The substitution box (S-box) is a fundamentally important component of symmetric key cryptosystem. An S-box is a primary source of non-linearity in modern block ciphers, and it resists the linear attack. Various approaches have been adopted to construct S-boxes. S-boxes are commonly constructed over commutative and associative algebraic structures including Galois fields, unitary commutative rings and cyclic and non-cyclic finite groups. In this paper, first a non-associative ring of order 512 is obtained by using computational techniques, and then by this ring a triplet of

Cryptology is the science dealing with storage and data communication in secure and typically secret form. There are two further subdivisions of cryptology viz; cryptography and cryptanalysis. Cryptography is the method of keeping the information confidentiality using mathematical tools. Cryptanalysis is the art of cracking encrypted information by the means of mathematical and computational devices. It is powerful enough to breach the cryptographic security systems, without accessing the cryptographic key, and it obtains permissions to the content of encrypted communications. Although, both cryptography and cryptanalysis aim at the same target, however the methods and techniques for cryptanalysis have been modified radically throughout the history of cryptography. Among several the Differential cryptanalysis is frequently used for block ciphers. It is based on the analysis of the concern of specific difference in plaintext pairs on the difference of the consequent cipher text pairs. These differences are used to allocate probabilities to the practicable keys and to find the virtually all possible keys [

A repetitive arrangement from the concept of single output Boolean function is the extension of that idea to multiple output Boolean functions, along with denoted as a substitution box (S-box) [^{k} and 2^{l} number of inputs and outputs, respectively. Formerly, an S-box is just a set of

It is concluded from the literature review that differential attack is the only attack which applies on such S-boxes that are constructed by finite Galois field extension of binary field

In last two decades, the notion of chaos has found several applications in various scientific. In Cryptography

A left almost semigroup (LA-semigroup) (or AG-groupoid) is a groupoid ^{−1} such that ^{−1} = ^{−1}

Using a special LA-ring _{n}^{m+1} = 0. There are ^{m+1} elements in ^{k} belong to _{n}_{n}_{0} is unit in _{n}

Take LA-ring

+ | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 6 | 5 | 0 | 2 | 7 | 4 | 3 | 1 | 0 | 4 | 0 | 2 | 1 | 3 | 7 | 6 | 5 | |

1 | 5 | 6 | 1 | 7 | 2 | 3 | 4 | 0 | 1 | 3 | 4 | 2 | 0 | 1 | 5 | 6 | 7 | |

2 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |

3 | 2 | 7 | 3 | 6 | 5 | 1 | 0 | 4 | 3 | 1 | 3 | 2 | 4 | 0 | 7 | 6 | 5 | |

4 | 7 | 2 | 4 | 5 | 6 | 0 | 1 | 3 | 4 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |

5 | 4 | 3 | 5 | 1 | 0 | 2 | 7 | 6 | 5 | 5 | 7 | 2 | 5 | 7 | 6 | 2 | 6 | |

6 | 3 | 4 | 6 | 0 | 1 | 7 | 2 | 5 | 6 | 6 | 6 | 2 | 6 | 6 | 2 | 2 | 2 | |

7 | 1 | 0 | 7 | 4 | 3 | 6 | 5 | 2 | 7 | 7 | 5 | 2 | 7 | 5 | 6 | 2 | 6 |

Here the element 0 is 2 and the left identity element is 4. Units in _{8} are: 0, 1, 3, and 4. The set _{8} +_{8} +^{2}_{8} (with ^{3} = 0) is a special LA-ring with 512 elements. The left identity element in ^{2} is a unit in _{8} +_{8} +^{2}_{8} if and only if _{8}. So, there are 256 units in _{8} +_{8} +^{2}_{8}. The scheme of the S-boxes triplets is based on two substructures of the special LA-ring ^{8})) to the Galois field ^{8}) yield the ultimate S-boxes.

