CMC CMC CMC Computers, Materials & Continua 1546-2226 1546-2218 Tech Science Press USA 27655 10.32604/cmc.2022.027655 Article Construction and Optimization of TRNG Based Substitution Boxes for Block Encryption Algorithms Construction and Optimization of TRNG Based Substitution Boxes for Block Encryption Algorithms Construction and Optimization of TRNG Based Substitution Boxes for Block Encryption Algorithms KhanMuhammad Fahad 1 2mfkhan@cs.qau.edu.pk SaleemKhalid 1 AlotaibiMohammed 3 HazzaziMohammad Mazyad 4 RehmanEid 2 AbbasiAaqif Afzaal 2 GondalMuhammad Asif 5 Quaid e Azam University, Islamabad, 45320, Pakistan Foundation University Islamabad, Islamabad, 44000, Pakistan College of Business Administration, University of Tabuk, Tabuk, 71491, Saudi Arabia Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia Department of Mathematics and Sciences, Dhofar University, Salalah, 211, Oman Corresponding Author: Muhammad Fahad Khan. Email: mfkhan@cs.qau.edu.pk 14 06 2022 73 2 2679 2696 22 1 2022 30 3 2022 © 2022 Khan et al. 2022 Khan et al. This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Internet of Things is an ecosystem of interconnected devices that are accessible through the internet. The recent research focuses on adding more smartness and intelligence to these edge devices. This makes them susceptible to various kinds of security threats. These edge devices rely on cryptographic techniques to encrypt the pre-processed data collected from the sensors deployed in the field. In this regard, block cipher has been one of the most reliable options through which data security is accomplished. The strength of block encryption algorithms against different attacks is dependent on its nonlinear primitive which is called Substitution Boxes. For the design of S-boxes mainly algebraic and chaos-based techniques are used but researchers also found various weaknesses in these techniques. On the other side, literature endorse the true random numbers for information security due to the reason that, true random numbers are purely non-deterministic. In this paper firstly a natural dynamical phenomenon is utilized for the generation of true random numbers based S-boxes. Secondly, a systematic literature review was conducted to know which metaheuristic optimization technique is highly adopted in the current decade for the optimization of S-boxes. Based on the outcome of Systematic Literature Review (SLR), genetic algorithm is chosen for the optimization of s-boxes. The results of our method validate that the proposed dynamic S-boxes are effective for the block ciphers. Moreover, our results showed that the proposed substitution boxes achieve better cryptographic strength as compared with state-of-the-art techniques.

 IoT security sensors data encryption substitution box generation True Random Number Generators (TRNG) heuristic optimization genetic algorithm Introduction

IoT created a new paradime by connecting various devices and everyday objects to the network but now days IoT devices have facing serious security issues to protect the confidentiality of transmitted data. Block ciphers are most reliable option for ensuring the data confidentiality. The strength of block ciphers against different attacks depends on their substitution boxes which provides confusion in the cryptosystem. S-box is a mapping of n-bits inputs to m-bits output and it can be seen as a Boolean function and this can be viewed as F:F2n⟶F2m. In the literature mainly algebraic methods and chaotic maps are used for the construction of S-boxes although there methods have favorable characteristics for S-box designs but many researchers pointed weaknesses in these methods such as Short Quantity of randomness [1–6], Interpolation attacks [7–10], eXtended Sparse Linearization (XSL) attack [11–15], Initial state limitation [16,17], Frail chaos [18,19], Small number of input parameters [20–23], Dynamical degradation [24–27], Gröbner basis attack [27–29], eXtended Linearization(XL) attacks [30–37].

On the other side, randomness is a fundamental aspect of many processes in nature and an indubitably valuable resource for cryptography. Researchers endorse the true random numbers in cryptography due to the fact that true random numbers are irreversible, unpredictable, and unreproducible even if their internal structure and response history is known to the adversaries. We are using the lightning strike phenomenon as an entropy source to generate true random numbers. In this research first of all, we intake the locations of lightning strikes in the row data format from the standard repository of National Aeronautics and Space Administration(NASA) which name is Lightning Detection and Ranging System (LDAR) [38]. Secondly, a novel technique is proposed for the generation of TRNG based substitution boxes. Thirdly genetic algorithm applied for the optimization of newly generated S-boxes but before this phase, a systematic literature review was conducted to know which metaheuristic optimization technique is highly adopted in the last 10 years. Based on the outcome of SLR, a genetic algorithm is chosen. The remaining paper is structured as follows; Sections 2 and 3 present our contribution and the proposed methodology respectively, Section 4 explains the results and evaluation section, Section 5 shows the conclusion section.

 Contribution

The main contributions of this research are follows:

A novel method is proposed for the generation of substitution boxes of symmetric encryption algorithms based on true random numbers.

Multi population genetic algorithm is applied for optimization of substitution boxes.

A systematic literature review was conducted to know which metaheuristic optimization technique is highly adopted in the last 10 years for the optimization of cryptographic substitution boxes.

A novel technique proposed for the true random numbers generation.

Proposed Design Methodology

The proposed technique has three phase’s first phase is true random bits extraction, second phase is construction of substitution boxes and the third phase is optimization of substitution boxes. These three phases are explained in the following and the proposed system architecture is depicted in Fig. 1.

