the image using the following formula:
SSIM(R,S)=(νRνS+a1)(2φRφS+a2)(ν2R+ν2R+a1)(φ2R+φ2R+a2) | (6.7) |
where φR and φS are the variances of R and S and νR and νS are the average scores of R and S respectively. The range of the SSIM score lies between -1 to 1, where a score of 1 indicates that the images are identical. A score close to 0 indicates a strong encryption scheme [48].
As stated in citation [49], the correlation function provides a means of measuring the proximity of two digital images. The NCC method is a well-established technique for assessing the similarity between two images. Its calculation is based on the following formula:
NCC=∑Uy2=1∑Vy1=1(O(y1,y2)×E(y1,y2)∑Uy2=1∑Vy1=1|O(y1,y2)|2) | (6.8) |
NAE [49] can be used to assess the efficiency of an image encryption process by comparing the pixel values of the original image with those of the encrypted (ciphered) image. To calculate the NAE between the plain and ciphered image, the formula is:
NAE=∑Uy2=1∑Vy1=1|O(y1,y2)−E(y1,y2)|∑Uy2=1∑Vy1=1|O(y1,y2)| | (6.9) |
The assessment of an image encryption algorithm's effectiveness can be facilitated by utilizing RMSE as a performance metric. The calculation of RMSE involves determining the square root of the average of all the squared errors [49]. Its frequent use and flexibility make it a versatile and valuable error metric for numerical forecasting. The mathematical expression for RMSE is indicated below;
RMSE=√∑Uy2=1∑Vy1=1|O(y1,y2)−E(y1,y2)|2U×V | (6.10) |
SC is a correlation-based measure that quantifies the similarity between two images. The following mathematical equation is used to compute its score;
SC=∑Uy2=1∑Vy1=1|O(y1,y2)|2∑Uy2=1∑Vy1=1|E(y1,y2)|2 | (6.11) |
A robust cryptosystem is extremely sensitive to modifications in one bit of the plaintext. Through UACI, NPCR and BACI testing, the sensitivity of the system is assessed.
UACI indicates the unified mean intensity change between original and encrypted image while NPCR calculates the number of pixels change rate of the encrypted image if a single pixel is altered in the original image. In BACI analysis, the image difference Δ=abs(E1−E2) is partitioned into blocks of pixels and arranged in a 2 × 2 matrix. This involves dividing the image into smaller, non-overlapping regions, or "blocks", to facilitate the comparison of pixel values before and after the intervention.
The following formulae are used to compute the values of UACI, NPCR and BACI:
UACI=1JK∑j,kE1(j,k)−E2(j,k)255×100% | (7.1) |
NPCR=∑jkD(j,k)JK×100% | (7.2) |
BACI=1(J−1)(K−1)∑(J−1)(K−1)i=1Zi255×100% | (7.3) |
where E1(j,k) and E2(j,k) denote the grayscale values of pixels obtained (j,k) th position and D(j,k)={0 if E1(j,k) and E2(j,k) are equal 1 otherwise and Zi=16(|a1−a2|+|a1−a3|+|a1−a4|+|a2−a3|+|a2−a4|+|a3−a4|) and Δi=[a1a2a3a4].
Table 16 depicts the findings of the differential analysis for NPCR, UACI, and BACI, confirming the excellent performance of encryption effect provided by the designed S-box.
Image | NPCR | UACI | BACI |
Cameraman | 99.63% | 33.12% | 24.60% |
Pepper | 99.81% | 33.21% | 26.38% |
Baboon | 99.76% | 32.86% | 24.25% |
Lena | 99.79% | 33.16% | 23.09% |
Summing up, the present work has discussed and examined the development of modular group coset graphs over a finite field of order 1024 and a matrix transformer for application in S-box construction. An initial S-box is formed through coset graphs and after that the application of a matrix transformer on it enhances its working efficiency significantly, resulting in a robust S-box. Comparison of proposed method with other state-of-the-art S-box construction algorithms shows that the proposed mechanism outperforms other algorithms in terms of mean nonlinear score, LP, SAC, BIC and DU scores. In addition, the performance of the designed S-box when applied to encrypt certain plaintext graphics has been determined to be extraordinary using a variety of assessment tools.
As our experience with applying matrix transformer to coset graph S-box to improve its resilience has been promising, we plan to research novel ways for designing S-boxes combining matrix transformers and chaotic systems. Moreover, we intend to evaluate the application of S-box to cloud encryption.
This work was supported by the Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia (Grant No. 3011).
The authors declare there is no conflict of interest.
[1] |
Acemoglu D, Johnson S, Robinson JA (2001) The colonial origins of comparative development: An empirical investigation. Am Econ Rev 91: 1369–1401. https://doi.org/10.1257/aer.91.5.1369 doi: 10.1257/aer.91.5.1369
![]() |
[2] |
Aggarwal P, Singh AK (2019) CSR and sustainability reporting practices in India: An in-depth content analysis of top-listed companies. Soc Responsib J 15: 1033–1053. https://doi.org/10.1108/SRJ-03-2018-0078 doi: 10.1108/SRJ-03-2018-0078
![]() |
[3] |
Ahammed Arif, Saha Sabuj (2018) Firm-specific Financial Determinants of Non-Performing Loan in the Banking Sector of Developing Countries: Evidence from the Listed Commercial Banks in Bangladesh. J Econ Bus 1: 555–563. https://doi.org/10.31014/aior.1992.01.04.49 doi: 10.31014/aior.1992.01.04.49
![]() |
[4] |
AIS D (2018) Firm-specific Financial Determinants of Non-Performing Loan in the Banking Sector of Developing Countries: Evidence from the Listed Commercial Banks in Bangladesh. J Econ Bus 1: 555–563. https://doi.org/10.31014/aior.1992.01.04.49 doi: 10.31014/aior.1992.01.04.49
![]() |
[5] |
Al Lawati H, Hussainey K (2022) Does sustainable development goals disclosure affect corporate financial performance? Sustainability 14: 7815. https://doi.org/10.3390/su14137815 doi: 10.3390/su14137815
![]() |
[6] |
Al Lawati H, Hussainey K, Sagitova R (2021) Disclosure quality vis-à-vis disclosure quantity: does audit committee matter in Omani financial institutions? Rev Quant Financ Account 57: 557–594. https://doi.org/10.1007/s11156-020-00955-0 doi: 10.1007/s11156-020-00955-0
![]() |
[7] |
Albertini E (2013) Does environmental management improve financial performance? A meta-analytical review. Organ Environ 26: 431–457. https://doi.org/10.1177/1086026613510301 doi: 10.1177/1086026613510301
![]() |
[8] | Ali MH, Hossain R, Mazumder R, et al. (2023) Does the extent of ownership by different shareholders enhance firm financial performance? Empirical evidence from an emerging economy. J Bus Econ Financ 12: 163–174. |
[9] | Alsaeed, K. (2006). The association between firm‐specific characteristics and disclosure: The case of Saudi Arabia. Manag Audit J 21: 476–496. https://doi.org/10.1108/02686900610667256 |
[10] |
Alshehhi A, Nobanee H, Khare N (2018) The impact of sustainability practices on corporate financial performance: Literature trends and future research potential. Sustainability 10: 494. https://doi.org/10.3390/su10020494 doi: 10.3390/su10020494
![]() |
[11] | Arayssi M, Jizi M, Tabaja HH (2020) The impact of board composition on the level of ESG disclosures in GCC countries. Sustainability Accounting. Manage Policy J 11: 137–161. https://doi.org/10.1108/SAMPJ-05-2018-0136 |
[12] | Arbolí-Pardo P, Moya-Rengifo M (2023) Assessing regional sustainability performance towards the SDGs: A multi-method approach. J Clean Prod 399: 137104. |
[13] |
Arellano M, Bover O (1995) Another look at the instrumental variable estimation of error-components models. J Econometrics 68: 29–51. https://doi.org/10.1016/0304-4076(94)01642-D doi: 10.1016/0304-4076(94)01642-D
![]() |
[14] |
Bagur‐Femenias L, Llach J, del Mar Alonso‐Almeida M (2013) Is the adoption of environmental practices a strategical decision for small service companies? An empirical approach. Manage Decis 51: 41–62. https://doi.org/10.1108/00251741311291300 doi: 10.1108/00251741311291300
![]() |
[15] |
Bansal P, Gao J (2006) Building the future by looking to the past: Examining research published on organizations and environment. Organ Environ 19: 458–478. https://doi.org/10.1177/1086026606294957 doi: 10.1177/1086026606294957
![]() |
[16] |
Barquet K, Järnberg L, Alva IL, et al. (2021) Exploring mechanisms for systemic thinking in decision-making through three country applications of SDG Synergies. Sustain Sci 1–16. https://doi.org/10.1007/s11625-021-01045-3 doi: 10.1007/s11625-021-01045-3