As

Finally, the linear fractional transformation is given as; ^{8}) such that ^{8}) on ^{8}). The newly constructed S-box, using the suggested algorithm is given in

136 | 12 | 95 | 103 | 137 | 169 | 92 | 101 | 158 | 198 | 128 | 6 | 44 | 195 | 171 | 152 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

247 | 162 | 217 | 253 | 255 | 78 | 133 | 86 | 14 | 49 | 161 | 105 | 225 | 214 | 130 | 182 |

165 | 237 | 254 | 164 | 246 | 151 | 102 | 199 | 93 | 230 | 150 | 190 | 179 | 70 | 176 | 94 |

219 | 229 | 117 | 18 | 50 | 143 | 157 | 248 | 146 | 184 | 45 | 30 | 224 | 110 | 228 | 159 |

187 | 173 | 239 | 96 | 118 | 73 | 116 | 25 | 31 | 41 | 227 | 232 | 201 | 226 | 8 | 91 |

178 | 156 | 154 | 3 | 56 | 68 | 7 | 9 | 209 | 43 | 180 | 125 | 106 | 17 | 62 | 191 |

39 | 244 | 54 | 84 | 10 | 149 | 40 | 11 | 81 | 218 | 66 | 99 | 177 | 203 | 27 | 71 |

170 | 202 | 135 | 55 | 167 | 147 | 207 | 129 | 109 | 189 | 13 | 181 | 186 | 126 | 47 | 172 |

245 | 0 | 175 | 5 | 61 | 76 | 82 | 72 | 75 | 85 | 231 | 64 | 144 | 174 | 107 | 213 |

249 | 32 | 240 | 132 | 33 | 153 | 215 | 204 | 139 | 205 | 148 | 193 | 210 | 252 | 212 | 24 |

236 | 221 | 97 | 15 | 59 | 134 | 200 | 74 | 155 | 192 | 98 | 100 | 20 | 19 | 123 | 197 |

16 | 35 | 194 | 120 | 242 | 108 | 28 | 113 | 34 | 79 | 38 | 36 | 211 | 58 | 42 | 46 |

60 | 67 | 89 | 222 | 90 | 111 | 216 | 168 | 69 | 208 | 88 | 104 | 238 | 22 | 52 | 185 |

140 | 183 | 234 | 141 | 1 | 2 | 220 | 29 | 142 | 87 | 163 | 114 | 206 | 166 | 112 | 138 |

48 | 223 | 124 | 21 | 23 | 188 | 37 | 26 | 251 | 65 | 122 | 121 | 241 | 63 | 77 | 4 |

80 | 233 | 51 | 235 | 160 | 127 | 115 | 196 | 243 | 250 | 57 | 131 | 119 | 53 | 145 | 83 |

We define the inverse and affine linear mappings _{m}^{8}) such that ^{8}). Ultimately, the function ^{8})) on ^{8}).

234 | 242 | 36 | 111 | 151 | 240 | 12 | 171 | 129 | 125 | 78 | 19 | 9 | 43 | 255 | 98 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

220 | 70 | 116 | 69 | 73 | 92 | 61 | 65 | 208 | 181 | 7 | 22 | 155 | 83 | 143 | 138 |

101 | 25 | 249 | 13 | 8 | 4 | 123 | 246 | 68 | 33 | 159 | 152 | 26 | 190 | 117 | 168 |

31 | 58 | 245 | 212 | 149 | 164 | 174 | 85 | 235 | 247 | 100 | 178 | 127 | 74 | 50 | 44 |

52 | 56 | 229 | 137 | 134 | 204 | 239 | 27 | 102 | 10 | 142 | 28 | 87 | 172 | 96 | 57 |

91 | 97 | 195 | 38 | 150 | 66 | 105 | 41 | 194 | 218 | 49 | 154 | 199 | 227 | 132 | 86 |

81 | 53 | 55 | 148 | 51 | 23 | 145 | 109 | 210 | 237 | 17 | 48 | 147 | 191 | 182 | 223 |

11 | 252 | 193 | 238 | 62 | 29 | 236 | 185 | 128 | 217 | 82 | 5 | 179 | 250 | 71 | 133 |

167 | 202 | 216 | 79 | 197 | 94 | 241 | 251 | 136 | 214 | 157 | 226 | 206 | 131 | 201 | 75 |

126 | 76 | 139 | 60 | 120 | 144 | 1 | 118 | 224 | 254 | 183 | 122 | 93 | 243 | 90 | 80 |

88 | 107 | 184 | 231 | 166 | 54 | 219 | 112 | 30 | 192 | 209 | 124 | 230 | 104 | 14 | 162 |

198 | 188 | 2 | 15 | 59 | 42 | 3 | 228 | 46 | 156 | 253 | 158 | 205 | 37 | 146 | 119 |