Proposed system architecture True Random Bits Extraction

To calculate the difference between each location of the lightning strike with other lightning strike locations, firstly we acquire the lightning strike locations (in the row data format) from the standard repository of NASA [38]. Lightning detection and the ranging system is a volumetric lightning mapping system, which stores the real-time location of the striking point. The format of the row data is dd,hh,mm,ss,ll,xx,yy, zz, where dd represents the day of the month, hh represents the hour, mm represents the minute, ss represents second, ll represents microsecond. xx and yy represent the distance in meters from site-1 to the east direction and north direction respectively where zz represents the distance in meters above the surface of the earth. Secondly, each location of the 1st lightning strike is subtracted from the other locations of the lightning strikes. For the experiment, data of the randomly picked 9613227 lightning strikes are processed from the proposed algorithm and then resultant binary stream enhanced through the Von Neumann extractor, after this, these random bits are tested through the National Institute of Standards and Technology (NIST) statistical test suite. Results of the NIST statistical test (shown in Appendix A) proved that lightning strikes are useful entropy source for the generation of true random numbers.

 Construction of Substitution Boxes

In the first step of dynamic substitution boxes construction, an algorithm proposed which name is SboxConstruction(). This algorithm takes, true random bits from the last phase and a total number of required S-boxes from the user as parameters. In the second step SboxConstruction() algorithm, further calls the RandomWalk() algorithm by passing the two-dimensional N * N space of truly random bits. On every run RandomWalk() algorithm generates a single dynamic s-box by using the 8 states random walk rule ( left = 0, left up = 1, up word = 2, right up = 3, right = 4, right down = 5, down = 6, left down = 7). SboxConstruction() algorithm is presented in the above. Randomly we plotted the two RandomWalk() runs as sample in the Figs. 2a and 2b and their resultant S-boxes in the Tabs. 1a and 1b. For the results, the total number of ten thousand S-boxes are constructed, where the nonlinearity score of 1674 S-boxes are ≤ 99, nonlinearity score of 3277 S-boxes are between 100 to 102, nonlinearity score of 4126 S-boxes are between 103 to 104, nonlinearity score of 923 S-boxes are between 105 to 106. The nonlinearity score of our sample S-boxes 2a, 2b is 105 and 104 respectively. As sample TRNG based S-box is shown in the Appendix B.

Proposed Sbox-1
155 253 60 189 42 238 93 209 202 129 164 75 240 85 151 254
44 138 251 28 223 230 95 62 231 121 149 31 180 57 161 73
203 72 84 227 218 210 56 243 245 190 135 9 69 255 219 166
140 198 239 225 250 143 120 63 134 103 186 207 2 64 27 144
241 37 108 92 98 65 220 79 4 249 228 24 205 10 102 156
8 122 119 185 188 58 236 216 226 17 217 13 35 237 78 242
80 33 127 125 14 83 192 66 221 169 48 112 59 100 146 74
199 97 141 52 173 107 224 68 55 152 247 110 157 181 170 196
131 32 104 86 96 128 50 208 158 244 214 159 234 142 22 118
81 43 6 89 187 7 177 67 204 171 5 235 195 123 0 139
109 3 178 172 18 54 76 53 99 88 212 46 21 39 15 201
101 87 246 184 165 233 105 179 232 206 49 70 252 126 191 147
114 71 229 26 1 29 132 248 91 154 25 211 16 106 34 111
116 183 168 117 193 51 47 137 115 200 174 153 133 20 213 194
45 40 124 150 130 11 77 175 12 222 19 160 30 182 82 41
61 113 36 167 38 136 145 163 90 94 162 23 215 176 197 148
Proposed Sbox-2
211 238 81 126 89 185 244 26 139 143 23 73 209 102 132 120
34 174 78 159 165 114 138 181 10 28 221 250 44 189 110 191
155 128 223 75 164 72 214 108 25 245 201 213 2 109 178 144
216 96 123 196 197 121 150 86 35 169 27 90 166 163 56 158
117 147 15 6 47 17 100 252 57 79 156 212 198 218 131 162
101 186 30 104 242 202 146 122 133 253 103 130 87 16 192 168
54 205 125 149 33 107 153 32 129 179 12 173 251 157 195 42
224 227 20 207 180 36 145 84 231 200 255 61 97 43 170 91
11 49 210 148 204 24 13 215 52 46 183 193 171 154 222 88
137 94 85 40 167 95 140 45 106 237 99 74 234 175 21 151
4 119 77 184 105 92 83 243 177 226 51 134 39 182 68 236
82 118 248 0 70 247 55 67 37 8 230 136 48 208 188 142
41 232 246 235 71 113 127 69 5 116 22 249 64 80 93 50
53 219 1 161 76 160 172 176 225 63 152 254 187 115 98 239
31 29 62 220 18 112 206 194 229 241 240 217 228 111 141 38
135 203 3 233 19 65 14 190 199 58 66 59 60 9 124 7
Optimized Sbox-3
162 5 201 199 126 220 204 9 155 242 2 39 166 221 133 15
63 192 73 164 254 23 11 185 247 34 98 149 40 22 96 33
176 75 113 53 50 165 44 29 132 156 169 206 225 85 0 208
36 103 64 218 198 122 137 136 104 159 118 88 154 32 193 57
183 135 160 24 228 152 234 172 17 177 232 70 175 210 14 31
142 188 227 141 151 76 219 131 119 197 212 251 65 100 97 145
190 68 158 110 214 61 146 116 3 238 101 49 181 54 239 92
179 147 30 143 109 170 223 215 157 51 250 106 153 13 241 79
129 140 78 18 248 6 196 252 58 89 184 134 115 59 203 124
81 112 195 84 74 235 82 28 105 243 237 230 95 173 80 94
138 83 66 12 38 45 87 10 191 121 86 99 189 217 249 168
236 102 231 1 205 107 62 202 233 253 27 56 144 72 8 125
167 55 128 25 255 229 187 178 35 246 171 226 26 240 47 16
211 77 117 41 20 67 123 180 111 91 174 224 7 46 52 127
120 108 182 244 222 207 150 60 130 148 42 139 194 93 21 216
209 161 48 245 4 37 19 43 114 90 69 213 186 71 163 200
Plotted S-boxes (a) 8-steps random walk of Sbox-1 (b) 8-steps random walk of Sbox-2 Optimization of Substitution Box