![]() |
[17] | Belal AR (2016) Corporate social responsibility reporting in developing countries: The case of Bangladesh. Routledge. https://doi.org/10.4324/9781315574332 |
[18] |
Betti G, Consolandi C, Eccles RG (2018) The relationship between investor materiality and the sustainable development goals: A methodological framework. Sustainability 10: 2248. https://doi.org/10.3390/su10072248 doi: 10.3390/su10072248
![]() |
[19] |
Bhandari KR, Ranta M, Salo J (2022) The resource‐based view, stakeholder capitalism, ESG, and sustainable competitive advantage: The firm's embeddedness into ecology, society, and governance. Bus Strateg Environ 31: 1525–1537. https://doi.org/10.1002/bse.2967 doi: 10.1002/bse.2967
![]() |
[20] | Bhattacherjee R, Botchway KO, Hu X, et al. (2022) Evaluating CO2 Storage Potential of Offshore Reservoirs and Saline Formations in Central Gulf of Mexico by Employing Data-driven Models with SAS Viya. arXiv preprin. |
[21] |
Bhattacherjee R, Botchway K, Pashin JC, et al. (2023) Machine learning-based prediction of CO2 fugacity coefficients: Application to estimation of CO2 solubility in aqueous brines as a function of pressure, temperature, and salinity. Int J Greenh Gas Con 128: 103971. https://doi.org/10.1016/j.ijggc.2023.103971 doi: 10.1016/j.ijggc.2023.103971
![]() |
[22] |
Bhuiyan J, Mazumder R, Afrose S, et al. (2024) Industry-4, Big Data, and Blockchain Research Prospects in Supply Chain Domain: A Bibliometric Review. Available at SSRN. https://doi.org/10.2139/ssrn.4685775 doi: 10.2139/ssrn.4685775
![]() |
[23] |
Bocken NM, Geradts TH (2020) Barriers and drivers to sustainable business model innovation: Organization design and dynamic capabilities. Long Range Plann 102025. https://doi.org/10.1016/j.lrp.2019.102025 doi: 10.1016/j.lrp.2019.102025
![]() |
[24] |
Buallay A (2020) Sustainability reporting and firm's performance: Comparative study between manufacturing and banking sectors. Int J Product Perfor 69: 431–445. https://doi.org/10.1108/IJPPM-10-2018-0371 doi: 10.1108/IJPPM-10-2018-0371
![]() |
[25] |
Buallay A, Fadel SM, Al-Ajmi JY, et al. (2020) Sustainability reporting and performance of MENA banks: is there a trade-off? Meas Bus Excell 24: 197–221. https://doi.org/10.1108/MBE-09-2018-0078 doi: 10.1108/MBE-09-2018-0078
![]() |
[26] |
Busse C, Schleper MC, Weilenmann J, et al. (2021) Extending the supply chain visibility boundary: Utilizing stakeholders for identifying supply chain sustainability risks. Int J Phys Distr Log Manag 51: 18–40. https://doi.org/10.1108/IJPDLM-02-2015-0043 doi: 10.1108/IJPDLM-02-2015-0043
![]() |
[27] |
Calabrese A, Costa R, Gastaldi M, et al. (2021) Implications for Sustainable Development Goals: A framework to assess company disclosure in sustainability reporting. J Clean Prod 319: 128624. https://doi.org/10.1016/j.jclepro.2021.128624 doi: 10.1016/j.jclepro.2021.128624
![]() |
[28] |
Chabowski BR, Mena JA, Gonzalez-Padron TL (2011) The structure of sustainability research in marketing, 1958–2008: A basis for future research opportunities. J Acad Market Sci 39: 55–70. https://doi.org/10.1007/s11747-010-0212-7 doi: 10.1007/s11747-010-0212-7
![]() |
[29] |
Costanza R, Daly L, Fioramonti L, et al. (2016) Modelling and measuring sustainable wellbeing in connection with the UN Sustainable Development Goals. Ecol Econ 130: 350–355. https://doi.org/10.1016/j.ecolecon.2016.07.009 doi: 10.1016/j.ecolecon.2016.07.009
![]() |
[30] |
Consolandi C, Phadke H, Hawley J, et al. (2020) Material ESG outcomes and SDG externalities: Evaluating the health care sector's contribution to the SDGs. Organ Environ 33: 511–533. https://doi.org/10.1177/1086026619899795 doi: 10.1177/1086026619899795
![]() |
[31] |
Dalampira ES, Nastis SA (2020) Mapping sustainable development goals: A network analysis framework. Sustain Dev 28: 46–55. https://doi.org/10.1002/sd.1964 doi: 10.1002/sd.1964
![]() |
[32] |
Di Tommaso C, Thornton J (2020) Do ESG scores effect bank risk taking and value? Evidence from European banks. Corp Soc Responsib Environ Manag 27: 2286–2298. https://doi.org/10.1002/csr.1964 doi: 10.1002/csr.1964
![]() |
[33] |
Durnev A, Kim EH (2005) To steal or not to steal: Firm attributes, legal environment, and valuation. J Financ 60: 1461–1493. https://doi.org/10.1111/j.1540-6261.2005.00767.x doi: 10.1111/j.1540-6261.2005.00767.x
![]() |
[34] | Eccles RG, Serafeim G (2013) The performance frontier. Harvard Bus Rev 91: 50–60. |
[35] | Eccles RG, Serafeim G (2017) The green swan: The coming surge of sustainability investing. Harvard Bus Rev 95: 102–114. |
[36] |
Eisenmenger N, Pichler M, Krenmayr N, et al. (2020) The Sustainable Development Goals prioritize economic growth over sustainable resource use: a critical reflection on the SDGs from a socio-ecological perspective. Sustain Sci 15: 1101–1110. https://doi.org/10.1007/s11625-020-00813-x doi: 10.1007/s11625-020-00813-x
![]() |
[37] |
Eizenberg E, Jabareen Y (2017) Social sustainability: A new conceptual framework. Sustainability 9: 68. https://doi.org/10.3390/su9010068 doi: 10.3390/su9010068
![]() |
[38] |
Emma GM, Jennifer MF (2021) Is SDG reporting substantial or symbolic? An examination of controversial and environmentally sensitive industries. J Clean Prod 298: 126781. https://doi.org/10.1016/j.jclepro.2021.126781 doi: 10.1016/j.jclepro.2021.126781
![]() |
[39] |
Endrikat J, Guenther E, Hoppe H (2014) Making sense of conflicting empirical findings: A meta-analytic review of the relationship between corporate environmental and financial performance. Eur Manag J 32: 735–751. https://doi.org/10.1016/j.emj.2013.12.004 doi: 10.1016/j.emj.2013.12.004
![]() |
[40] |
Erin OA, Bamigboye OA (2021) Evaluation and analysis of SDG reporting: Evidence from Africa. J Account Organ Change 18: 369–396. https://doi.org/10.1108/JAOC-02-2020-0025 doi: 10.1108/JAOC-02-2020-0025
![]() |
[41] |
Erin OA, Bamigboye OA, Oyewo B (2022) Sustainable development goals (SDG) reporting: an analysis of disclosure. J Account Emerg Econ 12: 761–789. https://doi.org/10.1108/JAEE-02-2020-0037 doi: 10.1108/JAEE-02-2020-0037
![]() |
[42] |
Galeazzo A, Miandar T, Carraro M (2023) SDGs in corporate responsibility reporting: a longitudinal investigation of institutional determinants and financial performance. J Manag Gov 1–24. https://doi.org/10.1007/s10997-023-09671-y doi: 10.1007/s10997-023-09671-y
![]() |
[43] |
Garcia AS, Mendes-Da-Silva W, Orsato RJ (2017) Sensitive industries produce better ESG performance: Evidence from emerging markets. J Clean Prod 150: 135–147. https://doi.org/10.1016/j.jclepro.2017.02.180 doi: 10.1016/j.jclepro.2017.02.180
![]() |
[44] |
Garcia-Castro R, Ariño MA, Canela MA (2010) Does social performance really lead to financial performance? Accounting for endogeneity. J Bus Econ 92: 107–126. https://doi.org/10.1007/s10551-009-0143-8 doi: 10.1007/s10551-009-0143-8
![]() |
[45] |
Gatimbu KK, Ogada MJ, Budambula N, et al. (2018) Environmental sustainability and financial performance of the small‐scale tea processors in Kenya. Bus Strateg Environ 27: 1765–1771. https://doi.org/10.1002/bse.2243 doi: 10.1002/bse.2243
![]() |
[46] |
Giannarakis G (2014) The determinants influencing the extent of CSR disclosure. Int J Law Manage 56: 393–416. https://doi.org/10.1108/IJLMA-05-2013-0021 doi: 10.1108/IJLMA-05-2013-0021
![]() |
[47] |
Glass LM, Newig J (2019) Governance for achieving the Sustainable Development Goals: How important are participation, policy coherence, reflexivity, adaptation and democratic institutions? Earth Syst Gov 2: 100031. https://doi.org/10.1016/j.esg.2019.100031 doi: 10.1016/j.esg.2019.100031
![]() |
[48] | Goldsmith S, Samson D (2005) Sustainable development and business success: Reaching beyond the rhetoric to superior performance. |
[49] |
Granly BM, Welo T (2014) EMS and sustainability: experiences with ISO 14001 and Eco-Lighthouse in Norwegian metal processing SMEs. J Clean Prod 64: 194–204. https://doi.org/10.1016/j.jclepro.2013.08.007 doi: 10.1016/j.jclepro.2013.08.007
![]() |
[50] |
Grewatsch S, Kleindienst I (2017) When does it pay to be good? Moderators and mediators in the corporate sustainability–corporate financial performance relationship: A critical review. J Bus Econ Ethics 145: 383–416. https://doi.org/10.1007/s10551-015-2852-5 doi: 10.1007/s10551-015-2852-5