163 | 89 | 21 | 203 | 20 | 34 | 211 | 215 | 108 | 106 | 207 | 140 | 24 | 161 | 72 | 95 |

18 | 114 | 222 | 169 | 244 | 121 | 176 | 170 | 160 | 200 | 130 | 77 | 35 | 99 | 39 | 232 |

248 | 135 | 221 | 141 | 165 | 45 | 153 | 225 | 177 | 40 | 180 | 103 | 6 | 189 | 187 | 16 |

115 | 64 | 213 | 84 | 0 | 47 | 233 | 67 | 173 | 110 | 175 | 196 | 113 | 186 | 32 | 63 |

To synthesize another S-box, we take the composition of above generated S-boxes. The S-box obtained by the composition is given by

144 | 247 | 250 | 195 | 18 | 215 | 217 | 105 | 187 | 228 | 196 | 92 | 78 | 188 | 211 | 177 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

254 | 47 | 126 | 226 | 136 | 185 | 63 | 87 | 100 | 171 | 84 | 227 | 205 | 167 | 32 | 24 |

213 | 88 | 206 | 115 | 122 | 141 | 66 | 3 | 133 | 253 | 135 | 77 | 95 | 182 | 161 | 82 |

120 | 119 | 81 | 208 | 111 | 222 | 189 | 131 | 165 | 39 | 19 | 85 | 158 | 154 | 156 | 16 |

130 | 89 | 231 | 97 | 53 | 238 | 145 | 212 | 174 | 255 | 46 | 112 | 192 | 146 | 178 | 128 |

106 | 6 | 180 | 73 | 246 | 147 | 116 | 127 | 251 | 98 | 207 | 56 | 194 | 83 | 25 | 200 |

168 | 80 | 234 | 142 | 50 | 248 | 43 | 235 | 96 | 118 | 17 | 150 | 72 | 124 | 58 | 223 |

203 | 209 | 186 | 151 | 233 | 45 | 162 | 113 | 199 | 35 | 44 | 140 | 160 | 52 | 129 | 34 |

93 | 70 | 20 | 61 | 101 | 11 | 10 | 62 | 252 | 28 | 37 | 210 | 225 | 163 | 49 | 202 |

201 | 68 | 90 | 110 | 33 | 40 | 197 | 230 | 244 | 104 | 153 | 15 | 79 | 157 | 94 | 149 |

219 | 1 | 91 | 74 | 4 | 175 | 30 | 29 | 103 | 59 | 41 | 38 | 138 | 7 | 239 | 2 |

143 | 152 | 42 | 229 | 224 | 86 | 31 | 55 | 159 | 236 | 117 | 26 | 241 | 8 | 125 | 9 |

123 | 48 | 179 | 144 | 71 | 218 | 76 | 21 | 191 | 216 | 5 | 132 | 107 | 22 | 240 | 99 |

169 | 108 | 166 | 176 | 220 | 65 | 60 | 245 | 121 | 102 | 64 | 51 | 14 | 67 | 109 | 170 |

36 | 139 | 204 | 155 | 181 | 232 | 190 | 164 | 75 | 237 | 137 | 27 | 243 | 13 | 193 | 69 |

172 | 184 | 12 | 54 | 0 | 134 | 23 | 198 | 183 | 214 | 249 | 173 | 148 | 242 | 221 | 57 |

In case when we consider the special LA-ring _{8} +_{8} +^{2}_{8}, the affine map

The key space is the total number of unlike keys cast-off in the encryption or decryption process. For an efficient cryptosystem, the key space must be sufficiently large to repel brute-force attacks. In the first case of proposed algorithm 256! Number of choices for affine function and from the action of ^{8})) on

An efficient S-box should satisfy some specific cryptographic criteria; bijectiveness, nonlinearity, outputs bit independence, strict avalanche and linear approximation probability. We device diverse analyses to test their strong suit and standing with respect to few other well-known S-boxes.

