Permutation | S-boxes | |
μt(S11¬); 1 ≤ t ≤ 16 | → | S1j∗;1≤j≤16 |
μt(S12¬); 1 ≤ t ≤ 16 | → | S2j∗;1≤j≤16 |
μt(S13¬); 1 ≤ t ≤ 16 | → | S3j∗;1≤j≤16 |
…… | …… | …… |
…… | …… | …… |
μt(S1010¬); 1 ≤ t ≤ 16 | → | S10j∗;1≤j≤16 |
The existence and the S-asymptotic ω-periodic of the solution in fractional-order Cohen-Grossberg neural networks with inertia are studied in this paper. Based on the properties of the Riemann-Liouville (R-L) fractional-order derivative and integral, the contraction mapping principle, and the Arzela-Ascoli theorem, sufficient conditions for the existence and the S-asymptotic ω-period of the system are achieved. In addition, an example is simulated to testify the theorem.
Citation: Zhiying Li, Wangdong Jiang, Yuehong Zhang. Dynamic analysis of fractional-order neural networks with inertia[J]. AIMS Mathematics, 2022, 7(9): 16889-16906. doi: 10.3934/math.2022927
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The existence and the S-asymptotic ω-periodic of the solution in fractional-order Cohen-Grossberg neural networks with inertia are studied in this paper. Based on the properties of the Riemann-Liouville (R-L) fractional-order derivative and integral, the contraction mapping principle, and the Arzela-Ascoli theorem, sufficient conditions for the existence and the S-asymptotic ω-period of the system are achieved. In addition, an example is simulated to testify the theorem.
In symmetric key cryptography, since 2000, the AES standard of 128 bits was adapted by the National Institute of Standard and Technology (NIST). For review, the original designers of AES, Joan Daemen, and Vincent Rijmen (known as Rijndael) submitted this designed approach along various other algorithms. There was a requirement to develop a strong enough algorithm that can be further used for encryption application. The reason that urges the cryptographers to build the AES is to retain the US Government document in private for a minimum of 20 years. Due to the advancement in computing power, the former methods of securing data i.e., Data Encryption Standard (DES) (developed by IBM in 1975 and break in 1998) and triple-DES has become weak for security purposes. Thus, the government of USA offered an open proposal to increase the standard of data encryption. Finally, the Rijndael cryptosystem (AES) was adapted for encryption scheme and it was circulated by FIPS in 26 NOV 2001 [1]. AES is largely being used for secure transactions through the internet and to transfer of money through banks [2].
S-box plays a seed role in AES. By understanding the concepts of its functionality, it comes to know that S-box is a non-linear factor in AES. It is a heart of any block cipher cryptosystem. The Symmetric block key algorithm uses substitution boxes that yield confusion and permutation boxes that yield diffusion in data when it is going to be encrypted. The significance of S-box is that it creates hurdles for cryptanalysis. Thus, no unauthorized person can get unlawful access to original messages [3]. Several attempts have been consequently followed to design valuable, highly secure, and robust S-boxes that many ciphers utilize to encrypt data. The usefulness of the original AES S-box is to provide substitute data, which is based on keys along with permutation to develop a substitution-permutation network. S-boxes have resulted in many interesting properties that are appropriate for different ciphers. Due to the shuffling of input bits, output bits also change. These changing of bits are analyzed to determine the confusion creating capability and the strength of S-boxes. Various S-boxes are presented in literature such as APA [4], Gray [5], S8 and residue prime [6,7,8], and AES [3], which have good cryptographic properties and algebraic complexity [9].
In literature, there is an insight upon the building of S-boxes under three irreducible polynomials of GF(24). These three polynomials are used for the manufacture of small 4×4 S-boxes [10]. Affine transformation is utilized that carries the best choice of 4×4 transformation matrices and 4×1 constant matrices for all irreducible polynomials of GF(24) [11]. It was very challenging and hard for code breakers to break the code because numerous irreducible polynomials are practiced instead of single ones like the Rijndael algorithm, which worked only for single S-box. Ten Small S-boxes are structured and the permutation of symmetric group S4 (consists of 24 permutations) [12] is operated on each of the small 10 S-boxes, and 240 new ones are obtained by applying permutation, one after the other. Formerly, 10 random S-boxes are selected. The number of choices for arbitrary selection is 240C10. Those innovative S-boxes play a very vital role for hiding data so that nobody can crack the code easily in a limited time.
In our projected algorithm, a new scheme is developed, which has very efficient algebraic complexity for safeguarding data. It safeguards the data in both text and image form. Our optimized research work will utilize the 10 S-boxes of GF(24) (Result of symmetric group permutation S4) [10] and Cartesian permutations of Klein four-group V4 [12] with itself. Our proposed algorithm seeks a new methodology that is sufficient for security purposes to develop 8×8 S-boxes using subfield GF(24) of GF(28). With the aid of this new stylist approach, 1600 independent S-boxes are obtained here and then random 10 S-boxes are picked. The key point is that we have billions of choices i.e., 1600C10≈(2.945764438E+37) to arbitrary pick any 10 S-boxes for utilization in AES. It is quite a large number that makes the process very impressive and safe, which nobody knows, instead of a receiver that is the choice of cryptographers to choose 10 S-boxes for encryption. For security purposes, the performance of our modified S-boxes is comparatively more accurate than other ones when we compare it with other S-boxes through different tests.
The structure of the paper layout is as follows. In Section 2, we briefly elaborate necessary algebraic expressions for AES S-boxes that use the Rijndael algorithm [1]. Section 3 displays the technique for already designed small substitution boxes [10]. In Section 4, we elaborate on the new scheme for the construction of modified S-boxes, permutation of Klein four group, and their use in proposed S-boxes. Section 5 depicts the random selection of S-boxes and pictorial representation of whole modified schemes. In Sections 6 and 7, message encryption and decryption by modified S-boxes, analysis of S-boxes, and image encryption by proposed schemes with their results is presented. In the last two sections, comparisons and conclusions are presented.
The Klein four-group is the smallest noncyclic Abelian group in which every element has order 2. It is ≅ to the direct sum of two abelian groups Z2×Z2 where Addition is defined component wise under mod (2) [12]. In group notation, the Klein four-group is defined by,
V4=<i,j|i2=j2=(ij)2=e>. | (1) |
Permutation Representation: The permutation illustration of this group entails four points [12].
V4=<e,(12)(34),(13)(24),(14)(23)>. | (2) |
As V4 is applicable only to four-bit data so for the application of this particular permutation on eight-bit data to increase the capability of diffusion of that cipher is to utilize the Cartesian structure of V4. It comprises 16 permutations that are signified by μt;1≤t≤16 and the permutation chart according to their data type is given in Table 1.
Permutation | S-boxes | |
μt(S11¬); 1 ≤ t ≤ 16 | → | S1j∗;1≤j≤16 |
μt(S12¬); 1 ≤ t ≤ 16 | → | S2j∗;1≤j≤16 |
μt(S13¬); 1 ≤ t ≤ 16 | → | S3j∗;1≤j≤16 |
…… | …… | …… |
…… | …… | …… |
μt(S1010¬); 1 ≤ t ≤ 16 | → | S10j∗;1≤j≤16 |
Let F=Fq be a field and F[x] is the Euclidean domain. For the extension of field F[x]m, the quotient rings
F[x]/<f(x)>≅GF(qm), |
where the maximal ideal <f(x)> is generated by f(x) an irreducible polynomial of degree m in F[x]. If we write α to denote the coset x+(f(x)) , then f(α)=0 and
F[x]m={a0+a1α+a2α2+⋯+am−1αm−1:∀ai∈F,i=0,1,2,…,m−1}. |
The field F[x]m is a Galois field ( m -degree extension field of the field F).
Two sub steps are discussed here for S-box function of input bytes that is utilized in AES for safeguarding data [3,13].
1) Multiplicative inversion: Let a be a nonzero input byte. Taking its inverse in GF(28) and acquire output byte f(a) .
f(a)=t={a−1a≠00a=0}. | (3) |
2)Affine transformation: Next sub step is to use the affine transformation i.e.,
S−box=c=M(f(a))⊕b. | (4) |
It is a required S-box function, where b is a stable byte and M is constant bit matrix. Affine transformation is given below [14,15].
(C1C2C3C4C5C6C7C8)=(1111100001111100001111100001111110001111110001111110001111110001)(t1t2t3t4t5t6t7t8)⊕(01100011). |
The small S-boxes comprises 16 elements that are defined over finite Galois field GF(24) [10] and they are designed under three distinct irreducible polynomials [13] through the best choice of 4×4 transformation matrices and 4×1 constant matrices (Table 2). B represents each member of GF(24) in transformation T, which is written in the form of 4×1 matrix.
Transformation: T=XB⊕C [16] | |||
Polynomials | Best Choice Matrix X | Inverse of Matrix X | Suitable constant Matric C (order 4 × 1) |
P1(t)=t4+t+1 | a1=(0010000110000100) | (a1)−1=(0010000110000100) | 0×aand0×f |
P2(t)=t4+t3+1 | a2=(1011110111100111) | (a2)−1=(1110011110111101) | 0×3,0×9,0×cand0×d |
P3(t)=t4+t3+t2+t+1 | a3=(1100010101100001) | (a3)−1=(1101010101110001) | 0×4,0×5,0×dand0×f |
The transformation matrices X and constant matrices C are fixed according to distinct irreducible polynomials P1 (t), P2 (t), and P3 (t). The chart presented below represents the whole information about transformation and constant matrices according to respective polynomials.
After achieving 10 S-boxes, the symmetric group S4 acts on them to permute the bytes S4×Si; 1≤i≤10 (Section 3). A total of 240 S-boxes are obtained under permutation of S4 [12]. Thus, 10 S-boxes have been arbitrarily picked for utilization in a cryptographic area.
For making practical and effective use, we demonstrate the configuration of proposed 8×8 S-boxes in this section. This novel technique depends on four steps by utilizing 10 small 4×4 S-boxes of GF(24) (output of Section 3). Also, the Cartesian structure of Klein four-group is practiced here and the performance of proposed algorithm is much better for security purpose.
Step 1. The initial step for designing 8×8 S-boxes is to follow the combination scheme of nibbles. As Si,Sj:GF(24)→GF(24). So the mapping ξ:SiSj→Sij for combination is known as joint mapping that joins the nibbles of Si and Sj for the formation of bytes of Sij. Where SiSj:GF(24)→GF(28) is defined as ξ(Si(u)Sj(v))=Sij(uv)=Sij(t);1≤i,j≤10. Here u,v are nibbles and t represents byte.
The process of combination is that first nibble of Si;1≤i≤10 is joint one by one by all nibbles of Sj;1≤j≤10 and makes one row of Sij. By following this scheme 100 new structured S-boxes Sij;1≤i,j≤10 of GF(28) are developed. The process of combination is presented in Table 3.
S-box combination | Number of S-boxes | Representation | |
ξ(S1Si) , 1≤i≤10 | ![]() |
10 S-boxes | S1j;1≤j≤10 |
ξ(S2Si) , 1≤i≤10 | ![]() |
10 S-boxes | S2j;1≤j≤10 |
ξ(S3Si) , 1≤i≤10 | ![]() |
10 S-boxes | S3j;1≤j≤10 |
………. | ……….. | …… | ………. |
ξ(S10Si) , 1≤i≤10 | ![]() |
10 S-boxes | S10j;1≤j≤10 |
Step 2. In this step we utilize the change of 8×8 basis matrix [14] for computing the S-box function of given byte. The algebraic expression for transformation β:GF(28)→GF(28) is defined by β(t)=Xt. It is a multiplication of 8 bit matrix of input block with this basis matrix X for enhancing complexity. Where t and β(t) both are 8. bit input matrix. The approach of using this transformation is to convert every input byte into output ones. The change of constant bit basis matrix X [2] is represented as,
X=(0001001011101011111011010100001001111110101100100010001000000100). | (5) |
This transformation is applied to each byte of Sij;1≤i,j≤10 (Step 1). So as a consequence of this transformation 100 modified S-boxes Sij';1≤i,j≤10 are achieved.
Step 3. Under this step, the affine linear transformation eqn(1−2) is applied in quite consistent format to each of the distinct S-box Sij;1≤i,j≤10 (Step 1) and resulting S-boxes are Sij'';1≤i,j≤10. Then the SubBytes transformation is practiced and transform different 8 bit to another different 8 bit data [13]. The key point in this substitution process is that unique 100 substitution boxes are utilized for subByte of modified 100 S-boxes Sij;1≤i,j≤10. Thus Sijγ is obtained by subByte of Sij'' (substitution box) to Sij' (Step 2) for each 1≤i,j≤10. The subByte pattern that is depicted in Figure 1.
Step 4. Now for enhancing more the algebraic power of the outcome of Step 3, it is to break each and every byte of input blocks Sijγ;1≤i,j≤10 into prefix and postfix nibbles for the evaluation of bijective transformation f(z) defined on GF(24). Where z represents an input byte. This specific bijective function is evaluated by the fixed values of a',b',c'andd' chosen from GF(28) against the range of z defined as [0,255]. The respective transformation is given as,
f(z)=f(x)f(y), |
where
{f(x)=(a'x+b')mod16;x=prefixNibble,f(y)=(c'x+d')mod16;x=postfixNibble. | (6) |
In above equation f(z) represents a byte and later on the group action of projective general linear group η:PGL(2,GF(28))×GF(28)→GF(28) [6] is defined on GF(28) referred as Mobius transformation. The expression for computational evaluation is η(f(z))=af(z)+bcf(z)+d for fixed constants a,b,candd chosen from GF(28). Large number of S-boxes have been synthesized by following this procedure but to make it easy for the reader the example is elaborated on this technique.
Example. This example will elaborate the whole technique of step 4 by fixed values a'=1B, b'=39, c'=25 and d'=6B for evaluation of f(z) and then particular Mobius transformation η(f(z))=35f(z)+159f(z)+5 , where 1B,39,25,6B,35,15,9,5∈GF(28) [17]. The resultant all entries after this transformation are from GF(28) and form 100 S-boxes Sij¬;1≤i,j≤10. One of them is given in Table 4.
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | |
0 | 216 | 198 | 97 | 110 | 207 | 107 | 203 | 31 | 36 | 64 | 166 | 181 | 146 | 212 | 125 | 39 |
1 | 65 | 252 | 26 | 240 | 45 | 78 | 90 | 235 | 83 | 151 | 162 | 87 | 59 | 111 | 135 | 250 |
2 | 227 | 22 | 241 | 105 | 92 | 225 | 10 | 215 | 35 | 113 | 117 | 37 | 178 | 100 | 177 | 246 |
3 | 123 | 52 | 46 | 24 | 20 | 11 | 89 | 251 | 126 | 42 | 130 | 51 | 153 | 234 | 17 | 49 |
4 | 81 | 84 | 229 | 48 | 94 | 19 | 106 | 73 | 221 | 62 | 176 | 165 | 180 | 47 | 171 | 190 |
5 | 196 | 12 | 195 | 194 | 132 | 155 | 224 | 200 | 189 | 197 | 33 | 237 | 164 | 186 | 3 | 38 |
6 | 182 | 147 | 140 | 77 | 144 | 8 | 248 | 70 | 222 | 86 | 148 | 82 | 184 | 118 | 187 | 239 |
7 | 142 | 232 | 121 | 53 | 30 | 191 | 236 | 172 | 192 | 71 | 50 | 54 | 95 | 80 | 44 | 2 |
8 | 223 | 179 | 137 | 136 | 7 | 188 | 112 | 230 | 66 | 255 | 32 | 139 | 18 | 206 | 93 | 173 |
9 | 152 | 143 | 149 | 1 | 163 | 231 | 72 | 244 | 109 | 60 | 69 | 116 | 68 | 174 | 211 | 128 |
A | 79 | 219 | 5 | 16 | 157 | 23 | 120 | 150 | 202 | 115 | 63 | 131 | 193 | 119 | 61 | 201 |
B | 96 | 58 | 254 | 133 | 91 | 168 | 85 | 204 | 161 | 158 | 101 | 103 | 160 | 228 | 124 | 245 |
C | 98 | 141 | 4 | 242 | 159 | 185 | 170 | 76 | 217 | 21 | 210 | 29 | 27 | 0 | 154 | 43 |
D | 167 | 208 | 220 | 104 | 108 | 213 | 249 | 238 | 233 | 14 | 28 | 134 | 129 | 34 | 243 | 40 |
E | 127 | 209 | 169 | 102 | 41 | 175 | 145 | 6 | 122 | 15 | 253 | 205 | 13 | 25 | 199 | 56 |
F | 156 | 99 | 226 | 67 | 55 | 88 | 138 | 218 | 214 | 75 | 114 | 57 | 183 | 247 | 9 | 74 |
In this section, we will discuss how to get permuted S-boxes by diffusion process. The use of Cartesian permutation V4×V4 in Sij¬;1≤i,j≤10 (Step 4) is quite important step in our research paper. The technique of permutation is
forx∈GF(28)ofanyofSij¬, |
G:(V4×V4)×GF(28)→GF(28), |
G(V4×V4,x)=(V4×V4)(x),(V4×V4)×Sij¬1≤i,j≤10(100S−boxes)=Sij∗1≤i≤10,1≤j≤16(1600S−boxes). | (7) |
The whole description is tabulated as.
Here μt;1≤t≤16 are the mixture of two permutations σ and π. σ is applicable to prefix (N1) and π is on postfix nibble (N2) for each byte x∈ GF(28) of S11¬. The application of 8th permutation μ8 on x is obtained as μ8(x)=σ8(N1(x))π8(N2(x)). As a consequence, 1600 S-boxes Sij∗;1≤i≤10,1≤j≤10 are achieved by the action of 16 permutations to each of Sij¬;1≤i,j≤10 (Step 4).
The main step that is the heart of our algorithm is to select arbitrarily 10 S-boxes from 1600. The total possible choice for this selection is 1600C10 ≈(2.945764438E+37). The reason behind selection in this paper is to utilize in AES encryption that makes the system much more complicated for cryptanalysts. In our case selected 10 S-boxes are S12∗,S45∗,S77∗,S510∗,S21∗,S1010∗,S810∗,S47∗,S69∗,S49∗ , presented in Table 5.