The most important strength of true random-based construction of S-boxes is that, these S-boxes are immune against the attacks which are mentioned in the introduction section. This is our first goal which is achieved in the above Sections 3.2 by using the true randomness. The 2nd goal of this research is to find out, which metaheuristic optimization technique is effective (highly adopted) in existing literature for the optimization of S-boxes (which are not based on true randomness). To discover the answer to this question, a SLR was conducted over the last 10 years. Query wise search results of SLR is mentioned in the Tab. 2 and based on the SLR recommendation, a technique is presented in the following for the optimization of newly constructed S-boxes using the genetic algorithm. Reverse S-box algorithm for the TRNG and GA based S-boxes is shown in the Appendix C.

Query wise search results
Query IEEE Springer ACM Elsevier
Genetic algorithm and S-boxes 14 241 33 62
Genetic algorithm and substitution box 5 93 24 29
Genetic algorithm and nonlinear block cipher primitive 4 0 66 0
Genetic algorithm and confusion component 5 3 54 0
Simulate annealing and S-boxes 4 99 13 19
Simulate annealing and substitution box 1 39 9 6
Simulate annealing and nonlinear block cipher primitive 0 0 14 0
Simulate annealing and confusion component 0 0 17 0
Tabu search and substitution box 0 4 10 2
Tabu search and S-boxes 2 9 12 8
Tabu search and nonlinear block cipher primitive 0 8 14 0
Tabu search and confusion component 0 0 14 0
Particle swarm optimization and S-boxes 2 79 51 21
Particle swarm optimization and substitution box 1 30 48 8
Particle swarm optimization and nonlinear block cipher primitive 0 0 48 0
Particle swarm optimization and confusion component 5 0 39 0
Artificial bee colony optimization and substitution box 1 9 48 1
Artificial bee colony optimization and S-boxes 2 8 50 3
Artificial bee colony optimization and nonlinear block cipher primitive 0 0 1 0
Artificial bee colony optimization and confusion component 0 0 6 0

GA is based on the Charles Darwin’s theory of natural selection and survival of the fittest In the standard genetic algorithm, selection, crossover, and mutation are the common processes. In our problem for the selection process, all the substitution boxes whose nonlinearity score lies in the range of 100 to 106 are acquired as the initial population. For the crossover process, we used the one-point crossover strategy in which pair of parents exchange the half part of each parent to each other and generate new offspring. Complete crossover process is represented with yellow color in the flowchart which is depicted in Fig. 1. Widely in the literature [39–44], the nonlinearity score is the highly desirable property that’s why we also chose the nonlinearity score as the fitness value. In the conventional genetic algorithm, crossover and mutation are the two independent processes but here for the substitution box generation, we combine the crossover and mutation process together. The reason is that, the substitution boxes generated by the crossover operation usually do not satisfy the bijective property due to repeated elements. So, repetition must be removed from the new offspring to achieve the bijective property and for that purpose, a simple strategy is adopted in the mutation process. In the mutation process we flipped the one bit from right side to the left side, and after flipping each bit, the corresponding number is checked within the s-box. If the corresponding number is unique, then we stop the flipping process, otherwise we flip the next bit and so on. In the numerous cases, we achieved the bijective property but in the few cases after flipping the eight bits, we did not get the unique element of the s-box and in those cases, we simply add one to the original element from where we start the flipping process. The mutation process is represented with green color in the flowchart of Fig. 1. From the results, we observed that numerous S-boxes and their subsets are repeated therefore we used SHA-3 based searching for removal and this process is shown with blue color in the flowchart. Here, for the experiment hundred thousand S-boxes are optimized and to examine the performance, we compared the highest quality ten thousand optimized S-boxes with the ten thousand S-boxes which are already constructed through the TRNG based technique. After optimization, it can be clearly seen from Fig. 3 that GA improves the overall quality of the S-Boxes. After optimization process, there are no S-box having non-linearity of less than and equal to 99 where TRNG based S-box construction technique 1674 S-boxes in that range. Similarly, GA produce more S-boxes in the range of 105 and 106 as compared to TRNG construction method. Furthermore, GA produce 616 new S-boxes having non-linearity of 107 and 108 and these S-Boxes were not discovered in TRNG based approach.

Nonlinearity score of TRNG and GA based S-box construction Results and Evaluation

In this section sample S-boxes of Section 3.2 are evaluated through the S-box evaluation criteria which are shown in the following 4.1 to 4.5.