The distance between the Boolean function

Analysis for S-box 1 and S-box 2 | Max. | Min. | Average | Square Deviation | Differential approximation probability (DP) | Linear approximation probability (LP) |
---|---|---|---|---|---|---|

Nonlinearity | 106 | 100 | ||||

106 | 100 | |||||

SAC | 0.625 | 0.40625 | ||||

0.59375 | 0.375 | |||||

BIC | 98 | 2.79577 | ||||

96 | 3.08055 | |||||

BIC-SAC | 0.476563 | 0.0139369 | ||||

0.464844 | 0.0155518 | |||||

DP | ||||||

LP | 164 | |||||

160 |

The SAC was first familiarized in 1895 by Webster et al. [

The BIC was also first introduced in [

The maximum value of the imbalance of an event is said to be the linear approximation probability. The parity of the input bits selected by the mask _{x}_{y}_{y}^{n} is the number of elements of

The differential approximation probability (DP) of S-box is a measure for differential uniformity and is defined as: _{8} AES, Skipjack, Xyi and residue prime S-boxes and we observed that the results of DP of proposed box are relatively better from skip jack, Xyi, prime and Lui S-boxes. As there are

S-boxes | Nonlinearity | SAC | BIC–SAC | BIC | DP | LP |
---|---|---|---|---|---|---|

AES S-box | 112 | 0.5058 | 0.504 | 112.0 | 0.0156 | 0.062 |

APA S-box | 112 | 0.4987 | 0.499 | 112.0 | 0.0156 | 0.062 |

Gray S-box | 112 | 0.5058 | 0.502 | 112.0 | 0.0156 | 0.062 |

Skipjack S-box | 105.7 | 0.4980 | 0.499 | 104.1 | 0.0468 | 0.109 |

Xyi S-box | 105 | 0.5048 | 0.503 | 103.7 | 0.0468 | 0.156 |

Residue Prime | 99.5 | 0.5012 | 0.502 | 101.7 | 0.2810 | 0.132 |

LuiS-box | 105 | 0.499756 | 0.500698 | 104.071 | 0.0390625 | 0.128906 |

Proposed S-box 1 | ||||||

Proposed S-box 2 |

The Arnold map is one the most important 2_{i}_{i}

The determinant of the matrix

Furthermore, the map of

where the matrix

The general form of matrix

In matrix _{x}_{y}_{z}_{x}_{y}_{z}_{i+1}, the initial values used in this work are

S-boxes are considered as a main part of a block cipher, the only component of a cipher that produces non-linearity and hence surety the resistance against linear and differential attacks. Currently, advancement in techniques of cryptanalysis and in computer technology, which enhances correspondingly support, generating S-boxes of good quality is the subject of core attention. Due to uncertainty in communication and in storage of RGB images, a need for the encryption is preferred. One of the aims of this article is to encrypt RGB images using 3 S-boxes originated by a non-associative structure of LA-ring. For the need of the RGB image encryption each layer is passed through the different _{1}, _{2} and _{3} in Red, Green and Blue channels of the color image. Thus, instead of a single S-box used for encryption our proposed scheme provides three different S-boxes _{1}, _{2}and _{3}. Use the 3

Texture is one of the further most significant parameters of a material that enlightens the physical appearance of a material surface except its chromatic character. Texture may be analyzed in diverse approaches but Fourier methodology among these techniques is the most operative. A fascinating analysis, however, is intriguing as it relates to how the human visual system realizes the texture, the first line of the texture, and is extensively used in the segmentation of photograph. Over and done with this method we can calculate 5 diverse characteristics of image which are: Contrast, Homogeneity, Correlation, Energy and Entropy to elucidate texture.

Through energy analysis we can measure the energy of an encrypted image which discards the gray-level co-occurrence matrix (GLCM). The energy is defined as the sum of squared components in GLCM and is given as

The entropy is the measure of level of disorder and randomness in a system. The maximal level of randomness makes the image difficult to recognize and the randomness of an image can be amplified by considering its non-linear components which is defined as _{i} defines the Histogram calculations.