![]() |
[51] |
Griffin JJ, Mahon JF (1997) The corporate social performance and corporate financial performance debate: Twenty-five years of incomparable research. Bus Soc 36: 5–31. https://doi.org/10.1177/000765039703600102 doi: 10.1177/000765039703600102
![]() |
[52] | Gujarati DN, Porter DC (2009) Basic Econometrics, International ed. McGraw-Hills, New York. |
[53] | Johnson C (2020) The measurement of environmental, social and governance (ESG) and sustainable investment: Developing a sustainable new world for financial services. J Secur Oper C 12: 336–356. |
[54] | Hahn T, Pinkse J, Preuss L, et al. (2023) Linking sustainability performance with SDG achievement: An empirical analysis of global public companies. Bus Soc 62: 329–362. |
[55] |
Hamad S, Draz MU, Lai FW (2020) The impact of corporate governance and sustainability reporting on integrated reporting: A conceptual framework. Sage Open 10: 2158244020927431. https://doi.org/10.1177/2158244020927431 doi: 10.1177/2158244020927431
![]() |
[56] |
Holden E, Linnerud K, Banister D (2017) The imperatives of sustainable development. Sustain Dev 25: 213–226. https://doi.org/10.1002/sd.1647 doi: 10.1002/sd.1647
![]() |
[57] |
Horváthová E (2010) Does environmental performance affect financial performance? A meta-analysis. Ecol Econ 70: 52–59. https://doi.org/10.1016/j.ecolecon.2010.04.004 doi: 10.1016/j.ecolecon.2010.04.004
![]() |
[58] |
Hu J, Wu H, Ying SX (2022) Environmental regulation, market forces, and corporate environmental responsibility: Evidence from the implementation of cleaner production standards in China. J Bus Econ Res 150: 606–622. https://doi.org/10.1016/j.jbusres.2022.06.049 doi: 10.1016/j.jbusres.2022.06.049
![]() |
[59] | Ioannou I, Serafeim G (2017) The consequences of mandatory corporate sustainability reporting: Evidence from four countries. Harvard Bus School Working Pap 11–100. |
[60] |
Jan A, Mata MN, Albinsson PA, et al. (2021) Alignment of islamic banking sustainability indicators with sustainable development goals: Policy recommendations for addressing the covid-19 pandemic. Sustainability 13: 2607. https://doi.org/10.3390/su13052607 doi: 10.3390/su13052607
![]() |
[61] | Johnson C (2020) The measurement of environmental, social and governance (ESG) and sustainable investment: Developing a sustainable new world for financial services. J Secur Oper C 12: 336–356. |
[62] |
Kaufmann D, Kraay A, Mastruzzi M (2011) The worldwide governance indicators: Methodology and analytical issues1. Hague J Rule Law 3: 220–246. https://doi.org/10.1017/S1876404511200046 doi: 10.1017/S1876404511200046
![]() |
[63] |
Khaled R, Ali H, Mohamed EK (2021) The Sustainable Development Goals and corporate sustainability performance: Mapping, extent and determinants. J Clean Prod 311: 127599. https://doi.org/10.1016/j.jclepro.2021.127599 doi: 10.1016/j.jclepro.2021.127599
![]() |
[64] |
Khaled R, Ali H, Mohamed EK (2021) The Sustainable Development Goals and corporate sustainability performance: Mapping, extent and determinants. J Clean Prod 311: 127599. https://doi.org/10.1016/j.jclepro.2021.127599 doi: 10.1016/j.jclepro.2021.127599
![]() |
[65] |
Khan PA, Johl SK, Akhtar S (2022) Vinculum of sustainable development goal practices and firms' financial performance: A moderation role of green innovation. J Risk Financ Manag 15: 96. https://doi.org/10.3390/jrfm15030096 doi: 10.3390/jrfm15030096
![]() |
[66] |
Khan PA, Johl SK, Johl SK (2021) Does adoption of ISO 56002‐2019 and green innovation reporting enhance the firm sustainable development goal performance? An emerging paradigm. Bus Strateg Environ 30: 2922–2936. https://doi.org/10.1002/bse.2779 doi: 10.1002/bse.2779
![]() |
[67] |
Khojastehpour M, Johns R (2014) The effect of environmental CSR issues on corporate/brand reputation and corporate profitability. Eur Bus Rev 26: 330–339. https://doi.org/10.1108/ebr-03-2014-0029 doi: 10.1108/ebr-03-2014-0029
![]() |
[68] |
Koehler G (2016) Assessing the SDGs from the standpoint of eco-social policy: Using the SDGs subversively. J Int Comp Soc Policy 32: 149–164. https://doi.org/10.1080/21699763.2016.1198715 doi: 10.1080/21699763.2016.1198715
![]() |
[69] |
Kolk A, Perego P (2010) Determinants of the adoption of sustainability assurance statements: An international investigation. Bus Strateg Environ 19: 182–198. https://doi.org/10.1002/bse.643 doi: 10.1002/bse.643
![]() |
[70] | KPMG (2022) ESG in 2022: A survey of global board directors. Available from: https://boardleadership.kpmg.us/esg.html. |
[71] |
Lahouel BB, Gaies B, Zaied YB, et al. (2019) Accounting for endogeneity and the dynamics of corporate social–corporate financial performance relationship. J Clean Prod 230: 352–364. https://doi.org/10.1016/j.jclepro.2019.04.377 doi: 10.1016/j.jclepro.2019.04.377
![]() |
[72] |
Lassala C, Orero-Blat M, Ribeiro-Navarrete S (2021) The financial performance of listed companies in pursuit of the Sustainable Development Goals (SDG). Econ Res-Ekonomska Istraživanja 34: 427–449. https://doi.org/10.1080/1331677X.2021.1877167 doi: 10.1080/1331677X.2021.1877167
![]() |
[73] |
Le Blanc D (2015) Towards integration at last? The Sustainable Development Goals as a network of targets. Sustain Dev 23: 176–187. https://doi.org/10.1002/sd.1582 doi: 10.1002/sd.1582
![]() |
[74] |
Lee J, Kim S, Kim E (2022) Environmental Responsibility, Social Responsibility, and Governance from the Perspective of Auditors. Int J Env Res Pub Health 19: 12181. https://doi.org/10.3390/ijerph191912181 doi: 10.3390/ijerph191912181
![]() |
[75] |
Lee KH, Barker M, Mouasher A (2013) Is it even espoused? An exploratory study of commitment to sustainability as evidenced in vision, mission, and graduate attribute statements in Australian universities. J Clean Prod 48: 20–28. https://doi.org/10.1016/j.jclepro.2013.01.007 doi: 10.1016/j.jclepro.2013.01.007
![]() |
[76] |
Lee M, Kim S (2020) Good governance and sustainable development goals. Sustainability 12: 6212. https://doi.org/10.3390/su12156212 doi: 10.3390/su12156212
![]() |
[77] |
Leinan Z, Zeng Q, Wang S, et al. (2022) Corporate Social Responsibility and Corporate Performance: A Meta-Analysis. Ind Eng Innov Manag 5: 9–22. https://doi.org/10.23977/ieim.2022.050202 doi: 10.23977/ieim.2022.050202
![]() |
[78] |
Li B, Wu K (2017) Environmental management system adoption and the operational performance of firm in the textile and apparel industry of China. Sustainability 9: 992. https://doi.org/10.3390/su9060992 doi: 10.3390/su9060992
![]() |
[79] |
Lopez MV, Garcia A, Rodriguez L (2007) Sustainable development and corporate performance: A study based on the dow jones sustainability index. J Bus Econ Ethics 75: 285–300. https://doi.org/10.1007/s10551-006-9157-7 doi: 10.1007/s10551-006-9157-7
![]() |
[80] |
Lougee B, Wallace J (2008) The corporate social responsibility (CSR) trend. J Appl Corp Financ 20: 96–108. https://doi.org/10.1111/j.1745-6622.2008.00172.x doi: 10.1111/j.1745-6622.2008.00172.x
![]() |
[81] | Luna-Rodríguez FJ, Delgado-Ceballos J, Galindo-Gutiérrez L (2023) Performance management for the SDGs: Towards an integrated framework. J Bus Econ Ethics 123: 469–492. |
[82] |
McWilliams A, Siegel D (2000) Corporate social responsibility and financial performance: correlation or misspecification? Strategic Manage J 21: 603–609. https://doi.org/10.1002/(SICI)1097-0266(200005)21:5<603::AID-SMJ101>3.3.CO;2-V doi: 10.1002/(SICI)1097-0266(200005)21:5<603::AID-SMJ101>3.3.CO;2-V
![]() |
[83] |
Miralles-Quirós MM, Miralles-Quirós JL, Redondo Hernández J (2019) ESG performance and shareholder value creation in the banking industry: International differences. Sustainability 11: 1404. https://doi.org/10.3390/su11051404 doi: 10.3390/su11051404
![]() |
[84] |
Mulaessa N, Lin L (2021) How do proactive environmental strategies affect green innovation? The moderating role of environmental regulations and firm performance. Int J Env Res Pub Health 18: 9083. https://doi.org/10.3390/ijerph18179083 doi: 10.3390/ijerph18179083
![]() |
[85] |
Ngobo PV, Fouda M (2012) Is 'Good'governance good for business? A cross-national analysis of firms in African countries. J World Bus 47: 435–449. https://doi.org/10.1016/j.jwb.2011.05.010 doi: 10.1016/j.jwb.2011.05.010