Nonlinearity

Out of all cryptographic properties, nonlinearity is said to be the most significant. For a strong encryption scheme, the mapping between input and output in an S-box must be nonlinear. Nonlinearity can be defined as the smallest distance of Boolean function to the set of affine functions. To get the closet affine function in the Boolean truth table, the total number of bits altered needs to be determined by the nonlinearity score. In the above Fig. 3 we saw that six hundred sixteen S-boxes attains a 108 nonlinearity score and from these S-boxes, we picked randomly one S-box as a sample which is shown in Tab. 1c. The Nonlinearity scores of proposed S-boxes are better or equal to the state-of-the-art. S-boxes which are shown in Tab. 3. By using Walsh spectrum, the nonlinearity of Boolean function is determined as:

Ng=2n−1(1−2−nmaxφϵGF(2n)|S(g)(φ)|)

where S(g)(φ)is defined as:S(g)(φ)=∑φ∈GF(2n)(−1)g(x)⊕x.φwhere φ is a n-bit vector and φ∈GF(2n). The dot product between x and φ is denoted by x.φ

x.φ=x1⊕φ1+x2⊕φ2⋅+ xn ⊕φn.

Nonlinearity of various S-boxes
S-box Nonlinearity S-box Nonlinearity
Ozkaynak [45], 2020 104 EI-Latif [46], 2020 107
Zahir et al. [47], 2020 104 EI-Latif [48], 2020 106
Faheem et al. [49], 2020 104 Liu et al. [50], 2017 108
Akram et al. [51], 2017 108 Özkaynak [52], 2018 108
Ünal et al. [53], 2017 106 Solami et al. [54] 2018 108
Lambić et al. [55], 2017 108 Lambić [56], 2020 106
Strict Avalanche Criteria (SAC)

SAC computes the number of output bits altered caused by inverting a single bit of input. To make the system more reliable, we need to deviate output vector with half probability when one input bit is inverted. To evaluate the SAC property, dependency matrix are used. For an S-box that can satisfy SAC property, all values need to be close to ideal value of 0.5 in its dependence matrix. The SAC value of our randomly picked optimized S-box is 0.501465 which satisfies the avalanche criteria. The offsets of the dependence matrix can be determined by:

S(g)=1n2∑1≤r≤n∑1≤w≤n|12−Qr,w(g)|

where Qr,w(g)=2−n∑xϵBngw(x)⊕gw(x⊕er)

er=[θr,1 θr,2…θr,n]Tθr,w=0,r≠w or θr,w=1,r=w

 BIT Independent Criterion (BIC)

BIC is another cryptographic metric used to measure the efficiency of S-boxes. For an S-box to satisfy the BIC property, all avalanche variables should be independent pair wise for a number of avalanche vectors created by modifying a single bit of plaintext. BIC states that reversing the input bit i modifies the output bits j and k in such a way that the no dependency lies between output bits. This would tend to improve the confusion function’s effectiveness. To satisfy the BIC property, the output bits must exhibits independent behavior. Therefore, efforts are being made to decrease the dependency of output bits. The correlation coefficient is used to calculate the degree of independence among avalanche variable pairs. The bit independence of the jth and kth bits of Bei is:

BIC(bj,bk)=max1≤i≤n|corr(bjei,bjei′|

S-box function (h) is defined as: h: {0, 1}n →{0, 1}n .BIC parameter for the S-box function is expressed as follows:

BIC(h)=max1≤j,k≤nBIC(bj,bk)

Average SAC-BIC score of our optimized S-box is 0.49937. Which is almost optimal and indicates that proposed S-box fulfills the required criteria.

 Linear Approximation Probability (LP)

LP is used to evaluate the security of S-box against linear cryptanalysis. S-box provides diffusion and confusion of bits through linear mapping between input and output. Maximum imbalance of an event is determined by LP. The input bit’s parity given by the mask γ1 is equal to the output bit’s parity given by the mask γ2. Linear approximation probability is represented as:

LP=maxγ1,γ2≠0|{xεX|x.γ1=S(x).γ2}2n−12|where the input mask is represented by γ1, γ2 represents the output mask. These masks are used to calculate the linear approximation probability. X denotes the set of all possible inputs and 2n is the total number of elements in the S-Box. An S-box having low linear probability represents high nonlinear mapping and have high resistance against linear cryptanalysis. The maximum optimized S-box LP value is 0.140625 which fulfills the desired criterion.

 Differential Approximation Probability (DP)

Differential approximation probability means that output shall have a difference of Δy every time the input is changed by Δx. DP examines the XOR distribution between input and output bit. Variations in output can be obtained from variations in input. For resilience against differential attacks, XOR values of all outputs and inputs must have equal probability. The exclusive-OR distributions among the inputs and outputs of S-box is calculated by:

DP (Δx⟶Δy)=[#{xεX|(S(x)⊕S(x⊕Δx)=Δy}2n]where X represents the set of all possible input values, 2n is a total number of all the elements in the S-box, Δx and Δy are the input and output differentials. S-boxes with small differentials values are strong and good at resisting differential cryptanalysis. The DP results of Sbox1 are following in the Tab. 4, and we can see that our proposed S-box fulfils the DP criteria.