To differentiate the objects of an image the observer has to contrast it is used. Owed to image encryption process, a robust encryption can be realized from the high level of contrast. This factor is directly linked to the confusion created by the S-box. Mathematically, the contrast is obtained by the formula:

In Homogeneity analysis, the closeness of distributed pixels of Gray Level Co-occurrence Matrix (GLCM) to GLCM is tested. Mathematical equation is

To analyse the adjacent pixel correlation of an image, correlation analysis is performed. Normally, three different types of correlation are performed to ensure the strength of the encrypted image. These are: the horizontal, the vertical, and the diagonal correlation. The following equation shows how to calculate the correlation:

Plain color components of image | Cipher color components of image | |||||
---|---|---|---|---|---|---|

Red | Green | Blue | Red | Green | Blue | |

Contrast | 0.445343 | 0.659896 | 0.483655 | 9.96034 | 10.0962 | 10.2181 |

Homogeneity | 0.857543 | 0.831937 | 0.845328 | 0.411186 | 0.404886 | 0.403524 |

Entropy | 7.27958 | 7.63153 | 6.98912 | 7.99712 | 7.99725 | 7.99744 |

Correlation | 0.910667 | 0.887815 | 0.804591 | 0.0516558 | 0.0379861 | 0.0239547 |

Energy | 0.135318 | 0.0838048 | 0.156122 | 0.0157684 | 0.0157087 | 0.0157107 |

Images | Red | Green | Blue | RGB Image |
---|---|---|---|---|

Proposed | ||||

Ref. [ |
7.9901 | 7.9898 | 7.9899 | 7.9899 |

Ref. [ |
7.9913 | 7.9914 | 7.9916 | 7.9914 |

Ref. [ |
7.9808 | 7.9811 | 7.9914 | 7.9844 |

Ref. [ |
7.9901 | 7.9912 | 7.9921 | 7.9113 |

Ref. [ |
7.9949 | 7.9953 | 7.9942 | 7.9948 |

Image | Horizontal | Vertical | Diagonal | ||||||
---|---|---|---|---|---|---|---|---|---|

R | G | B | R | G | B | R | G | B | |

Plain image | 0.9491 | 0.9175 | 0.8561 | 0.9602 | 0.9528 | 0.8962 | 0.9025 | 0.8984 | 0.8715 |

Encrypted image | 0.0569 | 0.0658 | −0.0014 | 0.0036 | −0.0180 | 0.0132 | −0.0499 | 0.0123 | −0.0210 |

Experimental analyses of the image encryption technique are given here. A standard Lena image of size

In statistics, the mean square error (MSE) or mean square deviation (MSD) of an image measures the common of the squares of the errors. This means the arithmetic mean square distinction between the calculable values and what’s estimated. MSE is a risk function, comparable to the mean of the squared error loss. Followed [

Signal representation dependability may be affected by corrupting noise [

The correlation function also gives the idea that how much two digital images are closed to each other as shown in [

The difference between reference signal and test image is given the name of Average difference (AD) [

One of the correlation based measure is the structural content (SC) [

Scheming maximum of the error signals gives what we call maximum difference (MD) (difference between the test image and reference signal) (see [

By [

It is the square root of the mean of the square of all the errors [

According to [

To obtain the amount of information from encrypted image for the agreeing plain image is termed as MI given in [

By [

No. | Quality measure | Encryption by 3 S-boxes and 3D Arnold chaotic map | Optimal values | ||||
---|---|---|---|---|---|---|---|

Red | Green | Blue | Red | Green | Blue | ||

8.1 | 10626.4 | 9224.93 | 7162.78 | ||||

8.2 | 7.86695 | 8.48117 | 9.57999 | ||||

8.3 | 0.66015 | 0.993966 | 1.09709 | ||||

8.4 | 52.1404 | −28.6657 | −22.7034 | ||||

8.5 | 1.59967 | 0.582213 | 0.562247 | ||||

8.6 | 250 | 234 | 216 | ||||

8.7 | 0.467414 | 0.796259 | 0.671177 | ||||

8.8 | 103.084 | 96.0465 | 84.6332 | ||||

8.9 | −0.00013497 | −0.000714523 | −0.0011433 | ||||

8.10 | 0.491086 | 0.689748 | 0.394636 | ||||

8.11 | 0.00982045 | 0.0084672 | 0.00937046 |

A uniform histogram for an image is the calmest and supreme approach to measure the security strength of an encryption procedure against various attacks. Here, we analyze an RGB Lena image of size

To exploit the strong suit of differential analyses on an image encryption arrangement the NPCR (Number of Pixels Change Rate) and UACI (unified average changing intensity) analyses are implemented. It measures the normal power of contrast between the two images, i.e., original and encrypted image. To compare the encrypted images cryptanalysts realize the bond among the plain image and ciphered image. Attack of this kind is famous for differential attack.The NPCR and UACI are the two typically used tests to ensure the strength of the encrypted scheme against differential analysis. For more details, see [

By [_{2}” has only one-pixel difference.