![]() |
[86] |
Njoku AC, Olayungbo DO (2021) Good governance and sustainable development in Africa. J Public Aff 22: e2532. https://doi.org/10.1002/pa.2532 doi: 10.1002/pa.2532
![]() |
[87] |
Nilsson M, Griggs D, Visbeck M (2016) Policy: map the interactions between Sustainable Development Goals. Nature 534: 320–322. https://doi.org/10.1038/534320a doi: 10.1038/534320a
![]() |
[88] |
Njoku AC, Olayungbo DO (2021) Good governance and sustainable development in Africa. J Public Aff 22: e2532. https://doi.org/10.1002/pa.2532 doi: 10.1002/pa.2532
![]() |
[89] |
Nollet J, Filis G, Mitrokostas E (2016) Corporate social responsibility and financial performance: A non-linear and disaggregated approach. Econ Model 52: 400–407. https://doi.org/10.1016/j.econmod.2015.09.019 doi: 10.1016/j.econmod.2015.09.019
![]() |
[90] | Okitasari M, Sunam R, Mishra R, et al. (2019) Governance and national implementation of the 2030 agenda: lessons from voluntary national reviews. |
[91] |
Onyango G, Ondiek JO (2021) Digitalization and integration of sustainable development goals (SGDs) in public organizations in Kenya. Public Organ Rev 21: 511–526. https://doi.org/10.1007/s11115-020-00504-2 doi: 10.1007/s11115-020-00504-2
![]() |
[92] |
Ordonez-Ponce E, Clarke A, MacDonald A (2021) Business contributions to the sustainable development goals through community sustainability partnerships. Sustain Account Mana Policy J 12: 1239–1267. https://doi.org/10.1108/SAMPJ-03-2020-0068 doi: 10.1108/SAMPJ-03-2020-0068
![]() |
[93] |
Orlitzky M, Schmidt FL, Rynes SL (2003) Corporate social and financial performance: A meta-analysis. Organ Stud 24: 403–441. https://doi.org/10.1177/0170840603024003910 doi: 10.1177/0170840603024003910
![]() |
[94] |
Pahl-Wostl C, Bhaduri A, Bruns A (2018) Editorial special issue: the nexus of water, energy and food–an environmental governance perspective. Environ Sci Policy 90: 161–163. https://doi.org/10.1016/j.envsci.2018.06.021 doi: 10.1016/j.envsci.2018.06.021
![]() |
[95] |
Perrini F, Russo A, Tencati A, et al. (2011) Deconstructing the relationship between corporate social and financial performance. J Bus Econ Ethics 102: 59–76. https://doi.org/10.1007/s10551-011-1194-1 doi: 10.1007/s10551-011-1194-1
![]() |
[96] | Porter ME, Kramer MR (2011) Creating shared value. Harvard Bus Rev 89: 62–77. |
[97] |
Pradhan P, Costa L, Rybski D, et al. (2017) A systematic study of sustainable development goal (SDG) interactions. Earth's Future 5: 1169–1179. https://doi.org/10.1002/2017EF000632 doi: 10.1002/2017EF000632
![]() |
[98] |
Ramos DL, Chen S, Rabeeu A, et al. (2022) Does SDG Coverage influence firm performance? Sustainability 14: 4870. https://doi.org/10.3390/su14094870 doi: 10.3390/su14094870
![]() |
[99] |
Ribeiro DMNM, Junior FH, Cunha CLL, et al. (2021) Digital sustainability: How information and communication technologies (ICTs) support sustainable development goals (SDGs) assessment in municipalities. Digit Policy Regul G 23: 229–247. https://doi.org/10.1108/DPRG-11-2020-0159 doi: 10.1108/DPRG-11-2020-0159
![]() |
[100] |
Rosati F, Faria LG (2019) Addressing the SDGs in sustainability reports: The relationship with institutional factors. J Clean Prod 215: 1312–1326. https://doi.org/10.1016/j.jclepro.2018.12.107 doi: 10.1016/j.jclepro.2018.12.107
![]() |
[101] | Rockström J, Sukhdev P (2016) Presentation at Stockholm Resilience Centre. Stockholm University Available from: https://www.stockholmresilience.org/research/research-news/2016-06-14-how-food-connects-all-the-sdgs.html. |
[102] |
Sabuj S, Arif A, Momotaz B (2019) Audit Expectation Gap: Empirical Evidence from Bangladesh, SSRG. Int J Econ Manag Stud 6: 32–36. https://doi.org/10.14445/23939125/IJEMS-V6I5P106 doi: 10.14445/23939125/IJEMS-V6I5P106
![]() |
[103] |
Sachs JD (2012) From millennium development goals to sustainable development goals. The Lancet 379: 2206–2211. https://doi.org/10.1016/S0140-6736(12)60685-0 doi: 10.1016/S0140-6736(12)60685-0
![]() |
[104] | Sachs JD, Schmidt-Traub G, Kroll C, et al. (2023) Assessing progress towards the SDGs: Challenges and opportunities for SDG performance reviews. The Lancet 402: 80–88. |
[105] |
Sachs JD, Schmidt-Traub G, Mazzucato M, et al. (2019) Six transformations to achieve the sustainable development goals. Nat Sustain 2: 805–814. https://doi.org/10.1038/s41893-019-0352-9 doi: 10.1038/s41893-019-0352-9
![]() |
[106] | Sachs J, Massa I, Marinescu S, et al. (2021) The decade of action and small island developing states: measuring and addressing SIDS'vulnerabilities to accelerate SDG progress. Sustain Dev Solutions Network, 2021-07. |
[107] |
Salama A (2005) A note on the impact of environmental performance on financial performance. Struct Change Econ D 16: 413–421. https://doi.org/10.1016/j.strueco.2004.04.005 doi: 10.1016/j.strueco.2004.04.005
![]() |
[108] |
Santos MJ, Silva Bastos C (2021) The adoption of sustainable development goals by large Portuguese companies. Soc Responsib J 17: 1079–1099. https://doi.org/10.1108/SRJ-07-2018-0184 doi: 10.1108/SRJ-07-2018-0184
![]() |
[109] |
Sarkis J, Gonzalez-Torre P, Adenso-Diaz B (2010) Stakeholder pressure and the stakeholders' environmental practices: The mediating effect of training. J Oper Manage 28: 163–176. https://doi.org/10.1016/j.jom.2009.10.001 doi: 10.1016/j.jom.2009.10.001
![]() |
[110] |
Schaltegger S, Wagner M (2011) Sustainable entrepreneurship and sustainability innovation: Categories and interactions. Bus Strateg Environ 20: 222–237. https://doi.org/10.1002/bse.682 doi: 10.1002/bse.682
![]() |
[111] |
Schaltegger S, Hörisch J, Freeman RE (2019) Business cases for sustainability: A stakeholder theory perspective. Organ Environ 32: 191–212. https://doi.org/10.1177/1086026617722882 doi: 10.1177/1086026617722882
![]() |
[112] |
Scharlemann JP, Brock RC, Balfour N, et al. (2020) Towards understanding interactions between Sustainable Development Goals: The role of environment–human linkages. Sustain Sci 15: 1573–1584. https://doi.org/10.1007/s11625-020-00799-6 doi: 10.1007/s11625-020-00799-6
![]() |
[113] |
Scheyvens R, Banks G, Hughes E (2016) The private sector and the SDGs: The need to move beyond 'business as usual'. Sustain Dev 24: 371–382. https://doi.org/10.1002/sd.1623 doi: 10.1002/sd.1623
![]() |
[114] |
Scholtens B, Zhou Y (2008) Stakeholder relations and financial performance. Sustain Dev 16: 213–232. https://doi.org/10.1002/sd.364 doi: 10.1002/sd.364
![]() |
[115] |
Simpson WG, Kohers T (2002) The link between corporate social and financial performance: Evidence from the banking industry. J Bus Econ ethics 35: 97–109. https://doi.org/10.1023/A:1013082525900 doi: 10.1023/A:1013082525900
![]() |
[116] |
Smith L, Jones B (2019) Limits of governance in attaining sustainability goals. Ecol Econ 165: 106391. https://doi.org/10.1016/j.ecolecon.2019.106391 doi: 10.1016/j.ecolecon.2019.106391
![]() |
[117] |
Stafford-Smith M, Griggs D, Gaffney O, et al. (2017) Integration: the key to implementing the Sustainable Development Goals. Sustain Sci 12: 911–919. https://doi.org/10.1007/s11625-016-0383-3 doi: 10.1007/s11625-016-0383-3
![]() |
[118] |
Stubbs W, Cocklin C (2008) Conceptualizing a "sustainability business model". Organ Environ 21: 103–127. https://doi.org/10.1177/1086026608318042 doi: 10.1177/1086026608318042
![]() |
[119] |
Sporchia F, Paneni A, Pulselli FM, et al. (2021) Investigating environment-society-economy relations in time series in Europe using a synthetic input-state-output framework. Environ Sci Policy 125: 54–65. https://doi.org/10.1016/j.envsci.2021.08.018 doi: 10.1016/j.envsci.2021.08.018
![]() |
[120] | Sulbahri RA, Fuadah LL (2022) Effect of Sustainable Report (CSR) on Return on Asset (ROA), Return on Equity (ROE) and Good Corporate Governance (GCG) (Empirical Study on Banking Companies for the 2016–2019 Period). In 7th Sriwijaya Economics, Accounting, and Business Conference (SEABC 2021), 34-41, Atlantis Press. https://doi.org/10.2991/aebmr.k.220304.005 |
[121] |
Surroca J, Tribó JA, Waddock S (2010) Corporate responsibility and financial performance: The role of intangible resources. Strategic Manage J 31: 463–490. https://doi.org/10.1002/smj.820 doi: 10.1002/smj.820
![]() |