S1∗2 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 226 | 201 | 148 | 155 | 207 | 158 | 206 | 47 | 17 | 128 | 89 | 117 | 104 | 225 | 183 | 29 | |
1 | 132 | 243 | 42 | 240 | 23 | 139 | 170 | 222 | 172 | 109 | 88 | 173 | 62 | 159 | 77 | 250 | |
2 | 220 | 41 | 244 | 150 | 163 | 212 | 10 | 237 | 28 | 180 | 181 | 21 | 120 | 145 | 116 | 249 | |
3 | 190 | 49 | 27 | 34 | 33 | 14 | 166 | 254 | 187 | 26 | 72 | 60 | 102 | 218 | 36 | 52 | |
4 | 164 | 161 | 213 | 48 | 171 | 44 | 154 | 134 | 231 | 59 | 112 | 85 | 113 | 31 | 94 | 123 | |
5 | 193 | 3 | 204 | 200 | 65 | 110 | 208 | 194 | 119 | 197 | 20 | 215 | 81 | 122 | 12 | 25 | |
6 | 121 | 108 | 67 | 135 | 96 | 2 | 242 | 137 | 235 | 169 | 97 | 168 | 114 | 185 | 126 | 223 | |
7 | 75 | 210 | 182 | 53 | 43 | 127 | 211 | 83 | 192 | 141 | 56 | 57 | 175 | 160 | 19 | 8 | |
8 | 239 | 124 | 70 | 66 | 13 | 115 | 176 | 217 | 136 | 249 | 16 | 78 | 40 | 203 | 167 | 87 | |
9 | 98 | 79 | 101 | 4 | 92 | 221 | 130 | 241 | 151 | 51 | 133 | 177 | 129 | 91 | 236 | 63 | |
A | 143 | 238 | 5 | 32 | 103 | 45 | 178 | 105 | 202 | 188 | 63 | 76 | 196 | 189 | 55 | 198 | |
B | 144 | 58 | 251 | 69 | 174 | 82 | 165 | 195 | 84 | 107 | 149 | 157 | 80 | 209 | 179 | 245 | |
C | 152 | 71 | 1 | 248 | 111 | 118 | 90 | 131 | 230 | 37 | 232 | 29 | 46 | 0 | 106 | 30 | |
D | 93 | 224 | 227 | 146 | 147 | 229 | 246 | 219 | 214 | 11 | 35 | 73 | 68 | 24 | 252 | 18 | |
E | 191 | 228 | 86 | 153 | 22 | 95 | 100 | 9 | 186 | 15 | 247 | 199 | 7 | 38 | 205 | 50 | |
F | 99 | 156 | 216 | 140 | 61 | 162 | 74 | 234 | 233 | 142 | 184 | 54 | 125 | 253 | 6 | 138 | |
S2∗1 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 180 | 253 | 126 | 44 | 234 | 188 | 41 | 139 | 116 | 133 | 228 | 19 | 12 | 146 | 16 | 64 | |
1 | 166 | 49 | 171 | 135 | 246 | 87 | 111 | 81 | 183 | 231 | 100 | 99 | 222 | 46 | 164 | 7 | |
2 | 140 | 144 | 109 | 218 | 232 | 102 | 203 | 98 | 214 | 160 | 244 | 223 | 56 | 104 | 201 | 63 | |
3 | 137 | 10 | 181 | 110 | 250 | 219 | 17 | 103 | 121 | 161 | 75 | 28 | 23 | 35 | 77 | 176 | |
4 | 122 | 127 | 136 | 117 | 209 | 221 | 195 | 147 | 68 | 205 | 130 | 236 | 157 | 115 | 3 | 94 | |
5 | 238 | 237 | 217 | 177 | 131 | 113 | 105 | 52 | 48 | 9 | 167 | 235 | 186 | 185 | 229 | 193 | |
6 | 73 | 79 | 184 | 50 | 173 | 165 | 251 | 108 | 2 | 212 | 172 | 220 | 13 | 119 | 199 | 226 | |
7 | 149 | 57 | 34 | 155 | 197 | 224 | 27 | 120 | 47 | 90 | 1 | 32 | 88 | 96 | 170 | 43 | |
8 | 36 | 200 | 15 | 163 | 192 | 37 | 247 | 182 | 112 | 69 | 76 | 168 | 153 | 80 | 123 | 202 | |
9 | 53 | 25 | 190 | 42 | 150 | 59 | 58 | 141 | 189 | 118 | 6 | 230 | 106 | 124 | 78 | 215 | |
A | 148 | 240 | 158 | 8 | 62 | 60 | 51 | 248 | 249 | 239 | 86 | 21 | 92 | 174 | 38 | 74 | |
B | 145 | 45 | 134 | 29 | 175 | 194 | 71 | 178 | 33 | 187 | 191 | 129 | 152 | 198 | 82 | 55 | |
C | 93 | 208 | 154 | 97 | 255 | 72 | 245 | 5 | 11 | 107 | 67 | 26 | 156 | 84 | 54 | 211 | |
D | 125 | 20 | 14 | 85 | 252 | 65 | 227 | 18 | 213 | 242 | 40 | 4 | 22 | 142 | 132 | 61 | |
E | 233 | 66 | 210 | 138 | 196 | 179 | 143 | 216 | 207 | 114 | 151 | 243 | 70 | 159 | 95 | 39 | |
F | 241 | 206 | 91 | 196 | 31 | 30 | 162 | 225 | 24 | 89 | 169 | 254 | 0 | 83 | 128 | 204 | |
S4∗5 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 124 | 233 | 166 | 181 | 117 | 75 | 174 | 246 | 2 | 235 | 248 | 15 | 184 | 69 | 200 | 60 | |
1 | 234 | 82 | 138 | 220 | 77 | 165 | 53 | 57 | 104 | 8 | 86 | 178 | 98 | 127 | 212 | 110 | |
2 | 76 | 172 | 182 | 158 | 52 | 245 | 111 | 99 | 219 | 102 | 120 | 54 | 32 | 185 | 112 | 88 | |
3 | 16 | 136 | 67 | 17 | 24 | 95 | 202 | 10 | 155 | 132 | 215 | 93 | 188 | 29 | 250 | 161 | |
4 | 209 | 105 | 97 | 47 | 59 | 252 | 229 | 30 | 118 | 213 | 139 | 237 | 44 | 128 | 119 | 103 | |
5 | 169 | 91 | 74 | 123 | 190 | 142 | 64 | 255 | 9 | 177 | 116 | 144 | 35 | 218 | 90 | 193 | |
6 | 68 | 0 | 240 | 216 | 176 | 242 | 230 | 187 | 78 | 31 | 238 | 101 | 33 | 23 | 173 | 156 | |
7 | 1 | 186 | 143 | 204 | 45 | 175 | 55 | 130 | 43 | 241 | 13 | 205 | 80 | 148 | 163 | 121 | |
8 | 84 | 14 | 207 | 159 | 168 | 239 | 249 | 134 | 21 | 66 | 48 | 70 | 151 | 131 | 5 | 73 | |
9 | 224 | 3 | 133 | 232 | 20 | 196 | 89 | 79 | 109 | 42 | 152 | 28 | 22 | 115 | 122 | 114 | |
A | 141 | 41 | 189 | 180 | 251 | 226 | 194 | 52 | 135 | 198 | 222 | 147 | 100 | 236 | 50 | 210 | |
B | 51 | 167 | 171 | 140 | 137 | 63 | 34 | 129 | 195 | 164 | 18 | 231 | 228 | 62 | 7 | 92 | |
C | 19 | 191 | 145 | 160 | 247 | 113 | 29 | 4 | 227 | 106 | 71 | 253 | 38 | 154 | 203 | 25 | |
D | 11 | 96 | 46 | 208 | 12 | 221 | 146 | 214 | 87 | 153 | 6 | 179 | 94 | 58 | 72 | 40 | |
E | 197 | 211 | 56 | 244 | 225 | 61 | 217 | 85 | 201 | 206 | 243 | 223 | 157 | 150 | 81 | 36 | |
F | 162 | 108 | 83 | 192 | 26 | 254 | 37 | 183 | 65 | 125 | 199 | 107 | 126 | 49 | 170 | 27 | |
S4∗7 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 121 | 221 | 55 | 23 | 113 | 48 | 215 | 54 | 111 | 245 | 204 | 86 | 37 | 82 | 161 | 124 | |
1 | 3 | 65 | 97 | 180 | 46 | 25 | 7 | 45 | 197 | 85 | 226 | 195 | 130 | 16 | 143 | 101 | |
2 | 39 | 6 | 154 | 56 | 59 | 167 | 153 | 229 | 106 | 115 | 131 | 147 | 100 | 145 | 247 | 11 | |
3 | 89 | 103 | 134 | 142 | 120 | 117 | 252` | 79 | 118 | 242 | 228 | 76 | 125 | 140 | 47 | 105 | |
4 | 122 | 81 | 151 | 10 | 159 | 58 | 175 | 129 | 66 | 207 | 166 | 220 | 173 | 38 | 22 | 24 | |
5 | 14 | 116 | 35 | 170 | 51 | 208 | 93 | 222 | 32 | 30 | 41 | 36 | 126 | 71 | 84 | 119 | |
6 | 0 | 98 | 171 | 250 | 104 | 127 | 249 | 136 | 235 | 255 | 156 | 240 | 135 | 49 | 8 | 210 | |
7 | 218 | 163 | 190 | 33 | 12 | 212 | 196 | 237 | 141 | 225 | 233 | 31 | 148 | 29 | 40 | 193 | |
8 | 152 | 27 | 227 | 184 | 234 | 230 | 181 | 219 | 74 | 109 | 112 | 42 | 186 | 21 | 132 | 177 | |
9 | 192 | 183 | 19 | 28 | 5 | 155 | 20 | 17 | 34 | 133 | 164 | 26 | 239 | 63 | 88 | 128 | |
A | 15 | 92 | 13 | 194 | 43 | 60 | 18 | 251 | 50 | 114 | 216 | 200 | 150 | 1 | 94 | 168 | |
B | 87 | 67 | 162 | 231 | 9 | 52 | 169 | 203 | 188 | 201 | 172 | 91 | 206 | 110 | 209 | 144 | |
C | 232 | 243 | 217 | 83 | 224 | 57 | 62 | 77 | 102 | 187 | 44 | 107 | 238 | 214 | 196 | 53 | |
D | 108 | 68 | 64 | 165 | 158 | 185 | 205 | 244 | 75 | 241 | 139 | 157 | 191 | 198 | 99 | 179 | |
E | 73 | 72 | 70 | 182 | 80 | 146 | 189 | 176 | 2 | 123 | 178 | 174 | 211 | 253 | 4 | 96 | |
F | 61 | 223 | 248 | 90 | 95 | 213 | 246 | 138 | 69 | 254 | 160 | 78 | 202 | 236 | 199 | 137 | |
S4∗9 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 109 | 237 | 127 | 208 | 221 | 166 | 196 | 114 | 21 | 188 | 244 | 17 | 137 | 246 | 85 | 229 | |
1 | 140 | 190 | 189 | 116 | 7 | 37 | 29 | 146 | 211 | 20 | 143 | 41 | 226 | 207 | 78 | 130 | |
2 | 233 | 222 | 230 | 12 | 231 | 202 | 24 | 11 | 142 | 155 | 74 | 48 | 6 | 87 | 170 | 105 | |
3 | 3 | 70 | 210 | 165 | 31 | 40 | 197 | 186 | 161 | 76 | 52 | 184 | 86 | 152 | 89 | 8 | |
4 | 14 | 103 | 25 | 46 | 38 | 153 | 16 | 169 | 151 | 22 | 191 | 111 | 212 | 9 | 249 | 225 | |
5 | 236 | 66 | 93 | 90 | 173 | 63 | 238 | 131 | 35 | 195 | 65 | 224 | 96 | 242 | 10 | 182 | |
6 | 108 | 26 | 0 | 69 | 30 | 84 | 18 | 49 | 192 | 122 | 58 | 79 | 91 | 124 | 95 | 201 | |
7 | 94 | 83 | 227 | 59 | 54 | 47 | 247 | 75 | 100 | 193 | 112 | 39 | 156 | 34 | 118 | 60 | |
8 | 171 | 180 | 206 | 203 | 33 | 32 | 215 | 113 | 145 | 183 | 5 | 44 | 43 | 214 | 168 | 117 | |
9 | 240 | 129 | 71 | 72 | 235 | 135 | 250 | 64 | 19 | 149 | 218 | 120 | 119 | 107 | 68 | 36 | |
A | 132 | 45 | 115 | 123 | 56 | 28 | 150 | 61 | 216 | 126 | 50 | 213 | 80 | 27 | 178 | 174 | |
B | 92 | 42 | 167 | 157 | 51 | 176 | 138 | 158 | 104 | 223 | 181 | 164 | 82 | 219 | 252 | 255 | |
C | 106 | 148 | 97 | 177 | 196 | 102 | 81 | 53 | 200 | 99 | 251 | 228 | 243 | 57 | 194 | 62 | |
D | 172 | 128 | 88 | 98 | 147 | 204 | 125 | 220 | 185 | 198 | 245 | 110 | 248 | 2 | 159 | 187 | |
E | 239 | 134 | 73 | 121 | 4 | 217 | 205 | 1 | 234 | 253 | 209 | 160 | 13 | 139 | 77 | 241 | |
F | 136 | 162 | 144 | 179 | 163 | 67 | 154 | 15 | 23 | 55 | 133 | 141 | 232 | 175 | 254 | 199 | |
S6∗9 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 81 | 123 | 151 | 209 | 6 | 13 | 92 | 80 | 3 | 27 | 251 | 116 | 68 | 201 | 217 | 111 | |
1 | 52 | 146 | 213 | 46 | 83 | 157 | 154 | 51 | 165 | 19 | 141 | 43 | 132 | 9 | 254 | 55 | |
2 | 48 | 11 | 104 | 203 | 187 | 172 | 24 | 181 | 108 | 139 | 224 | 71 | 18 | 66 | 135 | 84 | |
3 | 133 | 25 | 0 | 230 | 195 | 164 | 26 | 220 | 109 | 226 | 247 | 114 | 125 | 222 | 252 | 255 | |
4 | 240 | 248 | 60 | 59 | 218 | 168 | 177 | 54 | 131 | 188 | 10 | 76 | 16 | 182 | 233 | 44 | |
5 | 5 | 162 | 211 | 176 | 160 | 21 | 202 | 138 | 126 | 171 | 244 | 129 | 74 | 246 | 37 | 77 | |
6 | 30 | 9 | 178 | 50 | 70 | 72 | 128 | 155 | 121 | 7 | 161 | 231 | 190 | 17 | 249 | 113 | |
7 | 184 | 34 | 140 | 228 | 95 | 227 | 87 | 238 | 20 | 205 | 31 | 73 | 96 | 63 | 208 | 29 | |
8 | 122 | 212 | 185 | 40 | 1 | 41 | 137 | 253 | 127 | 2 | 186 | 232 | 75 | 107 | 153 | 110 | |
9 | 88 | 180 | 98 | 12 | 14 | 245 | 196 | 38 | 183 | 166 | 42 | 192 | 103 | 167 | 85 | 22 | |
A | 100 | 156 | 79 | 124 | 142 | 115 | 130 | 158 | 174 | 191 | 67 | 117 | 163 | 189 | 175 | 57 | |
B | 56 | 243 | 102 | 91 | 143 | 97 | 53 | 89 | 106 | 134 | 145 | 105 | 148 | 119 | 169 | 4 | |
C | 64 | 206 | 23 | 118 | 8 | 39 | 61 | 152 | 62 | 216 | 58 | 229 | 52 | 65 | 45 | 241 | |
D | 28 | 120 | 35 | 170 | 193 | 144 | 194 | 199 | 179 | 15 | 33 | 112 | 82 | 242 | 235 | 234 | |
E | 207 | 204 | 69 | 239 | 200 | 221 | 150 | 236 | 173 | 47 | 86 | 214 | 198 | 93 | 210 | 94 | |
F | 136 | 32 | 223 | 36 | 147 | 78 | 237 | 215 | 90 | 225 | 250 | 197 | 149 | 99 | 159 | 219 | |
S5∗10 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 209 | 15 | 168 | 151 | 7 | 253 | 88 | 17 | 167 | 222 | 166 | 110 | 188 | 235 | 123 | 115 | |
1 | 221 | 141 | 135 | 63 | 176 | 58 | 242 | 96 | 3 | 0 | 73 | 52 | 84 | 90 | 112 | 42 | |
2 | 41 | 129 | 145 | 233 | 68 | 231 | 97 | 2 | 54 | 205 | 1 | 38 | 192 | 104 | 155 | 5 | |
3 | 22 | 212 | 225 | 76 | 211 | 23 | 232 | 187 | 92 | 6 | 186 | 154 | 34 | 8 | 10 | 80 | |
4 | 121 | 208 | 61 | 223 | 119 | 219 | 64 | 9 | 148 | 174 | 216 | 248 | 44 | 120 | 32 | 189 | |
5 | 191 | 217 | 214 | 244 | 142 | 93 | 165 | 69 | 158 | 39 | 159 | 195 | 24 | 228 | 245 | 170 | |
6 | 75 | 14 | 111 | 241 | 33 | 196 | 27 | 51 | 131 | 215 | 237 | 31 | 160 | 182 | 98 | 107 | |
7 | 43 | 240 | 74 | 130 | 204 | 162 | 26 | 202 | 49 | 85 | 40 | 66 | 179 | 254 | 59 | 21 | |
8 | 137 | 238 | 56 | 220 | 62 | 140 | 95 | 210 | 124 | 246 | 226 | 78 | 133 | 213 | 29 | 207 | |
9 | 153 | 109 | 106 | 127 | 149 | 190 | 161 | 147 | 218 | 150 | 16 | 152 | 243 | 236 | 105 | 132 | |
A | 55 | 227 | 163 | 13 | 79 | 156 | 183 | 91 | 83 | 67 | 173 | 194 | 185 | 117 | 157 | 82 | |
B | 37 | 108 | 28 | 181 | 175 | 178 | 200 | 77 | 250 | 86 | 139 | 252 | 19 | 128 | 94 | 53 | |
C | 65 | 103 | 89 | 206 | 255 | 72 | 201 | 239 | 36 | 197 | 136 | 57 | 48 | 4 | 12 | 113 | |
D | 125 | 203 | 193 | 177 | 126 | 234 | 102 | 60 | 25 | 144 | 230 | 172 | 251 | 146 | 184 | 47 | |
E | 30 | 114 | 45 | 11 | 50 | 224 | 171 | 100 | 35 | 199 | 18 | 122 | 87 | 20 | 138 | 247 | |
F | 180 | 229 | 99 | 143 | 71 | 118 | 70 | 164 | 81 | 134 | 249 | 198 | 46 | 52 | 169 | 116 | |
S7∗7 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 106 | 153 | 247 | 122 | 217 | 243 | 151 | 184 | 220 | 74 | 79 | 56 | 242 | 68 | 81 | 64 | |
1 | 251 | 171 | 98 | 130 | 92 | 13 | 196 | 15 | 226 | 200 | 30 | 114 | 222 | 84 | 40 | 93 | |
2 | 211 | 22 | 175 | 100 | 105 | 140 | 155 | 228 | 131 | 125 | 187 | 178 | 77 | 224 | 5 | 57 | |
3 | 66 | 58 | 159 | 44 | 80 | 146 | 214 | 76 | 238 | 89 | 83 | 10 | 102 | 128 | 53 | 63 | |
4 | 28 | 145 | 11 | 129 | 177 | 21 | 96 | 112 | 207 | 186 | 241 | 34 | 244 | 158 | 253 | 185 | |
5 | 36 | 113 | 48 | 90 | 221 | 55 | 144 | 121 | 69 | 86 | 235 | 14 | 250 | 104 | 110 | 127 | |
6 | 42 | 59 | 167 | 165 | 6 | 154 | 24 | 39 | 75 | 147 | 118 | 152 | 142 | 120 | 38 | 117 | |
7 | 188 | 52 | 9 | 233 | 43 | 60 | 29 | 240 | 148 | 0 | 33 | 231 | 141 | 101 | 193 | 16 | |