By [

Schemes | NPCR | UACI | ||||
---|---|---|---|---|---|---|

Red | Green | Blue | Red | Blue | Green | |

Proposed | 0.995819 | 0.9961 | 0.995926 | 0.339945 | 0.338623 | 0.336869 |

Ref. [ |
0.9960 | 99.5895 | 0.9961 | 0.3343 | 0.3350 | 0.3343 |

Ref. [ |
0.9964 | 0.9962 | 0.9959 | 0.3353 | 0.3327 | 0.3343 |

Ref. [ |
0.9468 | 0.9568 | 0.9868 | 0.3346 | 0.3450 | 0.3549 |

Ref. [ |
0.9850 | 0.9850 | 0.9850 | 0.3210 | 0.3210 | 0.3210 |

Ref. [ |
0.9960 | 0.9963 | 0.9959 | 0.3343 | 0.3346 | 0. 3347 |

Uniform distribution, Long period and high complexity of the output are the main properties to observe the security strength of a cryptosystem. By a definite end objective to attain these prerequisites, we used NIST SP 800–22 [

Test | P-values for color encryptions of ciphered image | Results | |||
---|---|---|---|---|---|

Red | Green | Blue | |||

Frequency | 0.32694 | 0.80028 | 0.82481 | Pass | |

Block frequency | 0.74131 | 0.54713 | 0.97235 | Pass | |

Rank | 0.29191 | 0.29191 | 0.29191 | Pass | |

Runs ( |
0.084845 | 0.09393 | 0.52759 | Pass | |

Long runs of ones | 0.67514 | 0.7127 | 0.7127 | Pass | |

Overlapping templates | 0.85988 | 0.85988 | 0.85988 | Pass | |

No overlapping templates | 1 | 0.9994 | 0.24017 | Pass | |

Spectral DFT | 0.77167 | 0.56166 | 0.38399 | Pass | |

Approximate entropy | 0.84462 | 0.85692 | 0.11867 | Pass | |

Universal | 0.99437 | 0.99976 | 0.99498 | Pass | |

Serial | 0.0083409 | 0.13423 | 0.34362 | Pass | |

Serial | 0.12342 | 0.5943 | 0.15727 | Pass | |

Cumulative sums forward | 0.14445 | 0.24644 | 0.24227 | Pass | |

Cumulative sums reverse | 0.89099 | 1.16 | 0.79042 | Pass | |

Random excursions | 0.79553 | 0.98021 | 0.66539 | Pass | |

0.37236 | 0.88823 | 0.16569 | Pass | ||

0.57859 | 0.9465 | 0.41097 | Pass | ||

0.22905 | 0.9464 | 0.78375 | Pass | ||

0.48349 | 0.8282 | 0.44466 | Pass | ||

0.13673 | 0.32154 | 0.33772 | Pass | ||

0.6194 | 0.020103 | 0.39284 | Pass | ||

0.70227 | 0.34143 | 0.62245 | Pass | ||

Random excursions variants | 0.39287 | 0.0016344 | 0.46138 | Pass | |

0.66407 | 0.026809 | 0.59298 | Pass | ||

0.96847 | 0.12819 | 0.52709 | Pass | ||

0.44399 | 0.10171 | 0.91871 | Pass | ||

0.33092 | 0.18588 | 0.92957 | Pass | ||

0.65853 | 1 | 0.25054 | Pass | ||

0.54029 | 1 | 0.30743 | Pass | ||

0.81252 | 0.6726 | 0.40648 | Pass | ||

0.50404 | 0.31731 | 0.59298 | Pass | ||

1 | 0.37782 | 0.76828 | Pass |

Noticeably our proposed digital image encryption tool proficiently passes the NIST tests. Thus, due to the proficient outcomes, the designed random cryptosystem used for RGB Image Encryption constructed via S-boxes from a non-commutative and non-associative finite ring and 3

In this paper we constructed S-boxes through non-associative and non-commutative structures of rings having order 512. The main resolution of these S-boxes designing was to produce 256 times more

^{8})) S-boxes and TD-ERCS chaotic sequence