DP of the S-box1
.000000 .023438 .023438 .023438 .031250 .023438 .023438 .023438 .031250 .023438 .023438 .023438 .023438 .023438 .031250 .023438
.023438 .023438 .023438 .023438 .023438 .031250 .023438 .031250 .023438 .031250 .023438 .023438 .023438 .023438 .031250 .023438
.023438 .015625 .031250 .023438 .023438 .039062 .031250 .023438 .023438 .023438 .023438 .023438 .023438 .023438 .023438 .023438
.023438 .023438 .031250 .031250 .023438 .031250 .023438 .031250 .031250 .031250 .031250 .023438 .031250 .023438 .031250 .046875
.039062 .023438 .031250 .023438 .023438 .039062 .023438 .023438 .031250 .031250 .023438 .023438 .023438 .023438 .023438 .031250
.023438 .031250 .023438 .023438 .023438 .023438 .031250 .031250 .023438 .023438 .023438 .031250 .031250 .031250 .023438 .023438
.023438 .031250 .023438 .023438 .023438 .023438 .023438 .031250 .039062 .023438 .039062 .023438 .031250 .031250 .031250 .023438
.039062 .023438 .023438 .023438 .023438 .023438 .023438 .023438 .023438 .023438 .023438 .023438 .023438 .023438 .031250 .023438
.023438 .023438 .039062 .031250 .023438 .023438 .023438 .023438 .023438 .039062 .023438 .023438 .039062 .031250 .023438 .023438
.023438 .023438 .031250 .031250 .023438 .023438 .023438 .023438 .023438 .023438 .031250 .031250 .023438 .023438 .023438 .031250
.023438 .023438 .031250 .023438 .023438 .023438 .031250 .023438 .023438 .023438 .031250 .039062 .023438 .031250 .031250 .023438
.023438 .023438 .023438 .023438 .023438 .031250 .023438 .023438 .023438 .031250 .023438 .023438 .023438 .023438 .031250 .023438
.031250 .039062 .031250 .023438 .023438 .039062 .031250 .023438 .039062 .031250 .023438 .023438 .031250 .031250 .023438 .031250
.031250 .023438 .023438 .023438 .023438 .031250 .023438 .023438 .023438 .023438 .023438 .031250 .023438 .023438 .023438 .023438
.023438 .031250 .031250 .023438 .023438 .031250 .023438 .023438 .023438 .031250 .031250 .023438 .023438 .031250 .031250 .023438
.023438 .023438 .031250 .023438 .031250 .015625 .039062 .023438 .023438 .031250 .023438 .023438 .039062 .031250 .023438 .023438
Substitution Permutation based Image Encryption

In this section simple Substitution Permutation Network (SPN) used for the image encryption. Detailed steps of the SPN are mentioned bellow. Here for the substitution step optimize S-boxes of the Section 3.3 used, we used the P-boxes and keys from the [57].

Step-1: Extract the Red, Green and Blue channel values from the color image frames and repeat the following steps-2 to step-4 for every channel(R or G or B).

Step-2: Perform the bitwise XOR between the plain pixel values and sub keyi to obtain the key additive pixel values.

Step-3: Replace each value of step-2 with entries of the optimized (Sboxi) values.

Step 4: Diffuse the each value of step-3 by using (P-boxi) values.

Step 5: Repeat step-2 to step-4 for i<16.

Step 6: Combine the individual R, G, B encrypted pixel values into a single frame.

The NPCR and UACI are the two frequently used tests of the image cipher to check the strength against various attacks. NPCR, UACI are used to evaluate a large number of plain images to measure the impact of pixel change on the encrypted images. We examined the image encryption results on various standard color images (Lena, pepper, nature, bird, baboon, grapes, sparrow, butterfly). Ideal image encryption algorithm must produce different results when a pixel of the image is slightly varied. NCPR is the rate of change in the number of pixels between two encrypted images obtained from two slightly different images. To achieve maximum sensitivity in an algorithm the value of NCPR should close to 100%. UAIC measure the mean variation of pixel intensity of two encrypted images at same location. Following Tab. 5 indicates the values of NPCR and UACI. Constantly our NPCR values are around to 99.63 which is the very good value. Similarly the UACI values are around 33.5 which is also the good value.

NPCR and UACI results
Images Location NPCR UACI Images Location NPCR UACI
Proposed Proposed Proposed Proposed
Lena R 99.6221 33.5514 Baboon R 99.6578 33.6534
G 99.6127 33.5158 G 99.6256 33.6385
B 99.5517 33.5212 B 99.6344 33.7265
Pepper R 99.6231 33.4525 Grapes R 99.6231 33.7596
G 99.6462 33.4642 G 99.6652 32.7821
B 99.6652 33.4935 B 99.6632 33.5063
Nature R 99.5925 33.6789 Sparrow R 99.6551 33.4798
G 99.6186 33.4987 G 99.6225 33.4125
B 99.6245 33.6506 B 99.6432 32.9098
Bird R 99.6621 33.4065 Butterfly R 99.6591 33.5215
G 99.6651 32.9154 G 99.6652 32.9952
B 99.6266 32.9365 B 99.6063 33.0563
Conclusion

The IoT-based computationally intelligent schemes are expanding due to the growing concerns of privacy leakage and security attacks in connected systems. It has added a new potential to the internet by enabling communications between objects and humans, making a smarter and more intelligent ecosystem. In this regard, block encryption algorithms have been a standout amongst the most reliable option by which data security is accomplished. The strength of block encryption algorithms against different attacks is dependent on its nonlinear primitive which is called S-boxes. The objective of this research is dynamic generation and optimization of highly secure S-boxes for the block encryption algorithms. For this purpose we used the true random numbers as the entropy source of the proposed method because true random numbers are irreversible, unpredictable, and unreproducible. The proposed method passes all the security evaluation criteria including nonlinearity, linear approximation probability, differential approximation probability, strict avalanche criterion, bit independence criterion, differential analysis, histogram analysis, correlation coefficient tests, NPCR, and UACI tests. The results of our method validate that the proposed dynamic s-boxes are effective for the block encryption algorithms. In the future, we will extend this research to the design of cryptographic key generation technique for the IoT systems.