8 | 50 | 18 | 94 | 3 | 8 | 249 | 97 | 78 | 195 | 61 | 31 | 194 | 218 | 208 | 65 | 51 | |
9 | 2 | 189 | 4 | 192 | 47 | 252 | 19 | 157 | 26 | 108 | 107 | 182 | 232 | 230 | 183 | 234 | |
A | 111 | 215 | 161 | 87 | 190 | 163 | 162 | 170 | 91 | 32 | 136 | 23 | 255 | 223 | 67 | 248 | |
B | 85 | 7 | 143 | 160 | 35 | 116 | 236 | 54 | 202 | 245 | 206 | 45 | 172 | 246 | 137 | 199 | |
C | 133 | 20 | 88 | 139 | 227 | 27 | 198 | 229 | 191 | 115 | 173 | 17 | 166 | 205 | 179 | 99 | |
D | 150 | 209 | 169 | 37 | 210 | 49 | 25 | 156 | 204 | 135 | 225 | 216 | 237 | 12 | 46 | 212 | |
E | 180 | 82 | 124 | 203 | 119 | 71 | 168 | 41 | 201 | 126 | 254 | 197 | 138 | 95 | 1 | 213 | |
F | 176 | 134 | 103 | 239 | 72 | 70 | 62 | 73 | 164 | 174 | 109 | 123 | 219 | 132 | 196 | 181 | |
S8∗10 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 188 | 194 | 208 | 108 | 112 | 29 | 242 | 78 | 73 | 90 | 83 | 40 | 181 | 233 | 176 | 26 | |
1 | 191 | 18 | 196 | 161 | 22 | 159 | 154 | 52 | 32 | 198 | 116 | 132 | 228 | 10 | 126 | 152 | |
2 | 214 | 167 | 42 | 27 | 95 | 59 | 200 | 246 | 113 | 226 | 49 | 96 | 178 | 60 | 174 | 53 | |
3 | 250 | 204 | 150 | 189 | 142 | 120 | 82 | 0 | 21 | 144 | 41 | 62 | 37 | 207 | 138 | 229 | |
4 | 163 | 64 | 218 | 66 | 141 | 193 | 19 | 247 | 55 | 50 | 24 | 130 | 252 | 254 | 46 | 166 | |
5 | 146 | 30 | 136 | 128 | 231 | 169 | 239 | 11 | 43 | 179 | 16 | 124 | 213 | 15 | 232 | 51 | |
6 | 245 | 164 | 114 | 91 | 23 | 44 | 7 | 143 | 85 | 162 | 74 | 121 | 77 | 211 | 34 | 133 | |
7 | 20 | 227 | 145 | 25 | 104 | 107 | 39 | 70 | 129 | 84 | 54 | 101 | 160 | 68 | 209 | 220 | |
8 | 79 | 192 | 153 | 241 | 157 | 81 | 147 | 238 | 249 | 33 | 221 | 47 | 65 | 118 | 182 | 243 | |
9 | 63 | 251 | 45 | 244 | 222 | 175 | 71 | 131 | 137 | 171 | 111 | 195 | 203 | 212 | 58 | 69 | |
A | 234 | 158 | 235 | 253 | 135 | 61 | 134 | 17 | 105 | 155 | 88 | 80 | 219 | 13 | 89 | 180 | |
B | 67 | 184 | 72 | 168 | 6 | 206 | 103 | 9 | 139 | 123 | 187 | 151 | 248 | 48 | 86 | 94 | |
C | 110 | 36 | 75 | 119 | 148 | 117 | 14 | 165 | 127 | 202 | 109 | 156 | 186 | 35 | 93 | 199 | |
D | 2 | 28 | 216 | 38 | 255 | 5 | 201 | 102 | 217 | 99 | 172 | 205 | 224 | 1 | 12 | 177 | |
E | 87 | 8 | 215 | 140 | 223 | 97 | 100 | 125 | 225 | 183 | 122 | 106 | 57 | 4 | 185 | 197 | |
F | 236 | 115 | 173 | 3 | 92 | 230 | 56 | 170 | 210 | 52 | 237 | 190 | 240 | 31 | 76 | 98 | |
S10∗10 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 141 | 234 | 13 | 238 | 170 | 94 | 194 | 171 | 67 | 225 | 134 | 45 | 49 | 186 | 71 | 53 | |
1 | 218 | 229 | 52 | 17 | 249 | 173 | 190 | 252 | 23 | 16 | 68 | 96 | 136 | 0 | 3 | 177 | |
2 | 230 | 119 | 155 | 70 | 6 | 89 | 172 | 76 | 152 | 176 | 201 | 148 | 109 | 124 | 137 | 215 | |
3 | 242 | 103 | 135 | 114 | 65 | 97 | 41 | 227 | 126 | 7 | 139 | 18 | 66 | 48 | 86 | 184 | |
4 | 116 | 8 | 151 | 91 | 249 | 98 | 39 | 179 | 10 | 160 | 178 | 195 | 149 | 187 | 19 | 226 | |
5 | 113 | 165 | 207 | 140 | 131 | 38 | 112 | 208 | 188 | 69 | 209 | 51 | 200 | 120 | 78 | 108 | |
6 | 248 | 85 | 90 | 37 | 211 | 250 | 241 | 161 | 159 | 47 | 81 | 55 | 29 | 247 | 224 | 240 | |
7 | 210 | 125 | 22 | 11 | 182 | 236 | 174 | 92 | 121 | 145 | 129 | 214 | 26 | 115 | 185 | 132 | |
8 | 128 | 200 | 31 | 166 | 192 | 246 | 183 | 43 | 239 | 232 | 36 | 143 | 57 | 217 | 206 | 107 | |
9 | 61 | 244 | 54 | 44 | 153 | 12 | 216 | 198 | 20 | 4 | 213 | 88 | 228 | 25 | 162 | 147 | |
A | 50 | 63 | 175 | 245 | 104 | 142 | 219 | 204 | 117 | 144 | 74 | 169 | 205 | 46 | 158 | 59 | |
B | 133 | 253 | 212 | 163 | 95 | 105 | 223 | 60 | 199 | 138 | 203 | 42 | 33 | 75 | 157 | 202 | |
C | 118 | 110 | 150 | 191 | 14 | 181 | 56 | 73 | 1 | 100 | 180 | 220 | 243 | 15 | 111 | 80 | |
D | 32 | 189 | 84 | 233 | 40 | 254 | 101 | 235 | 64 | 222 | 99 | 122 | 130 | 77 | 221 | 5 | |
E | 146 | 24 | 82 | 72 | 9 | 102 | 164 | 2 | 123 | 62 | 34 | 58 | 154 | 127 | 231 | 93 | |
F | 87 | 35 | 83 | 197 | 237 | 156 | 196 | 193 | 21 | 251 | 27 | 30 | 167 | 168 | 28 | 79 |
The Modified AES algorithm is the most important section in our research paper for utilization of newly generated robust S-boxes. In our modified algorithm, all means of AES-128 [1] are changed to improve the complexity and make it unpredictable. Our case is key dependent, just like the original AES because if we build a key dependent framework [13], then cryptanalysis turns out to be more troublesome. Also, the Mixed column matrix is not fixed, so a better approach of shifting is adapted and S-box is not static. The elaboration is displayed below.
1) Add round key
The initial step add round key is the same as in the original AES, so that in each round, a new key is Xored with state. The State matrix and key [13] are both equal in order. These keys are originally built by AES key expansion.
2) Substitute bytes
A new strategy for byte substitution is accomplished here. As a consequence of (Step 5), ten S-boxes are utilized one by one in each round for substitution. The way of substitution is the same as in AES [1].
3) Shift bytes
In this step, bytes are moved by utilizing a new scheme known as shift box. Diverse shifts are attempted in various rounds. Shift boxes are not fixed for each round [15,18]. Their selection is based on a substitution box. If Sij∗ is used for substitution in Round 1 then Si will play the role of shift box for that specific one (presented in Table 6).
State Matrix | Shift Box | Result | |||||||||
S0,0 | S0,1 | S0,2 | S0,3 | S0,0 | S3,3 | S2,0 | S3,1 | S0,0 | S1,1 | S2,2 | S3,3 |
S1,0 | S1,1 | S1,2 | S1,3 | S1,0 | S0,1 | S2,2 | S2,3 | S1,0 | S2,1 | S3,2 | S2,0 |
S2,0 | S2,1 | S2,2 | S2,3 | S1,3 | S1,1 | S0,2 | S2,1 | S0,2 | S2,3 | S1,2 | S1,3 |
S3,0 | S3,1 | S3,2 | S3,3 | S3,0 | S3,2 | S1,2 | S0,3 | S3,0 | S0,3 | S3,1 | S0,1 |
The way of shifting is that if the first component of shift box is 14, then the shifting is that the primary component of state moves towards the fourteenth position of state. Likewise, all elements are shifted. The technique is shown in the Figure 2.
4) Mix column
The mix column is an essential element of the encryption scheme. Like shift boxes [18], different mix columns are utilized in different rounds. Their selection is also based on the substitution box. If Sij∗ is used for substitution in Round 1, then Sj will play the role of shift box for that specific one.
5) Round constant in key expansion
For each round, unique round constants (same as AES) [18], are used that are presented in Table 7.
Rounds | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Round constant | 01 | 02 | 04 | 08 | 10 | 20 | 40 | 80 | 1b | 36 |
The results of the message encryption and decryption by Modified AES structure are given in Table 8.
Encryption | Decryption | |
Plaintext TWOONENINETWO | Ciphertext | |
Round0 | 7F097A3667C0B786E59E7BED299B3853 | 70BAE70AEB6E28E5B61B87308F9A87F3 |
Round1 | 0C2A223FBE983E29CF03F40EA1478E80 | D5DAC6864CF89ED51A74F80D058117C4 |
Round2 | 411F171705861FDEDA2B3BE898E986C9 | 97D05A6454C195589FA0C446C5CD62B4 |
Round3 | 46159F31736643F2DBEC157BCCB659C3 | 3D3668E9EF4768A47F20EED2687AAE95 |
Round4 | E8145C9CBBAE049F029D20E31D8FA2C0 | 7AD27EB4EA69740BB33B44EC7B44A153 |
Round5 | 18D695C3DDF6BBF2B58330EF533AE156 | 745ACBE0832FFFA49A0210BC69B94B59 |
Round6 | 74613DDFBA037336CCD063823E2C2C32 | 0088533489FB1EEA73C544E6088D289C |
Round7 | 984E47AE1A5540DEF5D9E1C6A7EB2CE0 | B24455F9A9AF562F98E16B0BA8ECB79A |
Round8 | FDEE0A3DCBEDED7B8A75B3711F8997F6 | 732C69322B1EC0CB43EF5045BFBE16E0 |
Round9 | 0F4643FC0948638C4A1172638FA068E8 | 382F51A9A2339F19785F40B61FD47504 |
Round10 | B8AE1A606BCA28D666DA0D6DD57A7282 | 54776F204F6E65204E696E652054776F |
Ciphertext | Plaintext TWOONENINETWO |
Moreover, the flow chart of modified encryption scheme are depicted in Figure 3.
Many standard analyses have been depicted in the literature to evaluate the strength of S-boxes with fitting confusion. For testing security of S-boxes, many analyses like Bijectivity [13], SAC [16], Non-linearity [19], and differential and linear probability [7] are used in the checking process [20].
S-boxes are bijective if all elements of GF(28) are given as an input to a Boolean function and corresponding to each value, and a unique output of GF(28) is obtained [21]. It is visible from the above 10 tables that those corresponding to a single input there is a single output. Thus, our all newly constructed 1600 S-boxes that are designed by means of four steps are 100% bijective.
Checking for Nonlinearity is essential to identify how much our S-box creates hurdle for linear attack. A function φ(x) is defined from nth Boolean function GF(2n) to GF(2). So the nonlinearity for function φ(x) is defined in the form of
δφ=mintϵLndδ(φ,t). |
Here, members of Ln are all linear and affine functions as well, and dδ(φ,t) represents the Hamming distance amongst φ and t .
The Nonlinearity through Walsh transform is predicted for function φ is
N.Lin(φ)=2−n(1−maxσϵGF(2n)|S<φ>(σ)|). |
For function φ the notation S<φ>(σ) is termed as cyclic spectrum and it is evaluated by [19],
S<φ>(σ)=2−n∑x∈GF(2n)(−1)φ(x)+x.σ, |
where, x.σ represents dot product for each x,σ∈GF(2n). The radius bound of Nonlinearity is 2n−1−2n2−1. So, to counterattacks against linear cryptanalysis, the Nonlinearity of S-box should be close to its certain upper bound. It is represented in Table 9.
S-box 1 | S-box 2 | S-box 3 | S-box 4 | S-box 5 | S-box 6 | S-box 7 | S-box 8 | S-box 9 | S-box 10 | ||
Non-linearity | Max | 106 | 106 | 107 | 106 | 106 | 108 | 107 | 107 | 108 | 108 |
Min | 100 | 100 | 98 | 100 | 100 | 96 | 97 | 100 | 100 | 96 | |
Average | 103.25 | 103.375 | 103.875 | 102.875 | 103.625 | 102.375 | 103.625 | 104.125 | 104.375 | 103.875 | |
Strict Avalanche Criteria (SAC) | Max | 0.625 | 0.648438 | 0.601563 | 0.601563 | 0.59375 | 0.609375 | 0.625 | 0.585938 | 0.609375 | 0.578125 |
Min | 0.40625 | 0.0429688 | 0.429688 | 0.40625 | 0.382813 | 0.40625 | 0.375 | 0.40625 | 0.421875 | 0.390625 | |
Average | 0.501221 | 0.503906 | 0.506592 | 0.501709 | 0.505615 | 0.502686 | 0.505859 | 0.499756 | 0.501221 | 0.499023 | |
S.D | 0.0217624 | 0.0206006 | 0.0212301 | 0.0211541 | 0.0221775 | 0.0220563 | 0.0240203 | 0.0195796 | 0.0241116 | 0.0191802 | |
Bit Independent Criteria (BIC) | Min | 98 | 93 | 97 | 97 | 96 | 97 | 102 | 97 | 97 | 99 |
Average | 103.5 | 103.179 | 103.464 | 103.393 | 103.393 | 102.964 | 104.75 | 103.464 | 103.536 | 103.75 | |
S.D | 2.5425 | 3.20773 | 2.89682 | 2.78182 | 3.2551 | 2.51399 | 1.7243 | 2.74489 | 2.93358 | 2.30876 | |
BIC-SAC | Min | 0.464844 | 0.482422 | 0.466797 | 0.470703 | 0.476563 | 0.462891 | 0.470703 | 0.46875 | 0.462891 | 0.458984 |
Average | 0.498117 | 0.503278 | 0.501744 | 0.503418 | 0.506836 | 0.504534 | 0.501395 | 0.503976 | 0.504534 | 0.50007 | |
S.D | 0.0144139 | 0.011881 | 0.0193514 | 0.015125 | 0.0118402 | 0.0186685 | 0.0149098 | 0.0132311 | 0.0186685 | 0.0155593 | |
Differential Probability | D.P | 0.046875 | 0.015625 | 0.0390625 | 0.046875 | 0.0390625 | 0.046875 | 0.0390625 | 0.046875 | 0.046875 | 0.046875 |
Linear Probability | Max | 162 | 161 | 165 | 163 | 161 | 162 | 163 | 159 | 162 | 160 |
L.P | 0.140625 | 0.144531 | 0.136719 | 0.144531 | 0.132813 | 0.140625 | 0.136719 | 0.144531 | 0.13281 | 0.125 |
SAC [16] interprets the evidence about altering bits in the output and that alteration is approximately half of the output bits that are altered. These bits are changed by changing one single bit of eight-bit input i.e., 0 to 1 or 1 to 0 [7]. This analysis is vital for examining the confusion aptitude of S-boxes.
If Exclusive OR of a Boolean function φj and two bits output of S-box φk is extremely Non-linear and fulfills the properties of SAC, then for each and every pair of output bit, the correlation coefficient is near to 0 by inverting one input bit. Thus, for BIC, use φjxorφkfor(j≠k) [19] to determine whether it meets the criteria of nonlinearity and SAC.