[122] | UN Global Compact (2023) Business action for the SDGs. |
[123] | United Nations (2015) Transforming our world: The 2030 agenda for sustainable development. Retrieved from: https://sustainabledevelopment.un.org/post2015/transformingourworld. |
[124] |
Uyar A, Karaman AS, Kilic M (2020) Is corporate social responsibility reporting a tool of signaling or greenwashing? Evidence from the worldwide logistics sector. J Clean Prod 253: 119997. https://doi.org/10.1016/j.jclepro.2020.119997 doi: 10.1016/j.jclepro.2020.119997
![]() |
[125] | Van der Waal JW, Thijssens T (2020) Corporate involvement in sustainable development goals: Exploring the territory. J Clean Prod 252: 119625. https://doi.org/10.1016/j.jclepro.2019.119625 |
[126] | Van Egmond ND, De Vries HJM (2011) Sustainability: The search for the integral worldview. Futures, 43: 853–867. https://doi.org/10.1016/j.futures.2011.05.027 |
[127] |
Van Hoang TH, Pham L, Nguyen TTP (2023) Does country sustainability improve firm ESG reporting transparency? The moderating role of firm industry and CSR engagement. Econ Model 125: 106351. https://doi.org/10.1016/j.econmod.2023.106351 doi: 10.1016/j.econmod.2023.106351
![]() |
[128] |
Wang CW, Lee CC, Chen MC (2022) The effects of economic policy uncertainty and country governance on banks' liquidity creation: International evidence. Pac-Basin Financ J 71: 101708. https://doi.org/10.1016/j.pacfin.2022.101708 doi: 10.1016/j.pacfin.2022.101708
![]() |
[129] |
Wang X, Yang M, Park K, et al. (2022) Social sustainability of a firm: Orientation, practices, and performances. Int J Env Res Pub Health 19: 13391. https://doi.org/10.3390/ijerph192013391 doi: 10.3390/ijerph192013391
![]() |
[130] | World Bank. (2017) Worldwide governance indicators. Available from: https://info.worldbank.org/governance/wgi/. |
[131] |
Xie X, Huo J, Zou H (2019) Green process innovation, green product innovation, and corporate financial performance: A content analysis method. J Bus Econ research 101: 697–706. https://doi.org/10.1016/j.jbusres.2019.01.010 doi: 10.1016/j.jbusres.2019.01.010
![]() |
[132] |
Zhang Q, Ma Y (2021) The impact of environmental management on firm economic performance: The mediating effect of green innovation and the moderating effect of environmental leadership. J Clean Prod 292: 126057. https://doi.org/10.1016/j.jclepro.2021.126057 doi: 10.1016/j.jclepro.2021.126057
![]() |
[133] |
Zhao H, Luo Y, Suh T (2004) Transaction cost determinants and ownership-based entry mode choice: A meta analytical review. J Int Bus Stud 35: 524–544. https://doi.org/10.1057/palgrave.jibs.8400106 doi: 10.1057/palgrave.jibs.8400106
![]() |
![]() |
![]() |
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2. | Abdul Razaq, Louai A. Maghrabi, Musheer Ahmad, Qamar H. Naith, Novel substitution-box generation using group theory for secure medical image encryption in E-healthcare, 2024, 9, 2473-6988, 6207, 10.3934/math.2024303 | |
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7. | Jieun Ryu, Yongbhin Kim, Seungtai Yoon, Ju-Sung Kang, Yongjin Yeom, IPCC7: Post-Quantum Encryption Scheme Based on a Perfect Dominating Set in 3-Regular Graph, 2024, 12, 2169-3536, 4575, 10.1109/ACCESS.2024.3349704 | |
8. | Anand Prakash Dube, Raghav Yadav, 2024, Enhanced Dynamic S-Box Design Based on Adaptive Heuristic Evolution and Multi-Stage Nonlinearity for Securing IoT-Based Remote Health Monitoring Systems, 979-8-3315-0843-2, 1, 10.1109/ICEC59683.2024.10837025 | |
9. | Yong Zhang, Image encryption algorithm based on butterfly module and chaos, 2025, 03784754, 10.1016/j.matcom.2025.01.011 | |
10. | Amal S. Alali, Muhammad Kamran Jamil, Rashad Ali, Refah Alotaibi, Wedad Albalawi, Degree, closeness and eigenvector for the construction of cryptographically secure S-boxes, 2025, 16, 20904479, 103559, 10.1016/j.asej.2025.103559 |
Binary form | Decimal | 𝐺𝐹 (210) | Binary form | Decimal | 𝐺𝐹(210) | Binary form | Decimal | 𝐺𝐹(210) | Binary form | Decimal | 𝐺𝐹(210) |
0000000000 | 0 | 0 | 0000000001 | 1 | 1 | 0000000010 | 2 | κ1 | 0000000100 | 4 | κ2 |
0000001000 | 8 | κ3 | 0000010000 | 16 | κ4 | 0000100000 | 32 | κ5 | 0001000000 | 64 | κ6 |
0010000000 | 128 | κ7 | 0100000000 | 256 | κ8 | 1000000000 | 512 | κ9 | 0010000001 | 129 | κ10 |
0100000010 | 258 | κ11 | 1000000100 | 516 | κ12 | 0010001001 | 137 | κ13 | 0100010010 | 274 | κ14 |
1000100100 | 548 | κ15 | 0011001001 | 201 | κ16 | 0110010010 | 402 | κ17 | 1100100100 | 804 | κ18 |
1011001001 | 713 | κ19 | 0100010011 | 275 | κ20 | 1000100110 | 550 | κ21 | 0011001101 | 205 | κ22 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
1010111011 | 699 | κ311 | 0111110111 | 503 | κ312 | 1111101110 | 1006 | κ313 | 1101011101 | 861 | κ314 |
1000111011 | 571 | κ315 | 0011110111 | 247 | κ316 | 0111101110 | 494 | κ317 | 1111011100 | 988 | κ318 |
1100111001 | 825 | κ319 | 1011110011 | 755 | κ320 | 0101100111 | 359 | κ321 | 1011001110 | 718 | κ322 |
0100011101 | 285 | κ323 | 1000111010 | 570 | κ324 | 0011110101 | 245 | κ325 | 0111101010 | 490 | κ326 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
0100110000 | 304 | κ1007 | 1001100000 | 608 | κ1008 | 0001000001 | 65 | κ1009 | 0010000010 | 130 | κ1010 |
0100000100 | 260 | κ1011 | 1000001000 | 520 | κ1012 | 0010010001 | 145 | κ1013 | 0100100010 | 290 | κ1014 |
1001000100 | 580 | κ1015 | 0000001001 | 9 | κ1016 | 0000010010 | 18 | κ1017 | 0000100100 | 36 | κ1018 |
0001001000 | 72 | κ1019 | 0010010000 | 144 | κ1020 | 0100100000 | 288 | κ1021 | 1001000000 | 576 | κ1022 |
κ1 | κ77 | κ1021 | κ869 | κ1013 | κ5 | κ513 | κ1017 | κ1009 | κ9 | κ189 | κ13 | κ301 | κ709 | κ353 | κ193 |
κ209 | κ17 | κ729 | κ1005 | κ393 | κ21 | κ305 | κ1001 | κ645 | κ937 | κ25 | κ385 | κ997 | κ421 | κ817 | κ29 |
κ537 | κ457 | κ993 | κ317 | κ265 | κ637 | κ605 | κ33 | κ989 | κ401 | κ909 | κ149 | κ237 | κ273 | κ37 | κ161 |
κ985 | κ473 | κ545 | κ41 | κ849 | κ981 | κ413 | κ45 | κ977 | κ897 | κ673 | κ397 | κ49 | κ225 | κ749 | κ973 |
κ253 | κ109 | κ965 | κ181 | κ233 | κ53 | κ481 | κ969 | κ665 | κ213 | κ865 | κ57 | κ437 | κ529 | κ345 | κ737 |
κ449 | κ389 | κ61 | κ917 | κ961 | κ493 | κ65 | κ621 | κ957 | κ297 | κ945 | κ145 | κ153 | κ221 | κ69 | κ953 |
κ725 | κ261 | κ549 | κ477 | κ73 | κ949 | κ701 | κ405 | κ81 | κ177 | κ765 | κ941 | κ593 | κ785 | κ321 | κ113 |
κ197 | κ85 | κ349 | κ589 | κ489 | κ577 | κ89 | κ893 | κ933 | κ761 | κ93 | κ657 | κ929 | κ229 | κ721 | κ97 |
κ925 | κ573 | κ165 | κ417 | κ517 | κ101 | κ789 | κ133 | κ921 | κ805 | κ601 | κ525 | κ661 | κ557 | κ105 | κ837 |
κ269 | κ913 | κ597 | κ169 | κ705 | κ117 | κ461 | κ445 | κ905 | κ333 | κ553 | κ125 | κ245 | κ121 | κ357 | κ901 |
κ689 | κ257 | κ521 | κ649 | κ129 | κ561 | κ429 | κ889 | κ733 | κ329 | κ829 | κ717 | κ581 | κ137 | κ885 | κ873 |
κ141 | κ881 | κ501 | κ541 | κ877 | κ777 | κ853 | κ325 | κ157 | κ361 | κ505 | κ569 | κ613 | κ861 | κ669 | κ857 |
κ381 | κ797 | κ629 | κ173 | κ313 | κ845 | κ585 | κ841 | κ425 | κ465 | κ741 | κ185 | κ377 | κ565 | κ833 | κ609 |
κ825 | κ693 | κ201 | κ745 | κ821 | κ757 | κ205 | κ813 | κ441 | κ249 | κ809 | κ485 | κ409 | κ625 | κ217 | κ337 |
κ469 | κ801 | κ685 | κ793 | κ617 | κ773 | κ533 | κ241 | κ681 | κ781 | κ309 | κ497 | κ293 | κ769 | κ509 | κ433 |
κ633 | κ653 | κ753 | κ365 | κ277 | κ281 | κ453 | κ289 | κ285 | κ677 | κ641 | κ713 | κ373 | κ697 | κ369 | κ381 |
Binary form | Decimal | 𝐺𝐹 (28) | Binary form | Decimal | 𝐺𝐹 (28) | Binary form | Decimal | 𝐺𝐹 (28) | Binary form | Decimal | 𝐺𝐹 (28) |
00000000 | 0 | 0 | 00000001 | 1 | 1 | 00000010 | 2 | β1 | 00000100 | 4 | β2 |
00001000 | 8 | β3 | 00010000 | 16 | β4 | 00100000 | 32 | β5 | 01000000 | 64 | β6 |
10000000 | 128 | β7 | 01101001 | 105 | β8 | 11010010 | 210 | β9 | 11001101 | 205 | β10 |
11110011 | 243 | β11 | 10001111 | 143 | β12 | 01110111 | 119 | β13 | 11101110 | 238 | β14 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
10101100 | 172 | β163 | 00110001 | 49 | β164 | 01100010 | 98 | β165 | 11000100 | 196 | β166 |
11100001 | 225 | β167 | 10101011 | 171 | β168 | 00111111 | 63 | β169 | 01111110 | 126 | β170 |
11111100 | 252 | β171 | 10010001 | 145 | β172 | 01001011 | 75 | β173 | 10010110 | 150 | β174 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
11010111 | 215 | β243 | 11000111 | 199 | β244 | 11100111 | 231 | β245 | 10100111 | 167 | β246 |