We thank the R. G. P. 2/132/42, NASA Global Hydrology Resource Center DAAC DOI: http://dx.doi.org/10.5067/LIS/LDAR/DATA101. Accessed on Dec 04, 2021.

Funding Statement: The authors received no specific funding for this study.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

 References M. F. Khan, A. Ahmed and K. Saleem, “A novel cryptographic substitution box design using gaussian distribution,” IEEE Access, vol. 7, no. 4, pp. 15999–16007, 2019. M. F. Khan, A. Ahmed, K. Saleem and T. Shah, “A novel design of cryptographic SP-network based on gold sequences and chaotic logistic tent system,” IEEE Access, vol. 7, no. 1, pp. 84980–84991, 2019. X. Wu, D. Wang, J. Kurths and H. Kan, “A novel lossless color image encryption scheme using 2D DWT and 6D hyperchaotic system,” Information Sciences, vol. 349, no. 10, pp. 137–153, 2016. E. Y. Xie, C. Li, S. Yu and J. Lü, “On the cryptanalysis of Fridrich’s chaotic image encryption scheme,” Signal Processing, vol. 132, no. 2, pp. 150–154, 2017. R. Zahmoul, R. Ejbali and M. Zaied, “Image encryption based on new beta chaotic maps,” Optics and Lasers in Engineering, vol. 96, no. 3, pp. 39–49, 2017. Z. Hua, F. Jin, B. Xu and H. Huang, “2D LogisticSine-coupling map for image encryption,” Signal Processing, vol. 149, no. 3, pp. 148–161, 2018. R. Lan, J. He, S. Wang, T. Gu and X. Luo, “Integrated chaotic systems for image encryption,” Signal Processing, vol. 147, no. 2, pp. 133–145, 2018. Y. Zhou, Z. Hua, C. M. Pun and C. L. Philip Chen, “Cascade chaotic system with applications,” IEEE Transaction in Cybernetics, vol. 45, no. 9, pp. 2001–2012, 2015. M. Alawida, J. S. Teh, A. Samsudin and W. H. Alshoura, “An image encryption scheme based on hybridizing digital chaos and finite state machine,” Signal Processing, vol. 164, no. 1, pp. 249–266, 2019. Y. Liu, Y. Luo, S. Song, L. Cao, J. Liu et al., “Counteracting dynamical degradation of digital chaotic chebyshev map via perturbation,” International Journal of Bifurcation and Chaos, vol. 27, no. 3, pp. 1750033, 2017. C. Pak and L. Huang, “A new color image encryption using combination of the 1D chaotic map,” Signal Processing, vol. 138, no. 2, pp. 129–137, 2017. R. Parvaz and M. Zarebnia, “A combination chaotic system and application in color image encryption,” Optical Laser Technology, vol. 101, pp. 30–41, 2018. Y. Zhou, L. Bao and C. L. P. Chen, “A new 1D chaotic system for image encryption,” Signal Processing, vol. 97, no. 11, pp. 172–182, 2014. Y. Deng, H. Hu, N. Xiong, W. Xiong and L. Liu, “A general hybrid model for chaos robust synchronization and degradation reduction,” Information Sciences, vol. 305, pp. 146–164, 2015. C. Li, “Cracking a hierarchical chaotic image encryption algorithm based on permutation,” Signal Processing, vol. 118, no. 3, pp. 203–210, 2016. C. Li, B. Feng, S. Li, J. Kurths and G. Chen, “Dynamic analysis of digital chaotic maps via state-mapping networks,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 6, pp. 2322–2335, 2019. W. Zhang and E. Pasalic, “Highly nonlinear balanced S-boxes with good differential properties,” IEEE Transaction in Information Theory, vol. 60, no. 12, pp. 7970–7979, 2014. D. Arroyo, J. Diaz and F. B. Rodriguez, “Cryptanalysis of a one round chaos-based substitution permutation network,” Signal Processing, vol. 93, no. 5, pp. 1358–1364, 2013. G. Chen, Y. Chen and X. Liao, “An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps,” Chaos Solitons and Fractals, vol. 31, no. 3, pp. 571–579, 2007. M. Alawida, A. Samsudin, J. Sen Teh and R. S. Alkhawaldeh, “A new hybrid digital chaotic system with applications in image encryption,” Signal Processing, vol. 160, no. 8, pp. 45–58, 2019. L. Y. Zhang, X. Hu, Y. Liu, K. W. Wong and J. Gan, “A chaotic image encryption scheme owning temp-value feedback,” Communication in Nonlinear Science and Numerical Simulation, vol. 19, no. 10, pp. 3653–3659, 2014. Z. Hua and Y. Zhou, “Design of image cipher using block-based scrambling and image filtering,” Information Science, vol. 396, no. 4, pp. 97–113, 2017. Y. Q. Zhang and X. Y. Wang, “A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice,” Information Science, vol. 273, no. 15, pp. 329–351, 2014. F. Özkaynak, V. Çelik and A. B. Özer, “A new Sbox construction method based on the fractional-order chaotic Chen system,” Signal Image Video Process, vol. 11, no. 4, pp. 659–664, 2017. K. Majid, T. Shah and S. I. Batool, “Construction of S-box based on chaotic Boolean functions and its application in image encryption,” Neural Computing and Applications, vol. 27, no. 3, pp. 677–685, 