To conceptualize uniformity, apply the differential attack to input and notice the alteration in behavior and properties of output at the intermediate stage. Then, time linear and nonlinear responses due to differential attacks is observed. Here, corresponding input and output differentials are expressed by ∂xi and ∂yi. Mathematical expression is [7]
Dif.prob(∂x→∂y)=#{x∈X|S(x)⊕S(x⊕∂x)=∂y}2m. |
The subsequent numerical values of Dif.prob for the proposed S-box are inside a satisfactory range.
At the output bit, the estimation for unbalancing events is monitored through drawing changes at input bits. ωx and ωy are applied to each parity of individual bits and analyze each individual response and its effect at the output stage. Mathematically [19],
Lin.prob=maxωx,ωy≠0|#{x|x.ωx=S(x).ωy}2n−12|, |
where 2n represents cardinality and x represents input. The results are tabulated in Table 9. As smaller the Lin.prob, the more grounded the capacity of S-box for fighting against direct cryptanalysis attack. Thus, the consequence of Lin.prob is better. The analyses of the proposed S-boxes are displayed in Table 9.
The consequences of our proposed S-boxes and their average by means of comparison with others are depicted in Table 10. The proposed S-boxes' performance is concurrent with the aftereffects of the investigation for different S-boxes that are tried for comparison. The estimation of the proposed S-box is near to the ideal value that demonstrates its protection from attackers. The consequence of non-linearity [19] is near to Xyi and Skipjack S-box. An examination of SAC [16] for various S-boxes utilized as benchmarks is shown in this work. These outcomes run from a greatest value of 0.625 to at least 0.406, with an average estimation of 0.502. The average outcomes from SAC investigations yield esteems near the ideal estimation of 0.50. The subsequent numerical values of Dif.prob [7] for the proposed S-box are inside a satisfactory range and bring it into comparison with various other S-boxes that are utilized in this paper for analysis. The smaller the Lin.prob , the more grounded the capacity of S-box for fighting against direct cryptanalysis attack. Thus, the consequence of Lin.prob [19] is better.
S-boxes | Nonlinearity | SAC | BIC-SAC | BIC | DP | LP |
AES S-box [3] | 112 | 0.5058 | 0.504 | 112.0 | 0.0156 | 0.062 |
APA S-box [4] | 112 | 0.4987 | 0.499 | 112.0 | 0.0156 | 0.062 |
Gray S-box [5] | 112 | 0.5058 | 0.502 | 112.0 | 0.0156 | 0.062 |
Skipjack S-box [21] | 105.7 | 0.4980 | 0.499 | 104.1 | 0.0468 | 0.109 |
Xyi S-box [19] | 105 | 0.5048 | 0.503 | 103.7 | 0.0468 | 0.156 |
Residue Prime [8] | 99.5 | 0.5012 | 0.502 | 101.7 | 0.2810 | 0.132 |
Proposed S-box 1 | 103.25 | 0.501221 | 0.498117 | 103.5 | 0.046875 | 0.140625 |
Proposed S-box 2 | 103.375 | 0.503906 | 0.503278 | 103.179 | 0.015625 | 0.144531 |
Proposed S-box 3 | 103.875 | 0.506592 | 0.501744 | 103.464 | 0.0390625 | 0.136719 |
Proposed S-box 4 | 102.875 | 0.501709 | 0.503418 | 103.393 | 0.046875 | 0.144531 |
Proposed S-box 5 | 103.625 | 0.505615 | 0.506836 | 103.393 | 0.0390625 | 0.132813 |
Proposed S-box 6 | 102.375 | 0.502686 | 0.504534 | 102.964 | 0.046875 | 0.140625 |
Proposed S-box 7 | 103.625 | 0.505859 | 0.501395 | 104.75 | 0.0390625 | 0.136719 |
Proposed S-box 8 | 104.125 | 0.499756 | 0.503976 | 103.464 | 0.046875 | 0.144531 |
Proposed S-box 9 | 104.375 | 0.501221 | 0.504534 | 103.536 | 0.046875 | 0.13281 |
Proposed S-box 10 | 103.875 | 0.499023 | 0.50007 | 103.75 | 0.046875 | 0.125 |
Average proposed results | 103.538 | 0.502759 | 0.50279 | 103.539 | 0.041406 | 0.13789 |
It is concluded that this work is identified with the development of S-boxes. The whole process comprises a few stages i.e. Matrix multiplication, Affine Transformation, Substitution, Action of projective general linear group, and permutation with specific components of group V4×V4. The proposed strategy has numerous advantages. The principal advantage is that GF(24) works behind the development of 8×8 S-boxes, and when cryptanalysts apply different inverse methods for code break, they will use GF(28). Thus, they are not expected to break the code. Since the Galois field is cyclic, it implies one can develop every single other component of S-box with just a single generator. The second benefit is that it is known very well that diffusion is induced by permutation in a secure communication field. Thus, the shuffling by the permutations of cartesian product V4×V4 enhances the diffusion capacity of the cipher. In Section 3, with the proposed technique, we developed 1600 S-boxes subsequent to applying V4×V4 permutation. At that point, we chose 10 S-boxes arbitrarily, utilized it in AES calculations, and inspected their analyses in eminent cryptographic criteria. We inferred that our S-boxes have great cryptographic properties i.e., nonlinearity, differential probability, linear probability, SAC, and BIC. Since AES has used just a single S-box byte sub step and utilizes the same S-box in all, it relies on its key length. Hence, another advantage is that here we have 1600 boxes with great properties, chose 10 S-boxes, and use every one in distinctive rounds of AES. We have 1600C10 ≈(2.945764438E+37) possible outcomes to choose 10 S-boxes. Additionally, different steps of AES were changed. Therefore, we have new calculations and strong S-boxes that have crucial application in encryption algorithms of block cipher. We have given AES encryption and proposed encryption on which we have done work. In this way, it demonstrates that it is a profoundly secure framework, and in the event that somebody wants to break the code of this algorithm, they need to move through the opposite of all steps. That is the reason why it is difficult to break down the code of this proposed algorithm. Cryptanalysis requires numerous years to decode the message. Thus, they need to perform thousands or even millions of counts to register what 10 S-boxes have been chosen to conceal the information? This strategy is most noteworthy for anchoring information when two gatherings build up a secret communication with each other.
The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.
The authors extend their gratitude to the deanship of scientific research of King Khalid University, for funding this work through a research project under grant R.G.P.2/238/44.
The authors declare no conflicts of interest.
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Permutation | S-boxes | |
μt(S11¬); 1 ≤ t ≤ 16 | → | S1j∗;1≤j≤16 |
μt(S12¬); 1 ≤ t ≤ 16 | → | S2j∗;1≤j≤16 |
μt(S13¬); 1 ≤ t ≤ 16 | → | S3j∗;1≤j≤16 |
…… | …… | …… |
…… | …… | …… |
μt(S1010¬); 1 ≤ t ≤ 16 | → | S10j∗;1≤j≤16 |
Transformation: T=XB⊕C [16] | |||
Polynomials | Best Choice Matrix X | Inverse of Matrix X | Suitable constant Matric C (order 4 × 1) |
P1(t)=t4+t+1 | a1=(0010000110000100) | (a1)−1=(0010000110000100) | 0×aand0×f |
P2(t)=t4+t3+1 | a2=(1011110111100111) | (a2)−1=(1110011110111101) | 0×3,0×9,0×cand0×d |
P3(t)=t4+t3+t2+t+1 | a3=(1100010101100001) | (a3)−1=(1101010101110001) | 0×4,0×5,0×dand0×f |
S-box combination | Number of S-boxes | Representation | |
ξ(S1Si) , 1≤i≤10 | ![]() |
10 S-boxes | S1j;1≤j≤10 |
ξ(S2Si) , 1≤i≤10 | ![]() |
10 S-boxes | S2j;1≤j≤10 |
ξ(S3Si) , 1≤i≤10 | ![]() |
10 S-boxes | S3j;1≤j≤10 |
………. | ……….. | …… | ………. |
ξ(S10Si) , 1≤i≤10 | ![]() |
10 S-boxes | S10j;1≤j≤10 |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | |
0 | 216 | 198 | 97 | 110 | 207 | 107 | 203 | 31 | 36 | 64 | 166 | 181 | 146 | 212 | 125 | 39 |
1 | 65 | 252 | 26 | 240 | 45 | 78 | 90 | 235 | 83 | 151 | 162 | 87 | 59 | 111 | 135 | 250 |
2 | 227 | 22 | 241 | 105 | 92 | 225 | 10 | 215 | 35 | 113 | 117 | 37 | 178 | 100 | 177 | 246 |
3 | 123 | 52 | 46 | 24 | 20 | 11 | 89 | 251 | 126 | 42 | 130 | 51 | 153 | 234 | 17 | 49 |
4 | 81 | 84 | 229 | 48 | 94 | 19 | 106 | 73 | 221 | 62 | 176 | 165 | 180 | 47 | 171 | 190 |
5 | 196 | 12 | 195 | 194 | 132 | 155 | 224 | 200 | 189 | 197 | 33 | 237 | 164 | 186 | 3 | 38 |
6 | 182 | 147 | 140 | 77 | 144 | 8 | 248 | 70 | 222 | 86 | 148 | 82 | 184 | 118 | 187 | 239 |
7 | 142 | 232 | 121 | 53 | 30 | 191 | 236 | 172 | 192 | 71 | 50 | 54 | 95 | 80 | 44 | 2 |
8 | 223 | 179 | 137 | 136 | 7 | 188 | 112 | 230 | 66 | 255 | 32 | 139 | 18 | 206 | 93 | 173 |
9 | 152 | 143 | 149 | 1 | 163 | 231 | 72 | 244 | 109 | 60 | 69 | 116 | 68 | 174 | 211 | 128 |
A | 79 | 219 | 5 | 16 | 157 | 23 | 120 | 150 | 202 | 115 | 63 | 131 | 193 | 119 | 61 | 201 |
B | 96 | 58 | 254 | 133 | 91 | 168 | 85 | 204 | 161 | 158 | 101 | 103 | 160 | 228 | 124 | 245 |
C | 98 | 141 | 4 | 242 | 159 | 185 | 170 | 76 | 217 | 21 | 210 | 29 | 27 | 0 | 154 | 43 |
D | 167 | 208 | 220 | 104 | 108 | 213 | 249 | 238 | 233 | 14 | 28 | 134 | 129 | 34 | 243 | 40 |
E | 127 | 209 | 169 | 102 | 41 | 175 | 145 | 6 | 122 | 15 | 253 | 205 | 13 | 25 | 199 | 56 |
F | 156 | 99 | 226 | 67 | 55 | 88 | 138 | 218 | 214 | 75 | 114 | 57 | 183 | 247 | 9 | 74 |
S1∗2 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 226 | 201 | 148 | 155 | 207 | 158 | 206 | 47 | 17 | 128 | 89 | 117 | 104 | 225 | 183 | 29 | |
1 | 132 | 243 | 42 | 240 | 23 | 139 | 170 | 222 | 172 | 109 | 88 | 173 | 62 | 159 | 77 | 250 | |
2 | 220 | 41 | 244 | 150 | 163 | 212 | 10 | 237 | 28 | 180 | 181 | 21 | 120 | 145 | 116 | 249 | |
3 | 190 | 49 | 27 | 34 | 33 | 14 | 166 | 254 | 187 | 26 | 72 | 60 | 102 | 218 | 36 | 52 | |
4 | 164 | 161 | 213 | 48 | 171 | 44 | 154 | 134 | 231 | 59 | 112 | 85 | 113 | 31 | 94 | 123 | |
5 | 193 | 3 | 204 | 200 | 65 | 110 | 208 | 194 | 119 | 197 | 20 | 215 | 81 | 122 | 12 | 25 | |
6 | 121 | 108 | 67 | 135 | 96 | 2 | 242 | 137 | 235 | 169 | 97 | 168 | 114 | 185 | 126 | 223 | |
7 | 75 | 210 | 182 | 53 | 43 | 127 | 211 | 83 | 192 | 141 | 56 | 57 | 175 | 160 | 19 | 8 | |
8 | 239 | 124 | 70 | 66 | 13 | 115 | 176 | 217 | 136 | 249 | 16 | 78 | 40 | 203 | 167 | 87 | |
9 | 98 | 79 | 101 | 4 | 92 | 221 | 130 | 241 | 151 | 51 | 133 | 177 | 129 | 91 | 236 | 63 | |
A | 143 | 238 | 5 | 32 | 103 | 45 | 178 | 105 | 202 | 188 | 63 | 76 | 196 | 189 | 55 | 198 | |
B | 144 | 58 | 251 | 69 | 174 | 82 | 165 | 195 | 84 | 107 | 149 | 157 | 80 | 209 | 179 | 245 | |
C | 152 | 71 | 1 | 248 | 111 | 118 | 90 | 131 | 230 | 37 | 232 | 29 | 46 | 0 | 106 | 30 | |
D | 93 | 224 | 227 | 146 | 147 | 229 | 246 | 219 | 214 | 11 | 35 | 73 | 68 | 24 | 252 | 18 | |
E | 191 | 228 | 86 | 153 | 22 | 95 | 100 | 9 | 186 | 15 | 247 | 199 | 7 | 38 | 205 | 50 | |
F | 99 | 156 | 216 | 140 | 61 | 162 | 74 | 234 | 233 | 142 | 184 | 54 | 125 | 253 | 6 | 138 | |
S2∗1 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 180 | 253 | 126 | 44 | 234 | 188 | 41 | 139 | 116 | 133 | 228 | 19 | 12 | 146 | 16 | 64 | |
1 | 166 | 49 | 171 | 135 | 246 | 87 | 111 | 81 | 183 | 231 | 100 | 99 | 222 | 46 | 164 | 7 | |
2 | 140 | 144 | 109 | 218 | 232 | 102 | 203 | 98 | 214 | 160 | 244 | 223 | 56 | 104 | 201 | 63 | |
3 | 137 | 10 | 181 | 110 | 250 | 219 | 17 | 103 | 121 | 161 | 75 | 28 | 23 | 35 | 77 | 176 | |
4 | 122 | 127 | 136 | 117 | 209 | 221 | 195 | 147 | 68 | 205 | 130 | 236 | 157 | 115 | 3 | 94 | |
5 | 238 | 237 | 217 | 177 | 131 | 113 | 105 | 52 | 48 | 9 | 167 | 235 | 186 | 185 | 229 | 193 | |
6 | 73 | 79 | 184 | 50 | 173 | 165 | 251 | 108 | 2 | 212 | 172 | 220 | 13 | 119 | 199 | 226 | |
7 | 149 | 57 | 34 | 155 | 197 | 224 | 27 | 120 | 47 | 90 | 1 | 32 | 88 | 96 | 170 | 43 | |