00100111 | 39 | β247 | 01001110 | 78 | β248 | 10011100 | 156 | β249 | 01010001 | 81 | β250 |
10100010 | 162 | β251 | 00101101 | 45 | β252 | 01011010 | 90 | β253 | 10110100 | 180 | β254 |
24 | 41 | 1 | 180 | 2 | 140 | 113 | 52 | 32 | 4 | 190 | 42 | 125 | 102 | 90 | 60 |
8 | 128 | 205 | 45 | 253 | 16 | 250 | 86 | 162 | 109 | 17 | 115 | 244 | 81 | 217 | 64 |
238 | 48 | 101 | 57 | 156 | 59 | 148 | 78 | 35 | 105 | 122 | 98 | 100 | 39 | 210 | 182 |
104 | 167 | 50 | 239 | 46 | 231 | 38 | 13 | 243 | 221 | 213 | 97 | 72 | 132 | 199 | 143 |
248 | 164 | 83 | 215 | 119 | 55 | 214 | 223 | 219 | 181 | 177 | 200 | 3 | 135 | 224 | 235 |
111 | 216 | 6 | 54 | 80 | 99 | 108 | 241 | 12 | 73 | 30 | 94 | 27 | 76 | 149 | 185 |
96 | 232 | 87 | 129 | 192 | 195 | 67 | 116 | 240 | 166 | 233 | 188 | 254 | 23 | 69 | 58 |
7 | 187 | 133 | 51 | 203 | 63 | 212 | 29 | 68 | 31 | 153 | 186 | 62 | 74 | 93 | 79 |
124 | 157 | 28 | 173 | 154 | 141 | 77 | 14 | 92 | 146 | 171 | 91 | 229 | 137 | 144 | 85 |
5 | 155 | 193 | 10 | 82 | 36 | 20 | 168 | 174 | 230 | 18 | 121 | 21 | 40 | 71 | 249 |
227 | 130 | 196 | 9 | 252 | 61 | 176 | 134 | 201 | 160 | 178 | 43 | 88 | 117 | 107 | 44 |
22 | 208 | 11 | 150 | 33 | 19 | 66 | 236 | 114 | 246 | 112 | 202 | 118 | 152 | 34 | 194 |
138 | 251 | 197 | 169 | 237 | 26 | 145 | 158 | 56 | 179 | 95 | 15 | 255 | 161 | 159 | 106 |
234 | 120 | 220 | 198 | 110 | 222 | 147 | 183 | 142 | 218 | 123 | 191 | 228 | 131 | 139 | 151 |
245 | 165 | 89 | 163 | 209 | 189 | 206 | 65 | 47 | 225 | 175 | 103 | 53 | 247 | 207 | 75 |
211 | 136 | 226 | 25 | 170 | 242 | 70 | 184 | 126 | 84 | 172 | 49 | 37 | 127 | 204 | 0 |
102 | 62 | 108 | 235 | 184 | 163 | 44 | 240 | 53 | 89 | 70 | 150 | 160 | 155 | 220 | 164 |
191 | 172 | 135 | 79 | 174 | 109 | 12 | 201 | 144 | 251 | 133 | 186 | 134 | 71 | 228 | 147 |
96 | 14 | 50 | 114 | 65 | 32 | 106 | 120 | 255 | 218 | 94 | 177 | 136 | 233 | 115 | 219 |
226 | 250 | 211 | 176 | 68 | 230 | 6 | 199 | 156 | 61 | 9 | 165 | 26 | 196 | 139 | 41 |
1 | 22 | 209 | 125 | 215 | 180 | 63 | 113 | 193 | 192 | 241 | 43 | 17 | 127 | 20 | 67 |
169 | 208 | 256 | 198 | 33 | 28 | 243 | 54 | 234 | 45 | 247 | 101 | 73 | 202 | 252 | 248 |
246 | 154 | 207 | 78 | 19 | 3 | 232 | 236 | 224 | 131 | 59 | 31 | 171 | 39 | 238 | 34 |
40 | 24 | 142 | 72 | 83 | 217 | 103 | 82 | 187 | 52 | 210 | 23 | 7 | 205 | 124 | 123 |
64 | 110 | 170 | 153 | 57 | 112 | 253 | 189 | 56 | 229 | 188 | 60 | 86 | 42 | 36 | 121 |
30 | 140 | 76 | 168 | 122 | 141 | 97 | 152 | 146 | 137 | 27 | 16 | 162 | 195 | 145 | 25 |
221 | 105 | 111 | 69 | 81 | 13 | 194 | 15 | 107 | 48 | 249 | 119 | 8 | 74 | 254 | 35 |
117 | 128 | 173 | 2 | 18 | 242 | 90 | 84 | 167 | 116 | 143 | 132 | 11 | 26 | 99 | 46 |
138 | 88 | 190 | 77 | 104 | 231 | 200 | 204 | 151 | 197 | 178 | 158 | 183 | 213 | 87 | 222 |
55 | 58 | 92 | 161 | 37 | 95 | 100 | 166 | 157 | 85 | 148 | 245 | 91 | 179 | 181 | 4 |
75 | 214 | 38 | 98 | 212 | 149 | 5 | 130 | 244 | 175 | 21 | 203 | 51 | 227 | 182 | 66 |
185 | 225 | 47 | 10 | 129 | 206 | 118 | 49 | 80 | 223 | 216 | 237 | 239 | 126 | 93 | 159 |
248 | 150 | 195 | 151 | 206 | 38 | 62 | 88 | 213 | 25 | 118 | 250 | 61 | 48 | 134 | 121 |
3 | 33 | 192 | 224 | 175 | 164 | 186 | 187 | 249 | 152 | 18 | 99 | 72 | 5 | 188 | 59 |
80 | 58 | 44 | 144 | 110 | 89 | 23 | 7 | 143 | 137 | 200 | 113 | 73 | 194 | 226 | 160 |
184 | 101 | 53 | 31 | 32 | 241 | 234 | 92 | 154 | 120 | 233 | 91 | 221 | 41 | 214 | 124 |
156 | 75 | 235 | 46 | 9 | 190 | 81 | 51 | 27 | 117 | 245 | 193 | 169 | 129 | 45 | 126 |
252 | 29 | 203 | 236 | 218 | 229 | 159 | 251 | 4 | 66 | 228 | 220 | 204 | 122 | 222 | 238 |
20 | 163 | 34 | 147 | 94 | 24 | 212 | 237 | 130 | 148 | 201 | 1 | 16 | 157 | 196 | 141 |
223 | 57 | 210 | 246 | 22 | 70 | 43 | 78 | 85 | 82 | 79 | 93 | 215 | 127 | 135 | 208 |
170 | 65 | 166 | 202 | 17 | 244 | 205 | 100 | 230 | 138 | 199 | 155 | 36 | 133 | 112 | 162 |
71 | 174 | 64 | 123 | 189 | 42 | 56 | 168 | 173 | 232 | 102 | 243 | 142 | 15 | 0 | 125 |
198 | 21 | 140 | 60 | 97 | 183 | 114 | 10 | 111 | 28 | 254 | 128 | 11 | 253 | 225 | 239 |
98 | 95 | 131 | 55 | 139 | 207 | 255 | 2 | 211 | 115 | 68 | 171 | 14 | 197 | 8 | 181 |
219 | 176 | 40 | 132 | 179 | 54 | 13 | 145 | 86 | 76 | 103 | 158 | 74 | 242 | 87 | 216 |
83 | 153 | 50 | 209 | 161 | 165 | 119 | 172 | 63 | 105 | 182 | 90 | 227 | 106 | 84 | 240 |
136 | 104 | 247 | 217 | 146 | 231 | 26 | 67 | 39 | 12 | 180 | 116 | 49 | 69 | 37 | 52 |
177 | 19 | 108 | 47 | 191 | 96 | 30 | 185 | 178 | 167 | 109 | 149 | 77 | 107 | 35 | 6 |
Boolean mapping | θ0 | θ1 | θ2 | θ3 | θ4 | θ5 | θ6 | θ7 | Mean |
NL score | 110 | 112 | 110 | 112 | 110 | 110 | 110 | 112 | 110 |
0.4844 | 0.5469 | 0.4688 | 0.5625 | 0.5312 | 0.5312 | 0.5156 | 0.4844 |
0.4531 | 0.4844 | 0.5469 | 0.5 | 0.5 | 0.4844 | 0.4844 | 0.5625 |
0.5312 | 0.4688 | 0.5312 | 0.5312 | 0.4375 | 0.4688 | 0.5156 | 0.5 |
0.4375 | 0.5 | 0.5469 | 0.5 | 0.5469 | 0.5312 | 0.4844 | 0.5156 |
0.4531 | 0.5625 | 0.5625 | 0.4688 | 0.4688 | 0.5156 | 0.4375 | 0.5312 |
0.5781 | 0.4844 | 0.5312 | 0.5469 | 0.5156 | 0.5 | 0.5156 | 0.5 |
0.5 | 0.4531 | 0.4531 | 0.4219 | 0.5156 | 0.5469 | 0.5312 | 0.4844 |
0.5 | 0.4844 | 0.5312 | 0.5312 | 0.5 | 0.5312 | 0.4375 | 0.5469 |
- | 110 | 110 | 112 | 112 | 110 | 112 | 110 |
110 | - | 108 | 110 | 112 | 112 | 108 | 110 |
110 | 108 | - | 110 | 112 | 110 | 110 | 112 |
112 | 110 | 110 | - | 110 | 110 | 110 | 112 |
112 | 112 | 112 | 110 | - | 110 | 110 | 110 |
110 | 112 | 110 | 110 | 110 | - | 112 | 110 |
112 | 108 | 110 | 110 | 110 | 112 | - | 112 |
110 | 110 | 112 | 112 | 110 | 110 | 112 | - |
- | 0.4805 | 0.5098 | 0.4941 | 0.4902 | 0.498 | 0.5215 | 0.4824 |
0.4805 | - | 0.5195 | 0.5176 | 0.4922 | 0.4922 | 0.4766 | 0.4902 |
0.5098 | 0.5195 | - | 0.5 | 0.4902 | 0.5137 | 0.4922 | 0.498 |
0.4941 | 0.5176 | 0.5 | - | 0.4961 | 0.5117 | 0.5273 | 0.4902 |
0.4902 | 0.4922 | 0.4902 | 0.4961 | - | 0.4922 | 0.5293 | 0.5195 |
0.498 | 0.4922 | 0.5137 | 0.5117 | 0.4922 | - | 0.4707 | 0.4863 |
0.5215 | 0.4766 | 0.4922 | 0.5273 | 0.5293 | 0.4707 | - | 0.4883 |
0.4824 | 0.4902 | 0.498 | 0.4902 | 0.5195 | 0.4863 | 0.4883 | - |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 |
4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 6 | 4 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 6 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | - |
S-box | Nonlinearity Min Max Average |
SAC | BIC-SAC | BIC-NL | DU | LP | ||
Suggested S-box | 110 | 112 | 110.75 | 0.5051 | 0.4989 | 110.55 | 6 | 0.0781 |
AES [36] | 112 | 112 | 112 | 0.5058 | 0.5046 | 112 | 4 | 0.0625 |
Reference [37] | 106 | 108 | 106.25 | 0.5112 | 0.4975 | 103.93 | 12 | 0.1484 |
Reference [38] | 106 | 110 | 106.5 | 0.5010 | 0.4987 | 103.93 | 10 | 0.125 |
Reference [39] | 106 | 108 | 107 | 0.4949 | 0.5019 | 102.29 | 12 | 0.141 |
Reference [40] | 106 | 110 | 108.5 | 0.4995 | 0.5011 | 103.85 | 10 | 0.109 |
Reference [41] | 108 | 110 | 109.75 | 0.5042 | 0.4987 | 110.6 | 6 | 0.0859 |
Reference [42] | 102 | 110 | 106.5 | 0.4943 | 0.5019 | 103.35 | 12 | 0.1468 |
Reference [43] | 104 | 108 | 105.5 | 0.5065 | 0.5031 | 103.57 | 10 | 0.1328 |
Reference [44] | 104 | 110 | 107 | 0.4993 | 0.5050 | 103.29 | 10 | 0.1328 |
Image | Correlation | Entropy | Energy | Homogeneity | Contrast |
Cameraman Host | 0.9227 | 7.0097 | 0.1805 | 0.8952 | 0.5871 |
Cameraman-Enc | 0.0394 | 7.9972 | 0.0149 | 0.3999 | 10.0509 |
Pepper Host | 0.9312 | 7.5326 | 0.1096 | 0.8880 | 0.3849 |
Pepper-Enc | 0.0021 | 7.9972 | 0.0156 | 0.3902 | 10.4802 |
Baboon Host | 0.7983 | 7.2649 | 0.0943 | 0.7820 | 0.6326 |
Baboon-Enc | 0.0071 | 7.9975 | 0.0156 | 0.3945 | 10.3994 |
Lena Host | 0.9024 | 7.4439 | 0.1127 | 0.8622 | 0.4482 |
Lena-Enc | − 0.0379 | 7.9976 | 0.0157 | 0.3822 | 10.8896 |
Image | Cameraman | Pepper | Baboon | Lena | |
Vertical | Plain Image | 0.9745 | 0.9137 | 0.9090 | 0.9321 |
Distorted Image | 0.0310 | − 0.0392 | − 0.0128 | − 0.0117 | |
Horizontal | Plain Image | 0.9610 | 0.9204 | 0.8727 | 0.883 |
Distorted Image | − 0.0026 | − 0.0015 | 0.0039 | − 0.0021 |
Test | Cameraman-Enc | Pepper-Enc | Baboon-Enc | Lena-Enc |
MSE | 9212.16 | 8656.41 | 7854.44 | 8414.71 |
MSE [6] | 9079.09 | 8190.01 | 8011.23 | 8239.51 |
MSE [15] | 9189.41 | 8612.09 | 7599.03 | 7930.39 |
MSE [17] | 9187.38 | 8423.61 | 7865.21 | 8274.13 |
PSNR | 8.4723 | 8.8563 | 9.8912 | 8.9912 |
PSNR [6] | 8.1129 | 8.9710 | 8.5539 | 9.1902 |