2016. K. Majid, T. Shah, H. Mahmood, M. A. Gondal and I. Hussain, “A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems,” Nonlinear Dynamics, vol. 70, no. 3, pp. 2303–2311, 2012. K. Majid and T. Shah, “An efficient construction of substitution box with fractional chaotic system”,” Signal, Image and Video Processing, vol. 9, no. 6, pp. 1335–1338, 2015. M. A. Gondal, “A projective general linear group based algorithm for the construction of substitution box for block ciphers,” Neural Computing and Applications, vol. 22, no. 6, pp. 1085–1093, 2013. I. Hussain and T. Shah, “A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm,” Nonlinear Dynamics, vol. 70, no. 3, pp. 1791–1794, 2012. F. Özkaynak and S. Yavuz, “Designing chaotic S-boxes based on time-delay chaotic system,” Nonlinear Dynamics, vol. 74, no. 3, pp. 551–557, 2013. A. Ullah, S. S. Jamal and T. Shah, “A novel scheme for image encryption using substitution box and chaotic system,” Nonlinear Dynamics, vol. 91, no. 1, pp. 359–370, 2018. A. Belazi, M. Khan, A. A. Abd and E. S. Belghith, “Efficient cryptosystem approaches : S-boxes and permutation-substitution-based encryption,” Nonlinear Dynamics, vol. 87, no. 1, pp. 337–361, 2017. A. A. A. El-latif, B. Abd-el-atty and M. Amin, “Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications,” Scientific Report, vol. 10, no. 1, pp. 1–16, 2020. M. Khan, T. Shah and H. Mahmood, “An efficient method for the construction of block cipher with multi-chaotic systems,” Nonlinear Dynamics, vol. 71, no. 3, pp. 489–492, 2013. F. Özkaynak and A. Bedri, “A method for designing strong S-Boxes based on chaotic Lorenz system,” Physics Letter A, vol. 374, no. 36, pp. 3733–3738, 2010. Ü. Çavu and A. Zengin, “A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system,” Nonlinear Dynamics, vol. 87, no. 2, pp. 1081–1094, 2016. I. Hussain, T. Shah and M. Asif, “A group theoretic approach to construct cryptographically strong substitution boxes,” Neural Computing and Applications, vol. 23, no. 1, pp. 97–104, 2013. B. Richard J, M. Bateman and D. Mach, “Lightning detection and ranging (LDAR) raw data,” https://cmr.earthdata.nasa.gov/search/concepts/C1979878937-GHRC_DAAC.html Accessed on Dec 04, 2021. Y. Wang and K. W. Wong, “A method for constructing bijective S-box with high nonlinearity based on chaos and optimization,” International Journal of Bifurcation and Chaos, vol. 25, no. 10, pp. 127–155, 2015. W. Yung, Z. Zhang, L. Zhang, Y. Feng, J. Gao et al., “A genetic algorithm for constructing bijective substitution boxes with high nonlinearity,” Information Sciences, vol. 23, no. 1, pp. 152–166, 2020. F. Artuğer and F. Özkaynak, “An effective method to improve nonlinearity value of substitution boxes based on random selection,” Information Sciences, vol. 576, no. 1, pp. 577–588, 2021. M. Ahmad, I. A. Khaja, A. Baz, A. Alhakami and W. Alhakami, “Particle swarm optimization based highly nonlinear substitution-boxes generation for security applications,” IEEE Access, vol. 8, pp. 116132–116147, 2020. I. Ullah, N. A. Azam and U. Hayat, “Efficient and secure substitution box and random number generators over Mordell elliptic curves,” Journal of Information Security and Applications, vol. 56, no. 3, pp. 102–619, 2021. N. Siddiqui, F. Yousaf, F. Murtaza, M. Ehatisham-ul-Haq, M. U. Ashraf et al., “A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field,” PLOS ONE, vol. 15, no. 11, pp. 024–189, 2021. F. Özkaynak, “On the effect of chaotic system in performance characteristics of chaos-based S-box designs,” Physical A: Statistical Mechanics and its Applications, vol. 20, no. 10, pp. 48–57, 2020. A. A. A. El-Latif, B. Abd-El-Atty, W. Mazurczyk, C. Fung and S. E. Venegas-Andraca, “Secure data encryption based on quantum walks for 5G Internet of Things scenario,” IEEE Transactions on Network and Service Management, vol. 17, no. 1, pp. 118–131, 2020. Z. M. Zahir and F. Özkaynak, “A cryptographic confusion primitive based on Lotka–Volterra chaotic system and its practical applications in image encryption,” in PROC. TCSET, Slavske Ukraine, vol. 11, pp. 694–698, 2020. A. A. A. El-Latif, B. Abd-El-Atty, M. Amin and A. M. Iliyasu, “Quantuminspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic application,” Sci. Rep., vol. 10, no. 1, pp. 116--132, 2020. B. Faheem, A. Ali, M. A. Khan, M. E. Ul-Haq and W. Ahmad, “Highly dispersive substitution box (S-box) design using chaos,” ETRI Journal, vol. 42, no. 4, pp. 619–632, 2020. G. Liu and T. Guangjie, “Designing S-box based on 4D-4wing hyperchaotic system,” 3D Research, vol. 1, no. 