8 | 36 | 200 | 15 | 163 | 192 | 37 | 247 | 182 | 112 | 69 | 76 | 168 | 153 | 80 | 123 | 202 | |
9 | 53 | 25 | 190 | 42 | 150 | 59 | 58 | 141 | 189 | 118 | 6 | 230 | 106 | 124 | 78 | 215 | |
A | 148 | 240 | 158 | 8 | 62 | 60 | 51 | 248 | 249 | 239 | 86 | 21 | 92 | 174 | 38 | 74 | |
B | 145 | 45 | 134 | 29 | 175 | 194 | 71 | 178 | 33 | 187 | 191 | 129 | 152 | 198 | 82 | 55 | |
C | 93 | 208 | 154 | 97 | 255 | 72 | 245 | 5 | 11 | 107 | 67 | 26 | 156 | 84 | 54 | 211 | |
D | 125 | 20 | 14 | 85 | 252 | 65 | 227 | 18 | 213 | 242 | 40 | 4 | 22 | 142 | 132 | 61 | |
E | 233 | 66 | 210 | 138 | 196 | 179 | 143 | 216 | 207 | 114 | 151 | 243 | 70 | 159 | 95 | 39 | |
F | 241 | 206 | 91 | 196 | 31 | 30 | 162 | 225 | 24 | 89 | 169 | 254 | 0 | 83 | 128 | 204 | |
S4∗5 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 124 | 233 | 166 | 181 | 117 | 75 | 174 | 246 | 2 | 235 | 248 | 15 | 184 | 69 | 200 | 60 | |
1 | 234 | 82 | 138 | 220 | 77 | 165 | 53 | 57 | 104 | 8 | 86 | 178 | 98 | 127 | 212 | 110 | |
2 | 76 | 172 | 182 | 158 | 52 | 245 | 111 | 99 | 219 | 102 | 120 | 54 | 32 | 185 | 112 | 88 | |
3 | 16 | 136 | 67 | 17 | 24 | 95 | 202 | 10 | 155 | 132 | 215 | 93 | 188 | 29 | 250 | 161 | |
4 | 209 | 105 | 97 | 47 | 59 | 252 | 229 | 30 | 118 | 213 | 139 | 237 | 44 | 128 | 119 | 103 | |
5 | 169 | 91 | 74 | 123 | 190 | 142 | 64 | 255 | 9 | 177 | 116 | 144 | 35 | 218 | 90 | 193 | |
6 | 68 | 0 | 240 | 216 | 176 | 242 | 230 | 187 | 78 | 31 | 238 | 101 | 33 | 23 | 173 | 156 | |
7 | 1 | 186 | 143 | 204 | 45 | 175 | 55 | 130 | 43 | 241 | 13 | 205 | 80 | 148 | 163 | 121 | |
8 | 84 | 14 | 207 | 159 | 168 | 239 | 249 | 134 | 21 | 66 | 48 | 70 | 151 | 131 | 5 | 73 | |
9 | 224 | 3 | 133 | 232 | 20 | 196 | 89 | 79 | 109 | 42 | 152 | 28 | 22 | 115 | 122 | 114 | |
A | 141 | 41 | 189 | 180 | 251 | 226 | 194 | 52 | 135 | 198 | 222 | 147 | 100 | 236 | 50 | 210 | |
B | 51 | 167 | 171 | 140 | 137 | 63 | 34 | 129 | 195 | 164 | 18 | 231 | 228 | 62 | 7 | 92 | |
C | 19 | 191 | 145 | 160 | 247 | 113 | 29 | 4 | 227 | 106 | 71 | 253 | 38 | 154 | 203 | 25 | |
D | 11 | 96 | 46 | 208 | 12 | 221 | 146 | 214 | 87 | 153 | 6 | 179 | 94 | 58 | 72 | 40 | |
E | 197 | 211 | 56 | 244 | 225 | 61 | 217 | 85 | 201 | 206 | 243 | 223 | 157 | 150 | 81 | 36 | |
F | 162 | 108 | 83 | 192 | 26 | 254 | 37 | 183 | 65 | 125 | 199 | 107 | 126 | 49 | 170 | 27 | |
S4∗7 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 121 | 221 | 55 | 23 | 113 | 48 | 215 | 54 | 111 | 245 | 204 | 86 | 37 | 82 | 161 | 124 | |
1 | 3 | 65 | 97 | 180 | 46 | 25 | 7 | 45 | 197 | 85 | 226 | 195 | 130 | 16 | 143 | 101 | |
2 | 39 | 6 | 154 | 56 | 59 | 167 | 153 | 229 | 106 | 115 | 131 | 147 | 100 | 145 | 247 | 11 | |
3 | 89 | 103 | 134 | 142 | 120 | 117 | 252` | 79 | 118 | 242 | 228 | 76 | 125 | 140 | 47 | 105 | |
4 | 122 | 81 | 151 | 10 | 159 | 58 | 175 | 129 | 66 | 207 | 166 | 220 | 173 | 38 | 22 | 24 | |
5 | 14 | 116 | 35 | 170 | 51 | 208 | 93 | 222 | 32 | 30 | 41 | 36 | 126 | 71 | 84 | 119 | |
6 | 0 | 98 | 171 | 250 | 104 | 127 | 249 | 136 | 235 | 255 | 156 | 240 | 135 | 49 | 8 | 210 | |
7 | 218 | 163 | 190 | 33 | 12 | 212 | 196 | 237 | 141 | 225 | 233 | 31 | 148 | 29 | 40 | 193 | |
8 | 152 | 27 | 227 | 184 | 234 | 230 | 181 | 219 | 74 | 109 | 112 | 42 | 186 | 21 | 132 | 177 | |
9 | 192 | 183 | 19 | 28 | 5 | 155 | 20 | 17 | 34 | 133 | 164 | 26 | 239 | 63 | 88 | 128 | |
A | 15 | 92 | 13 | 194 | 43 | 60 | 18 | 251 | 50 | 114 | 216 | 200 | 150 | 1 | 94 | 168 | |
B | 87 | 67 | 162 | 231 | 9 | 52 | 169 | 203 | 188 | 201 | 172 | 91 | 206 | 110 | 209 | 144 | |
C | 232 | 243 | 217 | 83 | 224 | 57 | 62 | 77 | 102 | 187 | 44 | 107 | 238 | 214 | 196 | 53 | |
D | 108 | 68 | 64 | 165 | 158 | 185 | 205 | 244 | 75 | 241 | 139 | 157 | 191 | 198 | 99 | 179 | |
E | 73 | 72 | 70 | 182 | 80 | 146 | 189 | 176 | 2 | 123 | 178 | 174 | 211 | 253 | 4 | 96 | |
F | 61 | 223 | 248 | 90 | 95 | 213 | 246 | 138 | 69 | 254 | 160 | 78 | 202 | 236 | 199 | 137 | |
S4∗9 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 109 | 237 | 127 | 208 | 221 | 166 | 196 | 114 | 21 | 188 | 244 | 17 | 137 | 246 | 85 | 229 | |
1 | 140 | 190 | 189 | 116 | 7 | 37 | 29 | 146 | 211 | 20 | 143 | 41 | 226 | 207 | 78 | 130 | |
2 | 233 | 222 | 230 | 12 | 231 | 202 | 24 | 11 | 142 | 155 | 74 | 48 | 6 | 87 | 170 | 105 | |
3 | 3 | 70 | 210 | 165 | 31 | 40 | 197 | 186 | 161 | 76 | 52 | 184 | 86 | 152 | 89 | 8 | |
4 | 14 | 103 | 25 | 46 | 38 | 153 | 16 | 169 | 151 | 22 | 191 | 111 | 212 | 9 | 249 | 225 | |
5 | 236 | 66 | 93 | 90 | 173 | 63 | 238 | 131 | 35 | 195 | 65 | 224 | 96 | 242 | 10 | 182 | |
6 | 108 | 26 | 0 | 69 | 30 | 84 | 18 | 49 | 192 | 122 | 58 | 79 | 91 | 124 | 95 | 201 | |
7 | 94 | 83 | 227 | 59 | 54 | 47 | 247 | 75 | 100 | 193 | 112 | 39 | 156 | 34 | 118 | 60 | |
8 | 171 | 180 | 206 | 203 | 33 | 32 | 215 | 113 | 145 | 183 | 5 | 44 | 43 | 214 | 168 | 117 | |
9 | 240 | 129 | 71 | 72 | 235 | 135 | 250 | 64 | 19 | 149 | 218 | 120 | 119 | 107 | 68 | 36 | |
A | 132 | 45 | 115 | 123 | 56 | 28 | 150 | 61 | 216 | 126 | 50 | 213 | 80 | 27 | 178 | 174 | |
B | 92 | 42 | 167 | 157 | 51 | 176 | 138 | 158 | 104 | 223 | 181 | 164 | 82 | 219 | 252 | 255 | |
C | 106 | 148 | 97 | 177 | 196 | 102 | 81 | 53 | 200 | 99 | 251 | 228 | 243 | 57 | 194 | 62 | |
D | 172 | 128 | 88 | 98 | 147 | 204 | 125 | 220 | 185 | 198 | 245 | 110 | 248 | 2 | 159 | 187 | |
E | 239 | 134 | 73 | 121 | 4 | 217 | 205 | 1 | 234 | 253 | 209 | 160 | 13 | 139 | 77 | 241 | |
F | 136 | 162 | 144 | 179 | 163 | 67 | 154 | 15 | 23 | 55 | 133 | 141 | 232 | 175 | 254 | 199 | |
S6∗9 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 81 | 123 | 151 | 209 | 6 | 13 | 92 | 80 | 3 | 27 | 251 | 116 | 68 | 201 | 217 | 111 | |
1 | 52 | 146 | 213 | 46 | 83 | 157 | 154 | 51 | 165 | 19 | 141 | 43 | 132 | 9 | 254 | 55 | |
2 | 48 | 11 | 104 | 203 | 187 | 172 | 24 | 181 | 108 | 139 | 224 | 71 | 18 | 66 | 135 | 84 | |
3 | 133 | 25 | 0 | 230 | 195 | 164 | 26 | 220 | 109 | 226 | 247 | 114 | 125 | 222 | 252 | 255 | |
4 | 240 | 248 | 60 | 59 | 218 | 168 | 177 | 54 | 131 | 188 | 10 | 76 | 16 | 182 | 233 | 44 | |
5 | 5 | 162 | 211 | 176 | 160 | 21 | 202 | 138 | 126 | 171 | 244 | 129 | 74 | 246 | 37 | 77 | |
6 | 30 | 9 | 178 | 50 | 70 | 72 | 128 | 155 | 121 | 7 | 161 | 231 | 190 | 17 | 249 | 113 | |
7 | 184 | 34 | 140 | 228 | 95 | 227 | 87 | 238 | 20 | 205 | 31 | 73 | 96 | 63 | 208 | 29 | |
8 | 122 | 212 | 185 | 40 | 1 | 41 | 137 | 253 | 127 | 2 | 186 | 232 | 75 | 107 | 153 | 110 | |
9 | 88 | 180 | 98 | 12 | 14 | 245 | 196 | 38 | 183 | 166 | 42 | 192 | 103 | 167 | 85 | 22 | |
A | 100 | 156 | 79 | 124 | 142 | 115 | 130 | 158 | 174 | 191 | 67 | 117 | 163 | 189 | 175 | 57 | |
B | 56 | 243 | 102 | 91 | 143 | 97 | 53 | 89 | 106 | 134 | 145 | 105 | 148 | 119 | 169 | 4 | |
C | 64 | 206 | 23 | 118 | 8 | 39 | 61 | 152 | 62 | 216 | 58 | 229 | 52 | 65 | 45 | 241 | |
D | 28 | 120 | 35 | 170 | 193 | 144 | 194 | 199 | 179 | 15 | 33 | 112 | 82 | 242 | 235 | 234 | |
E | 207 | 204 | 69 | 239 | 200 | 221 | 150 | 236 | 173 | 47 | 86 | 214 | 198 | 93 | 210 | 94 | |
F | 136 | 32 | 223 | 36 | 147 | 78 | 237 | 215 | 90 | 225 | 250 | 197 | 149 | 99 | 159 | 219 | |
S5∗10 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 209 | 15 | 168 | 151 | 7 | 253 | 88 | 17 | 167 | 222 | 166 | 110 | 188 | 235 | 123 | 115 | |
1 | 221 | 141 | 135 | 63 | 176 | 58 | 242 | 96 | 3 | 0 | 73 | 52 | 84 | 90 | 112 | 42 | |
2 | 41 | 129 | 145 | 233 | 68 | 231 | 97 | 2 | 54 | 205 | 1 | 38 | 192 | 104 | 155 | 5 | |
3 | 22 | 212 | 225 | 76 | 211 | 23 | 232 | 187 | 92 | 6 | 186 | 154 | 34 | 8 | 10 | 80 | |
4 | 121 | 208 | 61 | 223 | 119 | 219 | 64 | 9 | 148 | 174 | 216 | 248 | 44 | 120 | 32 | 189 | |
5 | 191 | 217 | 214 | 244 | 142 | 93 | 165 | 69 | 158 | 39 | 159 | 195 | 24 | 228 | 245 | 170 | |
6 | 75 | 14 | 111 | 241 | 33 | 196 | 27 | 51 | 131 | 215 | 237 | 31 | 160 | 182 | 98 | 107 | |
7 | 43 | 240 | 74 | 130 | 204 | 162 | 26 | 202 | 49 | 85 | 40 | 66 | 179 | 254 | 59 | 21 | |
8 | 137 | 238 | 56 | 220 | 62 | 140 | 95 | 210 | 124 | 246 | 226 | 78 | 133 | 213 | 29 | 207 | |
9 | 153 | 109 | 106 | 127 | 149 | 190 | 161 | 147 | 218 | 150 | 16 | 152 | 243 | 236 | 105 | 132 | |
A | 55 | 227 | 163 | 13 | 79 | 156 | 183 | 91 | 83 | 67 | 173 | 194 | 185 | 117 | 157 | 82 | |
B | 37 | 108 | 28 | 181 | 175 | 178 | 200 | 77 | 250 | 86 | 139 | 252 | 19 | 128 | 94 | 53 | |
C | 65 | 103 | 89 | 206 | 255 | 72 | 201 | 239 | 36 | 197 | 136 | 57 | 48 | 4 | 12 | 113 | |
D | 125 | 203 | 193 | 177 | 126 | 234 | 102 | 60 | 25 | 144 | 230 | 172 | 251 | 146 | 184 | 47 | |
E | 30 | 114 | 45 | 11 | 50 | 224 | 171 | 100 | 35 | 199 | 18 | 122 | 87 | 20 | 138 | 247 | |
F | 180 | 229 | 99 | 143 | 71 | 118 | 70 | 164 | 81 | 134 | 249 | 198 | 46 | 52 | 169 | 116 | |
S7∗7 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 106 | 153 | 247 | 122 | 217 | 243 | 151 | 184 | 220 | 74 | 79 | 56 | 242 | 68 | 81 | 64 | |
1 | 251 | 171 | 98 | 130 | 92 | 13 | 196 | 15 | 226 | 200 | 30 | 114 | 222 | 84 | 40 | 93 | |
2 | 211 | 22 | 175 | 100 | 105 | 140 | 155 | 228 | 131 | 125 | 187 | 178 | 77 | 224 | 5 | 57 | |
3 | 66 | 58 | 159 | 44 | 80 | 146 | 214 | 76 | 238 | 89 | 83 | 10 | 102 | 128 | 53 | 63 | |
4 | 28 | 145 | 11 | 129 | 177 | 21 | 96 | 112 | 207 | 186 | 241 | 34 | 244 | 158 | 253 | 185 | |
5 | 36 | 113 | 48 | 90 | 221 | 55 | 144 | 121 | 69 | 86 | 235 | 14 | 250 | 104 | 110 | 127 | |
6 | 42 | 59 | 167 | 165 | 6 | 154 | 24 | 39 | 75 | 147 | 118 | 152 | 142 | 120 | 38 | 117 | |
7 | 188 | 52 | 9 | 233 | 43 | 60 | 29 | 240 | 148 | 0 | 33 | 231 | 141 | 101 | 193 | 16 | |
8 | 50 | 18 | 94 | 3 | 8 | 249 | 97 | 78 | 195 | 61 | 31 | 194 | 218 | 208 | 65 | 51 | |
9 | 2 | 189 | 4 | 192 | 47 | 252 | 19 | 157 | 26 | 108 | 107 | 182 | 232 | 230 | 183 | 234 | |
A | 111 | 215 | 161 | 87 | 190 | 163 | 162 | 170 | 91 | 32 | 136 | 23 | 255 | 223 | 67 | 248 | |
B | 85 | 7 | 143 | 160 | 35 | 116 | 236 | 54 | 202 | 245 | 206 | 45 | 172 | 246 | 137 | 199 | |
C | 133 | 20 | 88 | 139 | 227 | 27 | 198 | 229 | 191 | 115 | 173 | 17 | 166 | 205 | 179 | 99 | |
D | 150 | 209 | 169 | 37 | 210 | 49 | 25 | 156 | 204 | 135 | 225 | 216 | 237 | 12 | 46 | 212 | |
E | 180 | 82 | 124 | 203 | 119 | 71 | 168 | 41 | 201 | 126 | 254 | 197 | 138 | 95 | 1 | 213 | |
F | 176 | 134 | 103 | 239 | 72 | 70 | 62 | 73 | 164 | 174 | 109 | 123 | 219 | 132 | 196 | 181 | |
S8∗10 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 188 | 194 | 208 | 108 | 112 | 29 | 242 | 78 | 73 | 90 | 83 | 40 | 181 | 233 | 176 | 26 | |
1 | 191 | 18 | 196 | 161 | 22 | 159 | 154 | 52 | 32 | 198 | 116 | 132 | 228 | 10 | 126 | 152 | |
2 | 214 | 167 | 42 | 27 | 95 | 59 | 200 | 246 | 113 | 226 | 49 | 96 | 178 | 60 | 174 | 53 | |
3 | 250 | 204 | 150 | 189 | 142 | 120 | 82 | 0 | 21 | 144 | 41 | 62 | 37 | 207 | 138 | 229 | |
4 | 163 | 64 | 218 | 66 | 141 | 193 | 19 | 247 | 55 | 50 | 24 | 130 | 252 | 254 | 46 | 166 | |
5 | 146 | 30 | 136 | 128 | 231 | 169 | 239 | 11 | 43 | 179 | 16 | 124 | 213 | 15 | 232 | 51 | |
6 | 245 | 164 | 114 | 91 | 23 | 44 | 7 | 143 | 85 | 162 | 74 | 121 | 77 | 211 | 34 | 133 | |
7 | 20 | 227 | 145 | 25 | 104 | 107 | 39 | 70 | 129 | 84 | 54 | 101 | 160 | 68 | 209 | 220 | |
8 | 79 | 192 | 153 | 241 | 157 | 81 | 147 | 238 | 249 | 33 | 221 | 47 | 65 | 118 | 182 | 243 | |
9 | 63 | 251 | 45 | 244 | 222 | 175 | 71 | 131 | 137 | 171 | 111 | 195 | 203 | 212 | 58 | 69 | |