PSNR [15] | 8.2897 | 8.7091 | 8.1331 | 8.9500 |
PSNR [17] | 8.2891 | 8.3353 | 8.9361 | 8.0032 |
SSIM1 | 0.0009 | 0.0012 | 0.0010 | 0.0011 |
SSIM1 [6] | 0.0013 | 0.0008 | 0.0011 | 0.0012 |
SSIM1 [15] | 0.0010 | 0.0012 | 0.0008 | 0.0014 |
SSIM1 [17] | 0.0009 | 0.0015 | 0.0012 | 0.0013 |
NCC | 0.8633 | 0.8710 | 0.9121 | 0.8803 |
NCC [6] | 0.8537 | 0.8675 | 0.8912 | 0.9016 |
NCC [15] | 0.8733 | 0.8712 | 0.8543 | 0.8461 |
NCC [17] | 0.8640 | 0.87134 | 0.9001 | 0.8692 |
AD | −7.4523 | −4.9812 | −2.3419 | −5.3881 |
AD [6] | −3,4511 | −5.6634 | −1.4529 | −2.3319 |
AD [15] | −6,7819 | −3.8873 | −2.8827 | −4.1198 |
AD [17] | −3.4429 | −4.9821 | −2.3872 | −7.6594 |
SC | 0.8496 | 0.8345 | 0.8456 | 0.8247 |
SC [6] | 0.8455 | 0.8451 | 0.8401 | 0.8342 |
SC [15] | 0.8341 | 0.8489 | 0.8465 | 0.8231 |
SC [17] | 0.8436 | 0.8111 | 0.8265 | 0.8490 |
MD | 240 | 238 | 212 | 234 |
MD [6] | 211 | 231 | 233 | 241 |
MD [15] | 223 | 227 | 227 | 228 |
MD [17] | 234 | 238 | 221 | 219 |
NAE | 0.6358 | 0.6273 | 0.6147 | 0.6384 |
NAE [6] | 0.6455 | 0.5932 | 0.5813 | 0.6459 |
NAE [15] | 0.6040 | 0.6193 | 0.6388 | 0.6026 |
NAE [17] | 0.6219 | 0.6243 | 0.6012 | 0.5856 |
RMSE | 94.6682 | 91.7245 | 84.9561 | 87.9349 |
RMSE [6] | 90.6638 | 92.3402 | 88.3476 | 86.7938 |
RMSE [15] | 93,4428 | 89.7690 | 91.2398 | 87.3947 |
RMSE [17] | 90.4582 | 85.1109 | 84.8934 | 88.1831 |
UQI | 0.0218 | 0.0332 | 0.0314 | 0.0338 |
UQI [6] | 0.0127 | 0.0412 | 0.0279 | 0.0178 |
UQI [15] | 0.0347 | 0.0456 | 0.0127 | 0.0391 |
UQI [17] | 0.0234 | 0.0401 | 0.0298 | 0.0281 |
MI | −1.0292 | −1.0187 | −1.0184 | −1.0281 |
MI [6] | −1.0195 | −1.0490 | −1.0328 | −1.0402 |
MI [15] | −1.0371 | −1.0197 | −1.0294 | −1.0406 |
MI [17] | −1.341 | −1.0198 | −1.0384 | −1.0327 |
Image | NPCR | UACI | BACI |
Cameraman | 99.63% | 33.12% | 24.60% |
Pepper | 99.81% | 33.21% | 26.38% |
Baboon | 99.76% | 32.86% | 24.25% |
Lena | 99.79% | 33.16% | 23.09% |
Binary form | Decimal | 𝐺𝐹 (210) | Binary form | Decimal | 𝐺𝐹(210) | Binary form | Decimal | 𝐺𝐹(210) | Binary form | Decimal | 𝐺𝐹(210) |
0000000000 | 0 | 0 | 0000000001 | 1 | 1 | 0000000010 | 2 | κ1 | 0000000100 | 4 | κ2 |
0000001000 | 8 | κ3 | 0000010000 | 16 | κ4 | 0000100000 | 32 | κ5 | 0001000000 | 64 | κ6 |
0010000000 | 128 | κ7 | 0100000000 | 256 | κ8 | 1000000000 | 512 | κ9 | 0010000001 | 129 | κ10 |
0100000010 | 258 | κ11 | 1000000100 | 516 | κ12 | 0010001001 | 137 | κ13 | 0100010010 | 274 | κ14 |
1000100100 | 548 | κ15 | 0011001001 | 201 | κ16 | 0110010010 | 402 | κ17 | 1100100100 | 804 | κ18 |
1011001001 | 713 | κ19 | 0100010011 | 275 | κ20 | 1000100110 | 550 | κ21 | 0011001101 | 205 | κ22 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
1010111011 | 699 | κ311 | 0111110111 | 503 | κ312 | 1111101110 | 1006 | κ313 | 1101011101 | 861 | κ314 |
1000111011 | 571 | κ315 | 0011110111 | 247 | κ316 | 0111101110 | 494 | κ317 | 1111011100 | 988 | κ318 |
1100111001 | 825 | κ319 | 1011110011 | 755 | κ320 | 0101100111 | 359 | κ321 | 1011001110 | 718 | κ322 |
0100011101 | 285 | κ323 | 1000111010 | 570 | κ324 | 0011110101 | 245 | κ325 | 0111101010 | 490 | κ326 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
0100110000 | 304 | κ1007 | 1001100000 | 608 | κ1008 | 0001000001 | 65 | κ1009 | 0010000010 | 130 | κ1010 |
0100000100 | 260 | κ1011 | 1000001000 | 520 | κ1012 | 0010010001 | 145 | κ1013 | 0100100010 | 290 | κ1014 |
1001000100 | 580 | κ1015 | 0000001001 | 9 | κ1016 | 0000010010 | 18 | κ1017 | 0000100100 | 36 | κ1018 |
0001001000 | 72 | κ1019 | 0010010000 | 144 | κ1020 | 0100100000 | 288 | κ1021 | 1001000000 | 576 | κ1022 |
κ1 | κ77 | κ1021 | κ869 | κ1013 | κ5 | κ513 | κ1017 | κ1009 | κ9 | κ189 | κ13 | κ301 | κ709 | κ353 | κ193 |
κ209 | κ17 | κ729 | κ1005 | κ393 | κ21 | κ305 | κ1001 | κ645 | κ937 | κ25 | κ385 | κ997 | κ421 | κ817 | κ29 |
κ537 | κ457 | κ993 | κ317 | κ265 | κ637 | κ605 | κ33 | κ989 | κ401 | κ909 | κ149 | κ237 | κ273 | κ37 | κ161 |
κ985 | κ473 | κ545 | κ41 | κ849 | κ981 | κ413 | κ45 | κ977 | κ897 | κ673 | κ397 | κ49 | κ225 | κ749 | κ973 |
κ253 | κ109 | κ965 | κ181 | κ233 | κ53 | κ481 | κ969 | κ665 | κ213 | κ865 | κ57 | κ437 | κ529 | κ345 | κ737 |
κ449 | κ389 | κ61 | κ917 | κ961 | κ493 | κ65 | κ621 | κ957 | κ297 | κ945 | κ145 | κ153 | κ221 | κ69 | κ953 |
κ725 | κ261 | κ549 | κ477 | κ73 | κ949 | κ701 | κ405 | κ81 | κ177 | κ765 | κ941 | κ593 | κ785 | κ321 | κ113 |
κ197 | κ85 | κ349 | κ589 | κ489 | κ577 | κ89 | κ893 | κ933 | κ761 | κ93 | κ657 | κ929 | κ229 | κ721 | κ97 |
κ925 | κ573 | κ165 | κ417 | κ517 | κ101 | κ789 | κ133 | κ921 | κ805 | κ601 | κ525 | κ661 | κ557 | κ105 | κ837 |
κ269 | κ913 | κ597 | κ169 | κ705 | κ117 | κ461 | κ445 | κ905 | κ333 | κ553 | κ125 | κ245 | κ121 | κ357 | κ901 |
κ689 | κ257 | κ521 | κ649 | κ129 | κ561 | κ429 | κ889 | κ733 | κ329 | κ829 | κ717 | κ581 | κ137 | κ885 | κ873 |
κ141 | κ881 | κ501 | κ541 | κ877 | κ777 | κ853 | κ325 | κ157 | κ361 | κ505 | κ569 | κ613 | κ861 | κ669 | κ857 |
κ381 | κ797 | κ629 | κ173 | κ313 | κ845 | κ585 | κ841 | κ425 | κ465 | κ741 | κ185 | κ377 | κ565 | κ833 | κ609 |
κ825 | κ693 | κ201 | κ745 | κ821 | κ757 | κ205 | κ813 | κ441 | κ249 | κ809 | κ485 | κ409 | κ625 | κ217 | κ337 |
κ469 | κ801 | κ685 | κ793 | κ617 | κ773 | κ533 | κ241 | κ681 | κ781 | κ309 | κ497 | κ293 | κ769 | κ509 | κ433 |
κ633 | κ653 | κ753 | κ365 | κ277 | κ281 | κ453 | κ289 | κ285 | κ677 | κ641 | κ713 | κ373 | κ697 | κ369 | κ381 |
Binary form | Decimal | 𝐺𝐹 (28) | Binary form | Decimal | 𝐺𝐹 (28) | Binary form | Decimal | 𝐺𝐹 (28) | Binary form | Decimal | 𝐺𝐹 (28) |
00000000 | 0 | 0 | 00000001 | 1 | 1 | 00000010 | 2 | β1 | 00000100 | 4 | β2 |
00001000 | 8 | β3 | 00010000 | 16 | β4 | 00100000 | 32 | β5 | 01000000 | 64 | β6 |
10000000 | 128 | β7 | 01101001 | 105 | β8 | 11010010 | 210 | β9 | 11001101 | 205 | β10 |
11110011 | 243 | β11 | 10001111 | 143 | β12 | 01110111 | 119 | β13 | 11101110 | 238 | β14 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
10101100 | 172 | β163 | 00110001 | 49 | β164 | 01100010 | 98 | β165 | 11000100 | 196 | β166 |
11100001 | 225 | β167 | 10101011 | 171 | β168 | 00111111 | 63 | β169 | 01111110 | 126 | β170 |
11111100 | 252 | β171 | 10010001 | 145 | β172 | 01001011 | 75 | β173 | 10010110 | 150 | β174 |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
… | … | … | … | … | … | … | … | … | … | … | … |
11010111 | 215 | β243 | 11000111 | 199 | β244 | 11100111 | 231 | β245 | 10100111 | 167 | β246 |
00100111 | 39 | β247 | 01001110 | 78 | β248 | 10011100 | 156 | β249 | 01010001 | 81 | β250 |
10100010 | 162 | β251 | 00101101 | 45 | β252 | 01011010 | 90 | β253 | 10110100 | 180 | β254 |
24 | 41 | 1 | 180 | 2 | 140 | 113 | 52 | 32 | 4 | 190 | 42 | 125 | 102 | 90 | 60 |
8 | 128 | 205 | 45 | 253 | 16 | 250 | 86 | 162 | 109 | 17 | 115 | 244 | 81 | 217 | 64 |
238 | 48 | 101 | 57 | 156 | 59 | 148 | 78 | 35 | 105 | 122 | 98 | 100 | 39 | 210 | 182 |
104 | 167 | 50 | 239 | 46 | 231 | 38 | 13 | 243 | 221 | 213 | 97 | 72 | 132 | 199 | 143 |
248 | 164 | 83 | 215 | 119 | 55 | 214 | 223 | 219 | 181 | 177 | 200 | 3 | 135 | 224 | 235 |
111 | 216 | 6 | 54 | 80 | 99 | 108 | 241 | 12 | 73 | 30 | 94 | 27 | 76 | 149 | 185 |
96 | 232 | 87 | 129 | 192 | 195 | 67 | 116 | 240 | 166 | 233 | 188 | 254 | 23 | 69 | 58 |
7 | 187 | 133 | 51 | 203 | 63 | 212 | 29 | 68 | 31 | 153 | 186 | 62 | 74 | 93 | 79 |
124 | 157 | 28 | 173 | 154 | 141 | 77 | 14 | 92 | 146 | 171 | 91 | 229 | 137 | 144 | 85 |
5 | 155 | 193 | 10 | 82 | 36 | 20 | 168 | 174 | 230 | 18 | 121 | 21 | 40 | 71 | 249 |
227 | 130 | 196 | 9 | 252 | 61 | 176 | 134 | 201 | 160 | 178 | 43 | 88 | 117 | 107 | 44 |
22 | 208 | 11 | 150 | 33 | 19 | 66 | 236 | 114 | 246 | 112 | 202 | 118 | 152 | 34 | 194 |
138 | 251 | 197 | 169 | 237 | 26 | 145 | 158 | 56 | 179 | 95 | 15 | 255 | 161 | 159 | 106 |
234 | 120 | 220 | 198 | 110 | 222 | 147 | 183 | 142 | 218 | 123 | 191 | 228 | 131 | 139 | 151 |
245 | 165 | 89 | 163 | 209 | 189 | 206 | 65 | 47 | 225 | 175 | 103 | 53 | 247 | 207 | 75 |
211 | 136 | 226 | 25 | 170 | 242 | 70 | 184 | 126 | 84 | 172 | 49 | 37 | 127 | 204 | 0 |
102 | 62 | 108 | 235 | 184 | 163 | 44 | 240 | 53 | 89 | 70 | 150 | 160 | 155 | 220 | 164 |
191 | 172 | 135 | 79 | 174 | 109 | 12 | 201 | 144 | 251 | 133 | 186 | 134 | 71 | 228 | 147 |
96 | 14 | 50 | 114 | 65 | 32 | 106 | 120 | 255 | 218 | 94 | 177 | 136 | 233 | 115 | 219 |