9, pp. 1–9, 2017. B. Akram, M. Khan, A. El-Latif and S. Belghith, “Efficient cryptosystem approaches: S-boxes and permutation-substitution-based encryption,” Nonlinear Dynamics, vol. 87, no. 1, pp. 337–361, 2017. F. Özkaynak, “Construction of robust substitution boxes based on chaotic systems,” Neural Computing and Applications, vol. 29, no. 8, pp. 317–329, 2019. Ç. Ünal, A. Zengin, I. Pehlivan and S. Kaçar, “A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system,” Nonlinear Dynamics 87, vol. 2, pp. 1081–1094, 2017. E. A. Solami, M. Ahmad, C. Volos, M. Doja and M. Beg, “A new hyper chaotic system-based design for efficient bijective substitution-boxes,” Entropy, vol. 20, no. 7, pp. 525, 2018. D. Lambić, “A novel method of S-box design based on discrete chaotic map,” Nonlinear Dynamics, vol. 87, no. 4, pp. 2407–2413, 2017. D. Lambić, “A new discrete-space chaotic map based on the multiplication of integer numbers and its application in S-box design,” Nonlinear Dynamics, vol. 100, no. 1, pp. 699–711, 2020. M. F. Khan, A. Ahmed, K. Saleem and T. Shah, “A novel design of cryptographic SP-Network based on gold sequences and chaotic logistic tent system,” IEEE Access, vol. 7, no. 1, pp. 84980–84991, 2019. <table-wrap id="table-8"> <caption><title>Appendix A
Type of Test P-Value Conclusion
01. Frequency Test (Monobit) 6.711666215580028e−17 Non-Random
02. Frequency Test within a Block 0.21575971288691256 Random
03. Run Test 0.0 Non-Random
04. Longest Run of Ones in a Block 0.16958128602983685 Random
05. Binary Matrix Rank Test 0.7750321912480472 Random
06. Discrete Fourier Transform (Spectral) Test 0.44626281343698193 Random
07. Non-Overlapping Template Matching Test 0.014635340688886967 Random
08. Overlapping Template Matching Test 0.36023946288540937 Random
09. Maurer’s Universal Statistical test 0.7544062853856957 Random
10. Linear Complexity Test 0.9996378217856143 Random
11. Serial test:
0.5165245696277773 Random
0.6762539065001036 Random
12. Approximate Entropy Test 0.06688206161079184 Random
13. Cummulative Sums (Forward) Test 3.1895223249735723e−17 Non-Random
14. Cummulative Sums (Reverse) Test 3.13591282948427e−17 Non-Random
15. Random Excursions Test:
State Chi Squared P-Value Conclusion
−4 1.411911703456893 0.923005839169952 Random
−3 2.4854000000000003 0.7786922371169736 Random
−2 5.354938271604938 0.37411466651616343 Random
−1 5.25 0.3861379243372883 Random
+1 2.5 0.7764950711233227 Random
+2 2.567901234567901 0.7662360828950802 Random
+3 2.7176 0.7434253074909452 Random
+4 3.424406497292795 0.6348554712380596 Random
16. Random Excursions Variant Test:
State COUNTS P-Value Conclusion
−9.0 25 0.6995916043003889 Random
−8.0 36 0.3613104285261789 Random
−7.0 40 0.23931654122149537 Random
−6.0 42 0.16580656019401352 Random
−5.0 30 0.40939548620991884 Random
−4.0 20 0.7892680261342813 Random
−3.0 16 1.0 Random
−2.0 18 0.8382564863858263 Random
−1.0 16 1.0 Random
+1.0 18 0.7236736098317631 Random
+2.0 16 1.0 Random
+3.0 12 0.7518296340458492 Random
+4.0 8 0.5929800980174267 Random
+5.0 5 0.5168677495508638 Random
+6.0 2 0.45554509378932995 Random
+7.0 2 0.49245682377288025 Random
+8.0 1 0.4935627897033894 Random
<table-wrap id="table-9"> <caption><title>Appendix B
147 81 50 43 92 245 182 30 237 34 42 39 53 246 219 188
1 221 161 76 158 213 160 197 185 164 184 251 223 99 47 27
172 107 146 83 176 180 171 183 109 56 225 80 64 155 173 63
15 105 235 163 230 234 193 82 89 177 117 152 216 110 137 91
162 133 174 122 102 129 108 169 72 116 113 254 22 121 68 204
249 187 12 115 69 54 95 5 126 94 17 24 77 250 86 154
222 98 11 165 101 33 87 85 226 25 179 168 201 224 239 70
31 138 149 96 208 181 106 209 100 215 88 8 139 210 29 104
40 62 36 52 44 49 220 21 227 218 74 231 18 112 212 150
206 192 189 211 153 127 10 194 229 6 103 45 134 241 240 217
214 178 75 142 120 16 252 144 228 55 136 242 118 2 195 71
202 186 13 28 243 166 148 84 111 141 67 170 167 132 51 123
93 37 38 248 145 79 135 175 32 78 156 238 203 236 61 232
23 130 143 3 90 35 233 46 196 151 48 159 19 20 119 65
73 14 131 200 97 190 128 157 244 205 26 207 125 199 41 140
58 57 4 66 253 59 247 60 114 9 198 255 124 191 7 0
<table-wrap id="table-10"> <caption><title>Appendix C
Algorithm: ReverseSbox (S-box)
in: 2D array of integers, sbox [16] [16];
out: 2D array of integers, ReverseSbox [16] [16];
1: ReverseSbox → |16||16|
2: for row → 0 … (16) do
3:    for col → 0 … (16) do
4:      rowIS → sbox row,col div 16
5:      colIS → sbox row,col mod 16
6:      value → row*16+col
7:         ReverseSbox rowIS,colIS → value
8:    end for
9:  end for
10: return ReverseSbox