A | 234 | 158 | 235 | 253 | 135 | 61 | 134 | 17 | 105 | 155 | 88 | 80 | 219 | 13 | 89 | 180 | |
B | 67 | 184 | 72 | 168 | 6 | 206 | 103 | 9 | 139 | 123 | 187 | 151 | 248 | 48 | 86 | 94 | |
C | 110 | 36 | 75 | 119 | 148 | 117 | 14 | 165 | 127 | 202 | 109 | 156 | 186 | 35 | 93 | 199 | |
D | 2 | 28 | 216 | 38 | 255 | 5 | 201 | 102 | 217 | 99 | 172 | 205 | 224 | 1 | 12 | 177 | |
E | 87 | 8 | 215 | 140 | 223 | 97 | 100 | 125 | 225 | 183 | 122 | 106 | 57 | 4 | 185 | 197 | |
F | 236 | 115 | 173 | 3 | 92 | 230 | 56 | 170 | 210 | 52 | 237 | 190 | 240 | 31 | 76 | 98 | |
S10∗10 | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 141 | 234 | 13 | 238 | 170 | 94 | 194 | 171 | 67 | 225 | 134 | 45 | 49 | 186 | 71 | 53 | |
1 | 218 | 229 | 52 | 17 | 249 | 173 | 190 | 252 | 23 | 16 | 68 | 96 | 136 | 0 | 3 | 177 | |
2 | 230 | 119 | 155 | 70 | 6 | 89 | 172 | 76 | 152 | 176 | 201 | 148 | 109 | 124 | 137 | 215 | |
3 | 242 | 103 | 135 | 114 | 65 | 97 | 41 | 227 | 126 | 7 | 139 | 18 | 66 | 48 | 86 | 184 | |
4 | 116 | 8 | 151 | 91 | 249 | 98 | 39 | 179 | 10 | 160 | 178 | 195 | 149 | 187 | 19 | 226 | |
5 | 113 | 165 | 207 | 140 | 131 | 38 | 112 | 208 | 188 | 69 | 209 | 51 | 200 | 120 | 78 | 108 | |
6 | 248 | 85 | 90 | 37 | 211 | 250 | 241 | 161 | 159 | 47 | 81 | 55 | 29 | 247 | 224 | 240 | |
7 | 210 | 125 | 22 | 11 | 182 | 236 | 174 | 92 | 121 | 145 | 129 | 214 | 26 | 115 | 185 | 132 | |
8 | 128 | 200 | 31 | 166 | 192 | 246 | 183 | 43 | 239 | 232 | 36 | 143 | 57 | 217 | 206 | 107 | |
9 | 61 | 244 | 54 | 44 | 153 | 12 | 216 | 198 | 20 | 4 | 213 | 88 | 228 | 25 | 162 | 147 | |
A | 50 | 63 | 175 | 245 | 104 | 142 | 219 | 204 | 117 | 144 | 74 | 169 | 205 | 46 | 158 | 59 | |
B | 133 | 253 | 212 | 163 | 95 | 105 | 223 | 60 | 199 | 138 | 203 | 42 | 33 | 75 | 157 | 202 | |
C | 118 | 110 | 150 | 191 | 14 | 181 | 56 | 73 | 1 | 100 | 180 | 220 | 243 | 15 | 111 | 80 | |
D | 32 | 189 | 84 | 233 | 40 | 254 | 101 | 235 | 64 | 222 | 99 | 122 | 130 | 77 | 221 | 5 | |
E | 146 | 24 | 82 | 72 | 9 | 102 | 164 | 2 | 123 | 62 | 34 | 58 | 154 | 127 | 231 | 93 | |
F | 87 | 35 | 83 | 197 | 237 | 156 | 196 | 193 | 21 | 251 | 27 | 30 | 167 | 168 | 28 | 79 |
State Matrix | Shift Box | Result | |||||||||
S0,0 | S0,1 | S0,2 | S0,3 | S0,0 | S3,3 | S2,0 | S3,1 | S0,0 | S1,1 | S2,2 | S3,3 |
S1,0 | S1,1 | S1,2 | S1,3 | S1,0 | S0,1 | S2,2 | S2,3 | S1,0 | S2,1 | S3,2 | S2,0 |
S2,0 | S2,1 | S2,2 | S2,3 | S1,3 | S1,1 | S0,2 | S2,1 | S0,2 | S2,3 | S1,2 | S1,3 |
S3,0 | S3,1 | S3,2 | S3,3 | S3,0 | S3,2 | S1,2 | S0,3 | S3,0 | S0,3 | S3,1 | S0,1 |
Rounds | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Round constant | 01 | 02 | 04 | 08 | 10 | 20 | 40 | 80 | 1b | 36 |
Encryption | Decryption | |
Plaintext TWOONENINETWO | Ciphertext | |
Round0 | 7F097A3667C0B786E59E7BED299B3853 | 70BAE70AEB6E28E5B61B87308F9A87F3 |
Round1 | 0C2A223FBE983E29CF03F40EA1478E80 | D5DAC6864CF89ED51A74F80D058117C4 |
Round2 | 411F171705861FDEDA2B3BE898E986C9 | 97D05A6454C195589FA0C446C5CD62B4 |
Round3 | 46159F31736643F2DBEC157BCCB659C3 | 3D3668E9EF4768A47F20EED2687AAE95 |
Round4 | E8145C9CBBAE049F029D20E31D8FA2C0 | 7AD27EB4EA69740BB33B44EC7B44A153 |
Round5 | 18D695C3DDF6BBF2B58330EF533AE156 | 745ACBE0832FFFA49A0210BC69B94B59 |
Round6 | 74613DDFBA037336CCD063823E2C2C32 | 0088533489FB1EEA73C544E6088D289C |
Round7 | 984E47AE1A5540DEF5D9E1C6A7EB2CE0 | B24455F9A9AF562F98E16B0BA8ECB79A |
Round8 | FDEE0A3DCBEDED7B8A75B3711F8997F6 | 732C69322B1EC0CB43EF5045BFBE16E0 |
Round9 | 0F4643FC0948638C4A1172638FA068E8 | 382F51A9A2339F19785F40B61FD47504 |
Round10 | B8AE1A606BCA28D666DA0D6DD57A7282 | 54776F204F6E65204E696E652054776F |
Ciphertext | Plaintext TWOONENINETWO |
S-box 1 | S-box 2 | S-box 3 | S-box 4 | S-box 5 | S-box 6 | S-box 7 | S-box 8 | S-box 9 | S-box 10 | ||
Non-linearity | Max | 106 | 106 | 107 | 106 | 106 | 108 | 107 | 107 | 108 | 108 |
Min | 100 | 100 | 98 | 100 | 100 | 96 | 97 | 100 | 100 | 96 | |
Average | 103.25 | 103.375 | 103.875 | 102.875 | 103.625 | 102.375 | 103.625 | 104.125 | 104.375 | 103.875 | |
Strict Avalanche Criteria (SAC) | Max | 0.625 | 0.648438 | 0.601563 | 0.601563 | 0.59375 | 0.609375 | 0.625 | 0.585938 | 0.609375 | 0.578125 |
Min | 0.40625 | 0.0429688 | 0.429688 | 0.40625 | 0.382813 | 0.40625 | 0.375 | 0.40625 | 0.421875 | 0.390625 | |
Average | 0.501221 | 0.503906 | 0.506592 | 0.501709 | 0.505615 | 0.502686 | 0.505859 | 0.499756 | 0.501221 | 0.499023 | |
S.D | 0.0217624 | 0.0206006 | 0.0212301 | 0.0211541 | 0.0221775 | 0.0220563 | 0.0240203 | 0.0195796 | 0.0241116 | 0.0191802 | |
Bit Independent Criteria (BIC) | Min | 98 | 93 | 97 | 97 | 96 | 97 | 102 | 97 | 97 | 99 |
Average | 103.5 | 103.179 | 103.464 | 103.393 | 103.393 | 102.964 | 104.75 | 103.464 | 103.536 | 103.75 | |
S.D | 2.5425 | 3.20773 | 2.89682 | 2.78182 | 3.2551 | 2.51399 | 1.7243 | 2.74489 | 2.93358 | 2.30876 | |
BIC-SAC | Min | 0.464844 | 0.482422 | 0.466797 | 0.470703 | 0.476563 | 0.462891 | 0.470703 | 0.46875 | 0.462891 | 0.458984 |
Average | 0.498117 | 0.503278 | 0.501744 | 0.503418 | 0.506836 | 0.504534 | 0.501395 | 0.503976 | 0.504534 | 0.50007 | |
S.D | 0.0144139 | 0.011881 | 0.0193514 | 0.015125 | 0.0118402 | 0.0186685 | 0.0149098 | 0.0132311 | 0.0186685 | 0.0155593 | |
Differential Probability | D.P | 0.046875 | 0.015625 | 0.0390625 | 0.046875 | 0.0390625 | 0.046875 | 0.0390625 | 0.046875 | 0.046875 | 0.046875 |
Linear Probability | Max | 162 | 161 | 165 | 163 | 161 | 162 | 163 | 159 | 162 | 160 |
L.P | 0.140625 | 0.144531 | 0.136719 | 0.144531 | 0.132813 | 0.140625 | 0.136719 | 0.144531 | 0.13281 | 0.125 |
S-boxes | Nonlinearity | SAC | BIC-SAC | BIC | DP | LP |
AES S-box [3] | 112 | 0.5058 | 0.504 | 112.0 | 0.0156 | 0.062 |
APA S-box [4] | 112 | 0.4987 | 0.499 | 112.0 | 0.0156 | 0.062 |
Gray S-box [5] | 112 | 0.5058 | 0.502 | 112.0 | 0.0156 | 0.062 |
Skipjack S-box [21] | 105.7 | 0.4980 | 0.499 | 104.1 | 0.0468 | 0.109 |
Xyi S-box [19] | 105 | 0.5048 | 0.503 | 103.7 | 0.0468 | 0.156 |
Residue Prime [8] | 99.5 | 0.5012 | 0.502 | 101.7 | 0.2810 | 0.132 |
Proposed S-box 1 | 103.25 | 0.501221 | 0.498117 | 103.5 | 0.046875 | 0.140625 |
Proposed S-box 2 | 103.375 | 0.503906 | 0.503278 | 103.179 | 0.015625 | 0.144531 |
Proposed S-box 3 | 103.875 | 0.506592 | 0.501744 | 103.464 | 0.0390625 | 0.136719 |
Proposed S-box 4 | 102.875 | 0.501709 | 0.503418 | 103.393 | 0.046875 | 0.144531 |
Proposed S-box 5 | 103.625 | 0.505615 | 0.506836 | 103.393 | 0.0390625 | 0.132813 |
Proposed S-box 6 | 102.375 | 0.502686 | 0.504534 | 102.964 | 0.046875 | 0.140625 |
Proposed S-box 7 | 103.625 | 0.505859 | 0.501395 | 104.75 | 0.0390625 | 0.136719 |
Proposed S-box 8 | 104.125 | 0.499756 | 0.503976 | 103.464 | 0.046875 | 0.144531 |
Proposed S-box 9 | 104.375 | 0.501221 | 0.504534 | 103.536 | 0.046875 | 0.13281 |
Proposed S-box 10 | 103.875 | 0.499023 | 0.50007 | 103.75 | 0.046875 | 0.125 |
Average proposed results | 103.538 | 0.502759 | 0.50279 | 103.539 | 0.041406 | 0.13789 |
Permutation | S-boxes | |
μt(S11¬); 1 ≤ t ≤ 16 | → | S1j∗;1≤j≤16 |
μt(S12¬); 1 ≤ t ≤ 16 | → | S2j∗;1≤j≤16 |
μt(S13¬); 1 ≤ t ≤ 16 | → | S3j∗;1≤j≤16 |
…… | …… | …… |
…… | …… | …… |
μt(S1010¬); 1 ≤ t ≤ 16 | → | S10j∗;1≤j≤16 |
Transformation: T=XB⊕C [16] | |||
Polynomials | Best Choice Matrix X | Inverse of Matrix X | Suitable constant Matric C (order 4 × 1) |
P1(t)=t4+t+1 | a1=(0010000110000100) | (a1)−1=(0010000110000100) | 0×aand0×f |
P2(t)=t4+t3+1 | a2=(1011110111100111) | (a2)−1=(1110011110111101) | 0×3,0×9,0×cand0×d |
P3(t)=t4+t3+t2+t+1 | a3=(1100010101100001) | (a3)−1=(1101010101110001) | 0×4,0×5,0×dand0×f |
S-box combination | Number of S-boxes | Representation | |
ξ(S1Si) , 1≤i≤10 | ![]() |
10 S-boxes | S1j;1≤j≤10 |
ξ(S2Si) , 1≤i≤10 | ![]() |
10 S-boxes | S2j;1≤j≤10 |
ξ(S3Si) , 1≤i≤10 | ![]() |
10 S-boxes | S3j;1≤j≤10 |
………. | ……….. | …… | ………. |
ξ(S10Si) , 1≤i≤10 | ![]() |
10 S-boxes | S10j;1≤j≤10 |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | |
0 | 216 | 198 | 97 | 110 | 207 | 107 | 203 | 31 | 36 | 64 | 166 | 181 | 146 | 212 | 125 | 39 |
1 | 65 | 252 | 26 | 240 | 45 | 78 | 90 | 235 | 83 | 151 | 162 | 87 | 59 | 111 | 135 | 250 |
2 | 227 | 22 | 241 | 105 | 92 | 225 | 10 | 215 | 35 | 113 | 117 | 37 | 178 | 100 | 177 | 246 |
3 | 123 | 52 | 46 | 24 | 20 | 11 | 89 | 251 | 126 | 42 | 130 | 51 | 153 | 234 | 17 | 49 |
4 | 81 | 84 | 229 | 48 | 94 | 19 | 106 | 73 | 221 | 62 | 176 | 165 | 180 | 47 | 171 | 190 |
5 | 196 | 12 | 195 | 194 | 132 | 155 | 224 | 200 | 189 | 197 | 33 | 237 | 164 | 186 | 3 | 38 |
6 | 182 | 147 | 140 | 77 | 144 | 8 | 248 | 70 | 222 | 86 | 148 | 82 | 184 | 118 | 187 | 239 |
7 | 142 | 232 | 121 | 53 | 30 | 191 | 236 | 172 | 192 | 71 | 50 | 54 | 95 | 80 | 44 | 2 |
8 | 223 | 179 | 137 | 136 | 7 | 188 | 112 | 230 | 66 | 255 | 32 | 139 | 18 | 206 | 93 | 173 |
9 | 152 | 143 | 149 | 1 | 163 | 231 | 72 | 244 | 109 | 60 | 69 | 116 | 68 | 174 | 211 | 128 |
A | 79 | 219 | 5 | 16 | 157 | 23 | 120 | 150 | 202 | 115 | 63 | 131 | 193 | 119 | 61 | 201 |
B | 96 | 58 | 254 | 133 | 91 | 168 | 85 | 204 | 161 | 158 | 101 | 103 | 160 | 228 | 124 | 245 |
C | 98 | 141 | 4 | 242 | 159 | 185 | 170 | 76 | 217 | 21 | 210 | 29 | 27 | 0 | 154 | 43 |
D | 167 | 208 | 220 | 104 | 108 | 213 | 249 | 238 | 233 | 14 | 28 | 134 | 129 | 34 | 243 | 40 |
E | 127 | 209 | 169 | 102 | 41 | 175 | 145 | 6 | 122 | 15 | 253 | 205 | 13 | 25 | 199 | 56 |
F | 156 | 99 | 226 | 67 | 55 | 88 | 138 | 218 | 214 | 75 | 114 | 57 | 183 | 247 | 9 | 74 |
{\boldsymbol{S}}_{\bf{2}}^{{\bf{1}}^{\boldsymbol{*}}} | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 226 | 201 | 148 | 155 | 207 | 158 | 206 | 47 | 17 | 128 | 89 | 117 | 104 | 225 | 183 | 29 | |
1 | 132 | 243 | 42 | 240 | 23 | 139 | 170 | 222 | 172 | 109 | 88 | 173 | 62 | 159 | 77 | 250 | |
2 | 220 | 41 | 244 | 150 | 163 | 212 | 10 | 237 | 28 | 180 | 181 | 21 | 120 | 145 | 116 | 249 | |
3 | 190 | 49 | 27 | 34 | 33 | 14 | 166 | 254 | 187 | 26 | 72 | 60 | 102 | 218 | 36 | 52 | |
4 | 164 | 161 | 213 | 48 | 171 | 44 | 154 | 134 | 231 | 59 | 112 | 85 | 113 | 31 | 94 | 123 | |
5 | 193 | 3 | 204 | 200 | 65 | 110 | 208 | 194 | 119 | 197 | 20 | 215 | 81 | 122 | 12 | 25 | |
6 | 121 | 108 | 67 | 135 | 96 | 2 | 242 | 137 | 235 | 169 | 97 | 168 | 114 | 185 | 126 | 223 | |
7 | 75 | 210 | 182 | 53 | 43 | 127 | 211 | 83 | 192 | 141 | 56 | 57 | 175 | 160 | 19 | 8 | |
8 | 239 | 124 | 70 | 66 | 13 | 115 | 176 | 217 | 136 | 249 | 16 | 78 | 40 | 203 | 167 | 87 | |
9 | 98 | 79 | 101 | 4 | 92 | 221 | 130 | 241 | 151 | 51 | 133 | 177 | 129 | 91 | 236 | 63 | |
A | 143 | 238 | 5 | 32 | 103 | 45 | 178 | 105 | 202 | 188 | 63 | 76 | 196 | 189 | 55 | 198 | |
B | 144 | 58 | 251 | 69 | 174 | 82 | 165 | 195 | 84 | 107 | 149 | 157 | 80 | 209 | 179 | 245 | |
C | 152 | 71 | 1 | 248 | 111 | 118 | 90 | 131 | 230 | 37 | 232 | 29 | 46 | 0 | 106 | 30 | |
D | 93 | 224 | 227 | 146 | 147 | 229 | 246 | 219 | 214 | 11 | 35 | 73 | 68 | 24 | 252 | 18 | |
E | 191 | 228 | 86 | 153 | 22 | 95 | 100 | 9 | 186 | 15 | 247 | 199 | 7 | 38 | 205 | 50 | |
F | 99 | 156 | 216 | 140 | 61 | 162 | 74 | 234 | 233 | 142 | 184 | 54 | 125 | 253 | 6 | 138 | |
{\boldsymbol{S}}_{\bf{1}}^{{\bf{2}}^{\boldsymbol{*}}} | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 180 | 253 | 126 | 44 | 234 | 188 | 41 | 139 | 116 | 133 | 228 | 19 | 12 | 146 | 16 | 64 | |
1 | 166 | 49 | 171 | 135 | 246 | 87 | 111 | 81 | 183 | 231 | 100 | 99 | 222 | 46 | 164 | 7 | |