226 | 250 | 211 | 176 | 68 | 230 | 6 | 199 | 156 | 61 | 9 | 165 | 26 | 196 | 139 | 41 |
1 | 22 | 209 | 125 | 215 | 180 | 63 | 113 | 193 | 192 | 241 | 43 | 17 | 127 | 20 | 67 |
169 | 208 | 256 | 198 | 33 | 28 | 243 | 54 | 234 | 45 | 247 | 101 | 73 | 202 | 252 | 248 |
246 | 154 | 207 | 78 | 19 | 3 | 232 | 236 | 224 | 131 | 59 | 31 | 171 | 39 | 238 | 34 |
40 | 24 | 142 | 72 | 83 | 217 | 103 | 82 | 187 | 52 | 210 | 23 | 7 | 205 | 124 | 123 |
64 | 110 | 170 | 153 | 57 | 112 | 253 | 189 | 56 | 229 | 188 | 60 | 86 | 42 | 36 | 121 |
30 | 140 | 76 | 168 | 122 | 141 | 97 | 152 | 146 | 137 | 27 | 16 | 162 | 195 | 145 | 25 |
221 | 105 | 111 | 69 | 81 | 13 | 194 | 15 | 107 | 48 | 249 | 119 | 8 | 74 | 254 | 35 |
117 | 128 | 173 | 2 | 18 | 242 | 90 | 84 | 167 | 116 | 143 | 132 | 11 | 26 | 99 | 46 |
138 | 88 | 190 | 77 | 104 | 231 | 200 | 204 | 151 | 197 | 178 | 158 | 183 | 213 | 87 | 222 |
55 | 58 | 92 | 161 | 37 | 95 | 100 | 166 | 157 | 85 | 148 | 245 | 91 | 179 | 181 | 4 |
75 | 214 | 38 | 98 | 212 | 149 | 5 | 130 | 244 | 175 | 21 | 203 | 51 | 227 | 182 | 66 |
185 | 225 | 47 | 10 | 129 | 206 | 118 | 49 | 80 | 223 | 216 | 237 | 239 | 126 | 93 | 159 |
248 | 150 | 195 | 151 | 206 | 38 | 62 | 88 | 213 | 25 | 118 | 250 | 61 | 48 | 134 | 121 |
3 | 33 | 192 | 224 | 175 | 164 | 186 | 187 | 249 | 152 | 18 | 99 | 72 | 5 | 188 | 59 |
80 | 58 | 44 | 144 | 110 | 89 | 23 | 7 | 143 | 137 | 200 | 113 | 73 | 194 | 226 | 160 |
184 | 101 | 53 | 31 | 32 | 241 | 234 | 92 | 154 | 120 | 233 | 91 | 221 | 41 | 214 | 124 |
156 | 75 | 235 | 46 | 9 | 190 | 81 | 51 | 27 | 117 | 245 | 193 | 169 | 129 | 45 | 126 |
252 | 29 | 203 | 236 | 218 | 229 | 159 | 251 | 4 | 66 | 228 | 220 | 204 | 122 | 222 | 238 |
20 | 163 | 34 | 147 | 94 | 24 | 212 | 237 | 130 | 148 | 201 | 1 | 16 | 157 | 196 | 141 |
223 | 57 | 210 | 246 | 22 | 70 | 43 | 78 | 85 | 82 | 79 | 93 | 215 | 127 | 135 | 208 |
170 | 65 | 166 | 202 | 17 | 244 | 205 | 100 | 230 | 138 | 199 | 155 | 36 | 133 | 112 | 162 |
71 | 174 | 64 | 123 | 189 | 42 | 56 | 168 | 173 | 232 | 102 | 243 | 142 | 15 | 0 | 125 |
198 | 21 | 140 | 60 | 97 | 183 | 114 | 10 | 111 | 28 | 254 | 128 | 11 | 253 | 225 | 239 |
98 | 95 | 131 | 55 | 139 | 207 | 255 | 2 | 211 | 115 | 68 | 171 | 14 | 197 | 8 | 181 |
219 | 176 | 40 | 132 | 179 | 54 | 13 | 145 | 86 | 76 | 103 | 158 | 74 | 242 | 87 | 216 |
83 | 153 | 50 | 209 | 161 | 165 | 119 | 172 | 63 | 105 | 182 | 90 | 227 | 106 | 84 | 240 |
136 | 104 | 247 | 217 | 146 | 231 | 26 | 67 | 39 | 12 | 180 | 116 | 49 | 69 | 37 | 52 |
177 | 19 | 108 | 47 | 191 | 96 | 30 | 185 | 178 | 167 | 109 | 149 | 77 | 107 | 35 | 6 |
Boolean mapping | θ0 | θ1 | θ2 | θ3 | θ4 | θ5 | θ6 | θ7 | Mean |
NL score | 110 | 112 | 110 | 112 | 110 | 110 | 110 | 112 | 110 |
0.4844 | 0.5469 | 0.4688 | 0.5625 | 0.5312 | 0.5312 | 0.5156 | 0.4844 |
0.4531 | 0.4844 | 0.5469 | 0.5 | 0.5 | 0.4844 | 0.4844 | 0.5625 |
0.5312 | 0.4688 | 0.5312 | 0.5312 | 0.4375 | 0.4688 | 0.5156 | 0.5 |
0.4375 | 0.5 | 0.5469 | 0.5 | 0.5469 | 0.5312 | 0.4844 | 0.5156 |
0.4531 | 0.5625 | 0.5625 | 0.4688 | 0.4688 | 0.5156 | 0.4375 | 0.5312 |
0.5781 | 0.4844 | 0.5312 | 0.5469 | 0.5156 | 0.5 | 0.5156 | 0.5 |
0.5 | 0.4531 | 0.4531 | 0.4219 | 0.5156 | 0.5469 | 0.5312 | 0.4844 |
0.5 | 0.4844 | 0.5312 | 0.5312 | 0.5 | 0.5312 | 0.4375 | 0.5469 |
- | 110 | 110 | 112 | 112 | 110 | 112 | 110 |
110 | - | 108 | 110 | 112 | 112 | 108 | 110 |
110 | 108 | - | 110 | 112 | 110 | 110 | 112 |
112 | 110 | 110 | - | 110 | 110 | 110 | 112 |
112 | 112 | 112 | 110 | - | 110 | 110 | 110 |
110 | 112 | 110 | 110 | 110 | - | 112 | 110 |
112 | 108 | 110 | 110 | 110 | 112 | - | 112 |
110 | 110 | 112 | 112 | 110 | 110 | 112 | - |
- | 0.4805 | 0.5098 | 0.4941 | 0.4902 | 0.498 | 0.5215 | 0.4824 |
0.4805 | - | 0.5195 | 0.5176 | 0.4922 | 0.4922 | 0.4766 | 0.4902 |
0.5098 | 0.5195 | - | 0.5 | 0.4902 | 0.5137 | 0.4922 | 0.498 |
0.4941 | 0.5176 | 0.5 | - | 0.4961 | 0.5117 | 0.5273 | 0.4902 |
0.4902 | 0.4922 | 0.4902 | 0.4961 | - | 0.4922 | 0.5293 | 0.5195 |
0.498 | 0.4922 | 0.5137 | 0.5117 | 0.4922 | - | 0.4707 | 0.4863 |
0.5215 | 0.4766 | 0.4922 | 0.5273 | 0.5293 | 0.4707 | - | 0.4883 |
0.4824 | 0.4902 | 0.498 | 0.4902 | 0.5195 | 0.4863 | 0.4883 | - |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 |
4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 6 | 4 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 6 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | - |
S-box | Nonlinearity Min Max Average |
SAC | BIC-SAC | BIC-NL | DU | LP | ||
Suggested S-box | 110 | 112 | 110.75 | 0.5051 | 0.4989 | 110.55 | 6 | 0.0781 |
AES [36] | 112 | 112 | 112 | 0.5058 | 0.5046 | 112 | 4 | 0.0625 |
Reference [37] | 106 | 108 | 106.25 | 0.5112 | 0.4975 | 103.93 | 12 | 0.1484 |
Reference [38] | 106 | 110 | 106.5 | 0.5010 | 0.4987 | 103.93 | 10 | 0.125 |
Reference [39] | 106 | 108 | 107 | 0.4949 | 0.5019 | 102.29 | 12 | 0.141 |
Reference [40] | 106 | 110 | 108.5 | 0.4995 | 0.5011 | 103.85 | 10 | 0.109 |
Reference [41] | 108 | 110 | 109.75 | 0.5042 | 0.4987 | 110.6 | 6 | 0.0859 |
Reference [42] | 102 | 110 | 106.5 | 0.4943 | 0.5019 | 103.35 | 12 | 0.1468 |
Reference [43] | 104 | 108 | 105.5 | 0.5065 | 0.5031 | 103.57 | 10 | 0.1328 |
Reference [44] | 104 | 110 | 107 | 0.4993 | 0.5050 | 103.29 | 10 | 0.1328 |
Image | Correlation | Entropy | Energy | Homogeneity | Contrast |
Cameraman Host | 0.9227 | 7.0097 | 0.1805 | 0.8952 | 0.5871 |
Cameraman-Enc | 0.0394 | 7.9972 | 0.0149 | 0.3999 | 10.0509 |
Pepper Host | 0.9312 | 7.5326 | 0.1096 | 0.8880 | 0.3849 |
Pepper-Enc | 0.0021 | 7.9972 | 0.0156 | 0.3902 | 10.4802 |
Baboon Host | 0.7983 | 7.2649 | 0.0943 | 0.7820 | 0.6326 |
Baboon-Enc | 0.0071 | 7.9975 | 0.0156 | 0.3945 | 10.3994 |
Lena Host | 0.9024 | 7.4439 | 0.1127 | 0.8622 | 0.4482 |
Lena-Enc | − 0.0379 | 7.9976 | 0.0157 | 0.3822 | 10.8896 |
Image | Cameraman | Pepper | Baboon | Lena | |
Vertical | Plain Image | 0.9745 | 0.9137 | 0.9090 | 0.9321 |
Distorted Image | 0.0310 | − 0.0392 | − 0.0128 | − 0.0117 | |
Horizontal | Plain Image | 0.9610 | 0.9204 | 0.8727 | 0.883 |
Distorted Image | − 0.0026 | − 0.0015 | 0.0039 | − 0.0021 |
Test | Cameraman-Enc | Pepper-Enc | Baboon-Enc | Lena-Enc |
MSE | 9212.16 | 8656.41 | 7854.44 | 8414.71 |
MSE [6] | 9079.09 | 8190.01 | 8011.23 | 8239.51 |
MSE [15] | 9189.41 | 8612.09 | 7599.03 | 7930.39 |
MSE [17] | 9187.38 | 8423.61 | 7865.21 | 8274.13 |
PSNR | 8.4723 | 8.8563 | 9.8912 | 8.9912 |
PSNR [6] | 8.1129 | 8.9710 | 8.5539 | 9.1902 |
PSNR [15] | 8.2897 | 8.7091 | 8.1331 | 8.9500 |
PSNR [17] | 8.2891 | 8.3353 | 8.9361 | 8.0032 |
SSIM1 | 0.0009 | 0.0012 | 0.0010 | 0.0011 |
SSIM1 [6] | 0.0013 | 0.0008 | 0.0011 | 0.0012 |
SSIM1 [15] | 0.0010 | 0.0012 | 0.0008 | 0.0014 |
SSIM1 [17] | 0.0009 | 0.0015 | 0.0012 | 0.0013 |
NCC | 0.8633 | 0.8710 | 0.9121 | 0.8803 |
NCC [6] | 0.8537 | 0.8675 | 0.8912 | 0.9016 |
NCC [15] | 0.8733 | 0.8712 | 0.8543 | 0.8461 |
NCC [17] | 0.8640 | 0.87134 | 0.9001 | 0.8692 |
AD | −7.4523 | −4.9812 | −2.3419 | −5.3881 |
AD [6] | −3,4511 | −5.6634 | −1.4529 | −2.3319 |
AD [15] | −6,7819 | −3.8873 | −2.8827 | −4.1198 |
AD [17] | −3.4429 | −4.9821 | −2.3872 | −7.6594 |
SC | 0.8496 | 0.8345 | 0.8456 | 0.8247 |
SC [6] | 0.8455 | 0.8451 | 0.8401 | 0.8342 |
SC [15] | 0.8341 | 0.8489 | 0.8465 | 0.8231 |
SC [17] | 0.8436 | 0.8111 | 0.8265 | 0.8490 |
MD | 240 | 238 | 212 | 234 |
MD [6] | 211 | 231 | 233 | 241 |
MD [15] | 223 | 227 | 227 | 228 |
MD [17] | 234 | 238 | 221 | 219 |
NAE | 0.6358 | 0.6273 | 0.6147 | 0.6384 |
NAE [6] | 0.6455 | 0.5932 | 0.5813 | 0.6459 |
NAE [15] | 0.6040 | 0.6193 | 0.6388 | 0.6026 |
NAE [17] | 0.6219 | 0.6243 | 0.6012 | 0.5856 |
RMSE | 94.6682 | 91.7245 | 84.9561 | 87.9349 |
RMSE [6] | 90.6638 | 92.3402 | 88.3476 | 86.7938 |
RMSE [15] | 93,4428 | 89.7690 | 91.2398 | 87.3947 |
RMSE [17] | 90.4582 | 85.1109 | 84.8934 | 88.1831 |
UQI | 0.0218 | 0.0332 | 0.0314 | 0.0338 |
UQI [6] | 0.0127 | 0.0412 | 0.0279 | 0.0178 |
UQI [15] | 0.0347 | 0.0456 | 0.0127 | 0.0391 |
UQI [17] | 0.0234 | 0.0401 | 0.0298 | 0.0281 |
MI | −1.0292 | −1.0187 | −1.0184 | −1.0281 |
MI [6] | −1.0195 | −1.0490 | −1.0328 | −1.0402 |
MI [15] | −1.0371 | −1.0197 | −1.0294 | −1.0406 |
MI [17] | −1.341 | −1.0198 | −1.0384 | −1.0327 |
Image | NPCR | UACI | BACI |
Cameraman | 99.63% | 33.12% | 24.60% |
Pepper | 99.81% | 33.21% | 26.38% |
Baboon | 99.76% | 32.86% | 24.25% |
Lena | 99.79% | 33.16% | 23.09% |