2 | 140 | 144 | 109 | 218 | 232 | 102 | 203 | 98 | 214 | 160 | 244 | 223 | 56 | 104 | 201 | 63 | |
3 | 137 | 10 | 181 | 110 | 250 | 219 | 17 | 103 | 121 | 161 | 75 | 28 | 23 | 35 | 77 | 176 | |
4 | 122 | 127 | 136 | 117 | 209 | 221 | 195 | 147 | 68 | 205 | 130 | 236 | 157 | 115 | 3 | 94 | |
5 | 238 | 237 | 217 | 177 | 131 | 113 | 105 | 52 | 48 | 9 | 167 | 235 | 186 | 185 | 229 | 193 | |
6 | 73 | 79 | 184 | 50 | 173 | 165 | 251 | 108 | 2 | 212 | 172 | 220 | 13 | 119 | 199 | 226 | |
7 | 149 | 57 | 34 | 155 | 197 | 224 | 27 | 120 | 47 | 90 | 1 | 32 | 88 | 96 | 170 | 43 | |
8 | 36 | 200 | 15 | 163 | 192 | 37 | 247 | 182 | 112 | 69 | 76 | 168 | 153 | 80 | 123 | 202 | |
9 | 53 | 25 | 190 | 42 | 150 | 59 | 58 | 141 | 189 | 118 | 6 | 230 | 106 | 124 | 78 | 215 | |
A | 148 | 240 | 158 | 8 | 62 | 60 | 51 | 248 | 249 | 239 | 86 | 21 | 92 | 174 | 38 | 74 | |
B | 145 | 45 | 134 | 29 | 175 | 194 | 71 | 178 | 33 | 187 | 191 | 129 | 152 | 198 | 82 | 55 | |
C | 93 | 208 | 154 | 97 | 255 | 72 | 245 | 5 | 11 | 107 | 67 | 26 | 156 | 84 | 54 | 211 | |
D | 125 | 20 | 14 | 85 | 252 | 65 | 227 | 18 | 213 | 242 | 40 | 4 | 22 | 142 | 132 | 61 | |
E | 233 | 66 | 210 | 138 | 196 | 179 | 143 | 216 | 207 | 114 | 151 | 243 | 70 | 159 | 95 | 39 | |
F | 241 | 206 | 91 | 196 | 31 | 30 | 162 | 225 | 24 | 89 | 169 | 254 | 0 | 83 | 128 | 204 | |
{\boldsymbol{S}}_{\bf{5}}^{{\bf{4}}^{\boldsymbol{*}}} | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 124 | 233 | 166 | 181 | 117 | 75 | 174 | 246 | 2 | 235 | 248 | 15 | 184 | 69 | 200 | 60 | |
1 | 234 | 82 | 138 | 220 | 77 | 165 | 53 | 57 | 104 | 8 | 86 | 178 | 98 | 127 | 212 | 110 | |
2 | 76 | 172 | 182 | 158 | 52 | 245 | 111 | 99 | 219 | 102 | 120 | 54 | 32 | 185 | 112 | 88 | |
3 | 16 | 136 | 67 | 17 | 24 | 95 | 202 | 10 | 155 | 132 | 215 | 93 | 188 | 29 | 250 | 161 | |
4 | 209 | 105 | 97 | 47 | 59 | 252 | 229 | 30 | 118 | 213 | 139 | 237 | 44 | 128 | 119 | 103 | |
5 | 169 | 91 | 74 | 123 | 190 | 142 | 64 | 255 | 9 | 177 | 116 | 144 | 35 | 218 | 90 | 193 | |
6 | 68 | 0 | 240 | 216 | 176 | 242 | 230 | 187 | 78 | 31 | 238 | 101 | 33 | 23 | 173 | 156 | |
7 | 1 | 186 | 143 | 204 | 45 | 175 | 55 | 130 | 43 | 241 | 13 | 205 | 80 | 148 | 163 | 121 | |
8 | 84 | 14 | 207 | 159 | 168 | 239 | 249 | 134 | 21 | 66 | 48 | 70 | 151 | 131 | 5 | 73 | |
9 | 224 | 3 | 133 | 232 | 20 | 196 | 89 | 79 | 109 | 42 | 152 | 28 | 22 | 115 | 122 | 114 | |
A | 141 | 41 | 189 | 180 | 251 | 226 | 194 | 52 | 135 | 198 | 222 | 147 | 100 | 236 | 50 | 210 | |
B | 51 | 167 | 171 | 140 | 137 | 63 | 34 | 129 | 195 | 164 | 18 | 231 | 228 | 62 | 7 | 92 | |
C | 19 | 191 | 145 | 160 | 247 | 113 | 29 | 4 | 227 | 106 | 71 | 253 | 38 | 154 | 203 | 25 | |
D | 11 | 96 | 46 | 208 | 12 | 221 | 146 | 214 | 87 | 153 | 6 | 179 | 94 | 58 | 72 | 40 | |
E | 197 | 211 | 56 | 244 | 225 | 61 | 217 | 85 | 201 | 206 | 243 | 223 | 157 | 150 | 81 | 36 | |
F | 162 | 108 | 83 | 192 | 26 | 254 | 37 | 183 | 65 | 125 | 199 | 107 | 126 | 49 | 170 | 27 | |
{\boldsymbol{S}}_{\bf{7}}^{{\bf{4}}^{\boldsymbol{*}}} | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 121 | 221 | 55 | 23 | 113 | 48 | 215 | 54 | 111 | 245 | 204 | 86 | 37 | 82 | 161 | 124 | |
1 | 3 | 65 | 97 | 180 | 46 | 25 | 7 | 45 | 197 | 85 | 226 | 195 | 130 | 16 | 143 | 101 | |
2 | 39 | 6 | 154 | 56 | 59 | 167 | 153 | 229 | 106 | 115 | 131 | 147 | 100 | 145 | 247 | 11 | |
3 | 89 | 103 | 134 | 142 | 120 | 117 | 252` | 79 | 118 | 242 | 228 | 76 | 125 | 140 | 47 | 105 | |
4 | 122 | 81 | 151 | 10 | 159 | 58 | 175 | 129 | 66 | 207 | 166 | 220 | 173 | 38 | 22 | 24 | |
5 | 14 | 116 | 35 | 170 | 51 | 208 | 93 | 222 | 32 | 30 | 41 | 36 | 126 | 71 | 84 | 119 | |
6 | 0 | 98 | 171 | 250 | 104 | 127 | 249 | 136 | 235 | 255 | 156 | 240 | 135 | 49 | 8 | 210 | |
7 | 218 | 163 | 190 | 33 | 12 | 212 | 196 | 237 | 141 | 225 | 233 | 31 | 148 | 29 | 40 | 193 | |
8 | 152 | 27 | 227 | 184 | 234 | 230 | 181 | 219 | 74 | 109 | 112 | 42 | 186 | 21 | 132 | 177 | |
9 | 192 | 183 | 19 | 28 | 5 | 155 | 20 | 17 | 34 | 133 | 164 | 26 | 239 | 63 | 88 | 128 | |
A | 15 | 92 | 13 | 194 | 43 | 60 | 18 | 251 | 50 | 114 | 216 | 200 | 150 | 1 | 94 | 168 | |
B | 87 | 67 | 162 | 231 | 9 | 52 | 169 | 203 | 188 | 201 | 172 | 91 | 206 | 110 | 209 | 144 | |
C | 232 | 243 | 217 | 83 | 224 | 57 | 62 | 77 | 102 | 187 | 44 | 107 | 238 | 214 | 196 | 53 | |
D | 108 | 68 | 64 | 165 | 158 | 185 | 205 | 244 | 75 | 241 | 139 | 157 | 191 | 198 | 99 | 179 | |
E | 73 | 72 | 70 | 182 | 80 | 146 | 189 | 176 | 2 | 123 | 178 | 174 | 211 | 253 | 4 | 96 | |
F | 61 | 223 | 248 | 90 | 95 | 213 | 246 | 138 | 69 | 254 | 160 | 78 | 202 | 236 | 199 | 137 | |
{\boldsymbol{S}}_{\bf{9}}^{{\bf{4}}^{\boldsymbol{*}}} | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 109 | 237 | 127 | 208 | 221 | 166 | 196 | 114 | 21 | 188 | 244 | 17 | 137 | 246 | 85 | 229 | |
1 | 140 | 190 | 189 | 116 | 7 | 37 | 29 | 146 | 211 | 20 | 143 | 41 | 226 | 207 | 78 | 130 | |
2 | 233 | 222 | 230 | 12 | 231 | 202 | 24 | 11 | 142 | 155 | 74 | 48 | 6 | 87 | 170 | 105 | |
3 | 3 | 70 | 210 | 165 | 31 | 40 | 197 | 186 | 161 | 76 | 52 | 184 | 86 | 152 | 89 | 8 | |
4 | 14 | 103 | 25 | 46 | 38 | 153 | 16 | 169 | 151 | 22 | 191 | 111 | 212 | 9 | 249 | 225 | |
5 | 236 | 66 | 93 | 90 | 173 | 63 | 238 | 131 | 35 | 195 | 65 | 224 | 96 | 242 | 10 | 182 | |
6 | 108 | 26 | 0 | 69 | 30 | 84 | 18 | 49 | 192 | 122 | 58 | 79 | 91 | 124 | 95 | 201 | |
7 | 94 | 83 | 227 | 59 | 54 | 47 | 247 | 75 | 100 | 193 | 112 | 39 | 156 | 34 | 118 | 60 | |
8 | 171 | 180 | 206 | 203 | 33 | 32 | 215 | 113 | 145 | 183 | 5 | 44 | 43 | 214 | 168 | 117 | |
9 | 240 | 129 | 71 | 72 | 235 | 135 | 250 | 64 | 19 | 149 | 218 | 120 | 119 | 107 | 68 | 36 | |
A | 132 | 45 | 115 | 123 | 56 | 28 | 150 | 61 | 216 | 126 | 50 | 213 | 80 | 27 | 178 | 174 | |
B | 92 | 42 | 167 | 157 | 51 | 176 | 138 | 158 | 104 | 223 | 181 | 164 | 82 | 219 | 252 | 255 | |
C | 106 | 148 | 97 | 177 | 196 | 102 | 81 | 53 | 200 | 99 | 251 | 228 | 243 | 57 | 194 | 62 | |
D | 172 | 128 | 88 | 98 | 147 | 204 | 125 | 220 | 185 | 198 | 245 | 110 | 248 | 2 | 159 | 187 | |
E | 239 | 134 | 73 | 121 | 4 | 217 | 205 | 1 | 234 | 253 | 209 | 160 | 13 | 139 | 77 | 241 | |
F | 136 | 162 | 144 | 179 | 163 | 67 | 154 | 15 | 23 | 55 | 133 | 141 | 232 | 175 | 254 | 199 | |
{\boldsymbol{S}}_{\bf{9}}^{{\bf{6}}^{\boldsymbol{*}}} | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 81 | 123 | 151 | 209 | 6 | 13 | 92 | 80 | 3 | 27 | 251 | 116 | 68 | 201 | 217 | 111 | |
1 | 52 | 146 | 213 | 46 | 83 | 157 | 154 | 51 | 165 | 19 | 141 | 43 | 132 | 9 | 254 | 55 | |
2 | 48 | 11 | 104 | 203 | 187 | 172 | 24 | 181 | 108 | 139 | 224 | 71 | 18 | 66 | 135 | 84 | |
3 | 133 | 25 | 0 | 230 | 195 | 164 | 26 | 220 | 109 | 226 | 247 | 114 | 125 | 222 | 252 | 255 | |
4 | 240 | 248 | 60 | 59 | 218 | 168 | 177 | 54 | 131 | 188 | 10 | 76 | 16 | 182 | 233 | 44 | |
5 | 5 | 162 | 211 | 176 | 160 | 21 | 202 | 138 | 126 | 171 | 244 | 129 | 74 | 246 | 37 | 77 | |
6 | 30 | 9 | 178 | 50 | 70 | 72 | 128 | 155 | 121 | 7 | 161 | 231 | 190 | 17 | 249 | 113 | |
7 | 184 | 34 | 140 | 228 | 95 | 227 | 87 | 238 | 20 | 205 | 31 | 73 | 96 | 63 | 208 | 29 | |
8 | 122 | 212 | 185 | 40 | 1 | 41 | 137 | 253 | 127 | 2 | 186 | 232 | 75 | 107 | 153 | 110 | |
9 | 88 | 180 | 98 | 12 | 14 | 245 | 196 | 38 | 183 | 166 | 42 | 192 | 103 | 167 | 85 | 22 | |
A | 100 | 156 | 79 | 124 | 142 | 115 | 130 | 158 | 174 | 191 | 67 | 117 | 163 | 189 | 175 | 57 | |
B | 56 | 243 | 102 | 91 | 143 | 97 | 53 | 89 | 106 | 134 | 145 | 105 | 148 | 119 | 169 | 4 | |
C | 64 | 206 | 23 | 118 | 8 | 39 | 61 | 152 | 62 | 216 | 58 | 229 | 52 | 65 | 45 | 241 | |
D | 28 | 120 | 35 | 170 | 193 | 144 | 194 | 199 | 179 | 15 | 33 | 112 | 82 | 242 | 235 | 234 | |
E | 207 | 204 | 69 | 239 | 200 | 221 | 150 | 236 | 173 | 47 | 86 | 214 | 198 | 93 | 210 | 94 | |
F | 136 | 32 | 223 | 36 | 147 | 78 | 237 | 215 | 90 | 225 | 250 | 197 | 149 | 99 | 159 | 219 | |
{\boldsymbol{S}}_{\bf{10}}^{{\bf{5}}^{\boldsymbol{*}}} | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 209 | 15 | 168 | 151 | 7 | 253 | 88 | 17 | 167 | 222 | 166 | 110 | 188 | 235 | 123 | 115 | |
1 | 221 | 141 | 135 | 63 | 176 | 58 | 242 | 96 | 3 | 0 | 73 | 52 | 84 | 90 | 112 | 42 | |
2 | 41 | 129 | 145 | 233 | 68 | 231 | 97 | 2 | 54 | 205 | 1 | 38 | 192 | 104 | 155 | 5 | |
3 | 22 | 212 | 225 | 76 | 211 | 23 | 232 | 187 | 92 | 6 | 186 | 154 | 34 | 8 | 10 | 80 | |
4 | 121 | 208 | 61 | 223 | 119 | 219 | 64 | 9 | 148 | 174 | 216 | 248 | 44 | 120 | 32 | 189 | |
5 | 191 | 217 | 214 | 244 | 142 | 93 | 165 | 69 | 158 | 39 | 159 | 195 | 24 | 228 | 245 | 170 | |
6 | 75 | 14 | 111 | 241 | 33 | 196 | 27 | 51 | 131 | 215 | 237 | 31 | 160 | 182 | 98 | 107 | |
7 | 43 | 240 | 74 | 130 | 204 | 162 | 26 | 202 | 49 | 85 | 40 | 66 | 179 | 254 | 59 | 21 | |
8 | 137 | 238 | 56 | 220 | 62 | 140 | 95 | 210 | 124 | 246 | 226 | 78 | 133 | 213 | 29 | 207 | |
9 | 153 | 109 | 106 | 127 | 149 | 190 | 161 | 147 | 218 | 150 | 16 | 152 | 243 | 236 | 105 | 132 | |
A | 55 | 227 | 163 | 13 | 79 | 156 | 183 | 91 | 83 | 67 | 173 | 194 | 185 | 117 | 157 | 82 | |
B | 37 | 108 | 28 | 181 | 175 | 178 | 200 | 77 | 250 | 86 | 139 | 252 | 19 | 128 | 94 | 53 | |
C | 65 | 103 | 89 | 206 | 255 | 72 | 201 | 239 | 36 | 197 | 136 | 57 | 48 | 4 | 12 | 113 | |
D | 125 | 203 | 193 | 177 | 126 | 234 | 102 | 60 | 25 | 144 | 230 | 172 | 251 | 146 | 184 | 47 | |
E | 30 | 114 | 45 | 11 | 50 | 224 | 171 | 100 | 35 | 199 | 18 | 122 | 87 | 20 | 138 | 247 | |
F | 180 | 229 | 99 | 143 | 71 | 118 | 70 | 164 | 81 | 134 | 249 | 198 | 46 | 52 | 169 | 116 | |
{\boldsymbol{S}}_{\bf{7}}^{{\bf{7}}^{\boldsymbol{*}}} | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 106 | 153 | 247 | 122 | 217 | 243 | 151 | 184 | 220 | 74 | 79 | 56 | 242 | 68 | 81 | 64 | |
1 | 251 | 171 | 98 | 130 | 92 | 13 | 196 | 15 | 226 | 200 | 30 | 114 | 222 | 84 | 40 | 93 | |
2 | 211 | 22 | 175 | 100 | 105 | 140 | 155 | 228 | 131 | 125 | 187 | 178 | 77 | 224 | 5 | 57 | |
3 | 66 | 58 | 159 | 44 | 80 | 146 | 214 | 76 | 238 | 89 | 83 | 10 | 102 | 128 | 53 | 63 | |
4 | 28 | 145 | 11 | 129 | 177 | 21 | 96 | 112 | 207 | 186 | 241 | 34 | 244 | 158 | 253 | 185 | |
5 | 36 | 113 | 48 | 90 | 221 | 55 | 144 | 121 | 69 | 86 | 235 | 14 | 250 | 104 | 110 | 127 | |
6 | 42 | 59 | 167 | 165 | 6 | 154 | 24 | 39 | 75 | 147 | 118 | 152 | 142 | 120 | 38 | 117 | |
7 | 188 | 52 | 9 | 233 | 43 | 60 | 29 | 240 | 148 | 0 | 33 | 231 | 141 | 101 | 193 | 16 | |
8 | 50 | 18 | 94 | 3 | 8 | 249 | 97 | 78 | 195 | 61 | 31 | 194 | 218 | 208 | 65 | 51 | |
9 | 2 | 189 | 4 | 192 | 47 | 252 | 19 | 157 | 26 | 108 | 107 | 182 | 232 | 230 | 183 | 234 | |
A | 111 | 215 | 161 | 87 | 190 | 163 | 162 | 170 | 91 | 32 | 136 | 23 | 255 | 223 | 67 | 248 | |
B | 85 | 7 | 143 | 160 | 35 | 116 | 236 | 54 | 202 | 245 | 206 | 45 | 172 | 246 | 137 | 199 | |
C | 133 | 20 | 88 | 139 | 227 | 27 | 198 | 229 | 191 | 115 | 173 | 17 | 166 | 205 | 179 | 99 | |
D | 150 | 209 | 169 | 37 | 210 | 49 | 25 | 156 | 204 | 135 | 225 | 216 | 237 | 12 | 46 | 212 | |
E | 180 | 82 | 124 | 203 | 119 | 71 | 168 | 41 | 201 | 126 | 254 | 197 | 138 | 95 | 1 | 213 | |
F | 176 | 134 | 103 | 239 | 72 | 70 | 62 | 73 | 164 | 174 | 109 | 123 | 219 | 132 | 196 | 181 | |
{\boldsymbol{S}}_{\bf{10}}^{{\bf{8}}^{\boldsymbol{*}}} | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 188 | 194 | 208 | 108 | 112 | 29 | 242 | 78 | 73 | 90 | 83 | 40 | 181 | 233 | 176 | 26 | |
1 | 191 | 18 | 196 | 161 | 22 | 159 | 154 | 52 | 32 | 198 | 116 | 132 | 228 | 10 | 126 | 152 | |
2 | 214 | 167 | 42 | 27 | 95 | 59 | 200 | 246 | 113 | 226 | 49 | 96 | 178 | 60 | 174 | 53 | |
3 | 250 | 204 | 150 | 189 | 142 | 120 | 82 | 0 | 21 | 144 | 41 | 62 | 37 | 207 | 138 | 229 | |
4 | 163 | 64 | 218 | 66 | 141 | 193 | 19 | 247 | 55 | 50 | 24 | 130 | 252 | 254 | 46 | 166 | |
5 | 146 | 30 | 136 | 128 | 231 | 169 | 239 | 11 | 43 | 179 | 16 | 124 | 213 | 15 | 232 | 51 | |
6 | 245 | 164 | 114 | 91 | 23 | 44 | 7 | 143 | 85 | 162 | 74 | 121 | 77 | 211 | 34 | 133 | |
7 | 20 | 227 | 145 | 25 | 104 | 107 | 39 | 70 | 129 | 84 | 54 | 101 | 160 | 68 | 209 | 220 | |
8 | 79 | 192 | 153 | 241 | 157 | 81 | 147 | 238 | 249 | 33 | 221 | 47 | 65 | 118 | 182 | 243 | |
9 | 63 | 251 | 45 | 244 | 222 | 175 | 71 | 131 | 137 | 171 | 111 | 195 | 203 | 212 | 58 | 69 | |
A | 234 | 158 | 235 | 253 | 135 | 61 | 134 | 17 | 105 | 155 | 88 | 80 | 219 | 13 | 89 | 180 | |
B | 67 | 184 | 72 | 168 | 6 | 206 | 103 | 9 | 139 | 123 | 187 | 151 | 248 | 48 | 86 | 94 | |
C | 110 | 36 | 75 | 119 | 148 | 117 | 14 | 165 | 127 | 202 | 109 | 156 | 186 | 35 | 93 | 199 | |
D | 2 | 28 | 216 | 38 | 255 | 5 | 201 | 102 | 217 | 99 | 172 | 205 | 224 | 1 | 12 | 177 | |
E | 87 | 8 | 215 | 140 | 223 | 97 | 100 | 125 | 225 | 183 | 122 | 106 | 57 | 4 | 185 | 197 | |
F | 236 | 115 | 173 | 3 | 92 | 230 | 56 | 170 | 210 | 52 | 237 | 190 | 240 | 31 | 76 | 98 | |
{\boldsymbol{S}}_{\bf{10}}^{{\bf{10}}^{\boldsymbol{*}}} | |||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | ||
0 | 141 | 234 | 13 | 238 | 170 | 94 | 194 | 171 | 67 | 225 | 134 | 45 | 49 | 186 | 71 | 53 | |
1 | 218 | 229 | 52 | 17 | 249 | 173 | 190 | 252 | 23 | 16 | 68 | 96 | 136 | 0 | 3 | 177 | |
2 | 230 | 119 | 155 | 70 | 6 | 89 | 172 | 76 | 152 | 176 | 201 | 148 | 109 | 124 | 137 | 215 | |
3 | 242 | 103 | 135 | 114 | 65 | 97 | 41 | 227 | 126 | 7 | 139 | 18 | 66 | 48 | 86 | 184 | |
4 | 116 | 8 | 151 | 91 | 249 | 98 | 39 | 179 | 10 | 160 | 178 | 195 | 149 | 187 | 19 | 226 | |
5 | 113 | 165 | 207 | 140 | 131 | 38 | 112 | 208 | 188 | 69 | 209 | 51 | 200 | 120 | 78 | 108 | |
6 | 248 | 85 | 90 | 37 | 211 | 250 | 241 | 161 | 159 | 47 | 81 | 55 | 29 | 247 | 224 | 240 | |
7 | 210 | 125 | 22 | 11 | 182 | 236 | 174 | 92 | 121 | 145 | 129 | 214 | 26 | 115 | 185 | 132 | |
8 | 128 | 200 | 31 | 166 | 192 | 246 | 183 | 43 | 239 | 232 | 36 | 143 | 57 | 217 | 206 | 107 | |
9 | 61 | 244 | 54 | 44 | 153 | 12 | 216 | 198 | 20 | 4 | 213 | 88 | 228 | 25 | 162 | 147 | |
A | 50 | 63 | 175 | 245 | 104 | 142 | 219 | 204 | 117 | 144 | 74 | 169 | 205 | 46 | 158 | 59 | |
B | 133 | 253 | 212 | 163 | 95 | 105 | 223 | 60 | 199 | 138 | 203 | 42 | 33 | 75 | 157 | 202 | |
C | 118 | 110 | 150 | 191 | 14 | 181 | 56 | 73 | 1 | 100 | 180 | 220 | 243 | 15 | 111 | 80 | |
D | 32 | 189 | 84 | 233 | 40 | 254 | 101 | 235 | 64 | 222 | 99 | 122 | 130 | 77 | 221 | 5 | |
E | 146 | 24 | 82 | 72 | 9 | 102 | 164 | 2 | 123 | 62 | 34 | 58 | 154 | 127 | 231 | 93 | |
F | 87 | 35 | 83 | 197 | 237 | 156 | 196 | 193 | 21 | 251 | 27 | 30 | 167 | 168 | 28 | 79 |
State Matrix | Shift Box | Result | |||||||||
{S}_{\mathrm{0, 0}} | {S}_{\mathrm{0, 1}} | {S}_{\mathrm{0, 2}} | {S}_{\mathrm{0, 3}} | {S}_{\mathrm{0, 0}} | {S}_{\mathrm{3, 3}} | {S}_{\mathrm{2, 0}} | {S}_{\mathrm{3, 1}} | {S}_{\mathrm{0, 0}} | {S}_{\mathrm{1, 1}} | {S}_{\mathrm{2, 2}} | {S}_{\mathrm{3, 3}} |
{S}_{\mathrm{1, 0}} | {S}_{\mathrm{1, 1}} | {S}_{\mathrm{1, 2}} | {S}_{\mathrm{1, 3}} | {S}_{\mathrm{1, 0}} | {S}_{\mathrm{0, 1}} | {S}_{\mathrm{2, 2}} | {S}_{\mathrm{2, 3}} | {S}_{\mathrm{1, 0}} | {S}_{\mathrm{2, 1}} | {S}_{\mathrm{3, 2}} | {S}_{\mathrm{2, 0}} |
{S}_{\mathrm{2, 0}} | {S}_{\mathrm{2, 1}} | {S}_{\mathrm{2, 2}} | {S}_{\mathrm{2, 3}} | {S}_{\mathrm{1, 3}} | {S}_{\mathrm{1, 1}} | {S}_{\mathrm{0, 2}} | {S}_{\mathrm{2, 1}} | {S}_{\mathrm{0, 2}} | {S}_{\mathrm{2, 3}} | {S}_{\mathrm{1, 2}} | {S}_{\mathrm{1, 3}} |
{S}_{\mathrm{3, 0}} | {S}_{\mathrm{3, 1}} | {S}_{\mathrm{3, 2}} | {S}_{\mathrm{3, 3}} | {S}_{\mathrm{3, 0}} | {S}_{\mathrm{3, 2}} | {S}_{\mathrm{1, 2}} | {S}_{\mathrm{0, 3}} | {S}_{\mathrm{3, 0}} | {S}_{\mathrm{0, 3}} | {S}_{\mathrm{3, 1}} | {S}_{\mathrm{0, 1}} |
Rounds | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Round constant | 01 | 02 | 04 | 08 | 10 | 20 | 40 | 80 | 1b | 36 |
\mathbf{E}\mathbf{n}\mathbf{c}\mathbf{r}\mathbf{y}\mathbf{p}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n} | \mathbf{D}\mathbf{e}\mathbf{c}\mathbf{r}\mathbf{y}\mathbf{p}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n} | |
\mathbf{P}\mathbf{l}\mathbf{a}\mathbf{i}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{x}\mathbf{t} \mathrm{T}\mathrm{W}\mathrm{O}\;\mathrm{O}\mathrm{N}\mathrm{E}\;\mathrm{N}\mathrm{I}\mathrm{N}\mathrm{E}\;\mathrm{T}\mathrm{W}\mathrm{O} | \mathbf{C}\mathbf{i}\mathbf{p}\mathbf{h}\mathbf{e}\mathbf{r}\mathbf{t}\mathbf{e}\mathbf{x}\mathbf{t} | |
\mathbf{R}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{d}\;\bf{0} | 7\mathrm{F}097\mathrm{A}3667\mathrm{C}0\mathrm{B}786\mathrm{E}59\mathrm{E}7\mathrm{B}\mathrm{E}\mathrm{D}299\mathrm{B}3853 | 70\mathrm{B}\mathrm{A}\mathrm{E}70\mathrm{A}\mathrm{E}\mathrm{B}6\mathrm{E}28\mathrm{E}5\mathrm{B}61\mathrm{B}87308\mathrm{F}9\mathrm{A}87\mathrm{F}3 |
\mathbf{R}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{d}\;\bf{1} | 0\mathrm{C}2\mathrm{A}223\mathrm{F}\mathrm{B}\mathrm{E}983\mathrm{E}29\mathrm{C}\mathrm{F}03\mathrm{F}40\mathrm{E}\mathrm{A}1478\mathrm{E}80 | \mathrm{D}5\mathrm{D}\mathrm{A}\mathrm{C}6864\mathrm{C}\mathrm{F}89\mathrm{E}\mathrm{D}51\mathrm{A}74\mathrm{F}80\mathrm{D}058117\mathrm{C}4 |
\mathbf{R}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{d}\;\bf{2} | 411\mathrm{F}171705861\mathrm{F}\mathrm{D}\mathrm{E}\mathrm{D}\mathrm{A}2\mathrm{B}3\mathrm{B}\mathrm{E}898\mathrm{E}986\mathrm{C}9 | 97\mathrm{D}05\mathrm{A}6454\mathrm{C}195589\mathrm{F}\mathrm{A}0\mathrm{C}446\mathrm{C}5\mathrm{C}\mathrm{D}62\mathrm{B}4 |
\mathbf{R}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{d}\;\bf{3} | 46159\mathrm{F}31736643\mathrm{F}2\mathrm{D}\mathrm{B}\mathrm{E}\mathrm{C}157\mathrm{B}\mathrm{C}\mathrm{C}\mathrm{B}659\mathrm{C}3 | 3\mathrm{D}3668\mathrm{E}9\mathrm{E}\mathrm{F}4768\mathrm{A}47\mathrm{F}20\mathrm{E}\mathrm{E}\mathrm{D}2687\mathrm{A}\mathrm{A}\mathrm{E}95 |
\mathbf{R}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{d}\;\bf{4} | \mathrm{E}8145\mathrm{C}9\mathrm{C}\mathrm{B}\mathrm{B}\mathrm{A}\mathrm{E}049\mathrm{F}029\mathrm{D}20\mathrm{E}31\mathrm{D}8\mathrm{F}\mathrm{A}2\mathrm{C}0 | 7\mathrm{A}\mathrm{D}27\mathrm{E}\mathrm{B}4\mathrm{E}\mathrm{A}69740\mathrm{B}\mathrm{B}33\mathrm{B}44\mathrm{E}\mathrm{C}7\mathrm{B}44\mathrm{A}153 |
\mathbf{R}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{d}\;\bf{5} | 18\mathrm{D}695\mathrm{C}3\mathrm{D}\mathrm{D}\mathrm{F}6\mathrm{B}\mathrm{B}\mathrm{F}2\mathrm{B}58330\mathrm{E}\mathrm{F}533\mathrm{A}\mathrm{E}156 | 745\mathrm{A}\mathrm{C}\mathrm{B}\mathrm{E}0832\mathrm{F}\mathrm{F}\mathrm{F}\mathrm{A}49\mathrm{A}0210\mathrm{B}\mathrm{C}69\mathrm{B}94\mathrm{B}59 |
\mathbf{R}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{d}\;\bf{6} | 74613\mathrm{D}\mathrm{D}\mathrm{F}\mathrm{B}\mathrm{A}037336\mathrm{C}\mathrm{C}\mathrm{D}063823\mathrm{E}2\mathrm{C}2\mathrm{C}32 | 0088533489\mathrm{F}\mathrm{B}1\mathrm{E}\mathrm{E}\mathrm{A}73\mathrm{C}544\mathrm{E}6088\mathrm{D}289\mathrm{C} |
\mathbf{R}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{d}\;\bf{7} | 984\mathrm{E}47\mathrm{A}\mathrm{E}1\mathrm{A}5540\mathrm{D}\mathrm{E}\mathrm{F}5\mathrm{D}9\mathrm{E}1\mathrm{C}6\mathrm{A}7\mathrm{E}\mathrm{B}2\mathrm{C}\mathrm{E}0 | \mathrm{B}24455\mathrm{F}9\mathrm{A}9\mathrm{A}\mathrm{F}562\mathrm{F}98\mathrm{E}16\mathrm{B}0\mathrm{B}\mathrm{A}8\mathrm{E}\mathrm{C}\mathrm{B}79\mathrm{A} |
\mathbf{R}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{d}\;\bf{8} | \mathrm{F}\mathrm{D}\mathrm{E}\mathrm{E}0\mathrm{A}3\mathrm{D}\mathrm{C}\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{E}\mathrm{D}7\mathrm{B}8\mathrm{A}75\mathrm{B}3711\mathrm{F}8997\mathrm{F}6 | 732\mathrm{C}69322\mathrm{B}1\mathrm{E}\mathrm{C}0\mathrm{C}\mathrm{B}43\mathrm{E}\mathrm{F}5045\mathrm{B}\mathrm{F}\mathrm{B}\mathrm{E}16\mathrm{E}0 |
\mathbf{R}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{d}\;\bf{9} | 0\mathrm{F}4643\mathrm{F}\mathrm{C}0948638\mathrm{C}4\mathrm{A}1172638\mathrm{F}\mathrm{A}068\mathrm{E}8 | 382\mathrm{F}51\mathrm{A}9\mathrm{A}2339\mathrm{F}19785\mathrm{F}40\mathrm{B}61\mathrm{F}\mathrm{D}47504 |
\mathbf{R}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{d}\;\bf{10} | \mathrm{B}8\mathrm{A}\mathrm{E}1\mathrm{A}606\mathrm{B}\mathrm{C}\mathrm{A}28\mathrm{D}666\mathrm{D}\mathrm{A}0\mathrm{D}6\mathrm{D}\mathrm{D}57\mathrm{A}7282 | 54776\mathrm{F}204\mathrm{F}6\mathrm{E}65204\mathrm{E}696\mathrm{E}652054776\mathrm{F} |
\mathbf{C}\mathbf{i}\mathbf{p}\mathbf{h}\mathbf{e}\mathbf{r}\mathbf{t}\mathbf{e}\mathbf{x}\mathbf{t} | \mathbf{P}\mathbf{l}\mathbf{a}\mathbf{i}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{x}\mathbf{t} \mathrm{T}\mathrm{W}\mathrm{O}\;\mathrm{O}\mathrm{N}\mathrm{E}\;\mathrm{N}\mathrm{I}\mathrm{N}\mathrm{E}\;\mathrm{T}\mathrm{W}\mathrm{O} |
S-box 1 | S-box 2 | S-box 3 | S-box 4 | S-box 5 | S-box 6 | S-box 7 | S-box 8 | S-box 9 | S-box 10 | ||
Non-linearity | Max | 106 | 106 | 107 | 106 | 106 | 108 | 107 | 107 | 108 | 108 |
Min | 100 | 100 | 98 | 100 | 100 | 96 | 97 | 100 | 100 | 96 | |
Average | 103.25 | 103.375 | 103.875 | 102.875 | 103.625 | 102.375 | 103.625 | 104.125 | 104.375 | 103.875 | |
Strict Avalanche Criteria (SAC) | Max | 0.625 | 0.648438 | 0.601563 | 0.601563 | 0.59375 | 0.609375 | 0.625 | 0.585938 | 0.609375 | 0.578125 |
Min | 0.40625 | 0.0429688 | 0.429688 | 0.40625 | 0.382813 | 0.40625 | 0.375 | 0.40625 | 0.421875 | 0.390625 | |
Average | 0.501221 | 0.503906 | 0.506592 | 0.501709 | 0.505615 | 0.502686 | 0.505859 | 0.499756 | 0.501221 | 0.499023 | |
S.D | 0.0217624 | 0.0206006 | 0.0212301 | 0.0211541 | 0.0221775 | 0.0220563 | 0.0240203 | 0.0195796 | 0.0241116 | 0.0191802 | |
Bit Independent Criteria (BIC) | Min | 98 | 93 | 97 | 97 | 96 | 97 | 102 | 97 | 97 | 99 |
Average | 103.5 | 103.179 | 103.464 | 103.393 | 103.393 | 102.964 | 104.75 | 103.464 | 103.536 | 103.75 | |
S.D | 2.5425 | 3.20773 | 2.89682 | 2.78182 | 3.2551 | 2.51399 | 1.7243 | 2.74489 | 2.93358 | 2.30876 | |
BIC-SAC | Min | 0.464844 | 0.482422 | 0.466797 | 0.470703 | 0.476563 | 0.462891 | 0.470703 | 0.46875 | 0.462891 | 0.458984 |
Average | 0.498117 | 0.503278 | 0.501744 | 0.503418 | 0.506836 | 0.504534 | 0.501395 | 0.503976 | 0.504534 | 0.50007 | |
S.D | 0.0144139 | 0.011881 | 0.0193514 | 0.015125 | 0.0118402 | 0.0186685 | 0.0149098 | 0.0132311 | 0.0186685 | 0.0155593 | |
Differential Probability | D.P | 0.046875 | 0.015625 | 0.0390625 | 0.046875 | 0.0390625 | 0.046875 | 0.0390625 | 0.046875 | 0.046875 | 0.046875 |
Linear Probability | Max | 162 | 161 | 165 | 163 | 161 | 162 | 163 | 159 | 162 | 160 |
L.P | 0.140625 | 0.144531 | 0.136719 | 0.144531 | 0.132813 | 0.140625 | 0.136719 | 0.144531 | 0.13281 | 0.125 |
S-boxes | Nonlinearity | SAC | BIC-SAC | BIC | DP | LP |
AES S-box [3] | 112 | 0.5058 | 0.504 | 112.0 | 0.0156 | 0.062 |
APA S-box [4] | 112 | 0.4987 | 0.499 | 112.0 | 0.0156 | 0.062 |
Gray S-box [5] | 112 | 0.5058 | 0.502 | 112.0 | 0.0156 | 0.062 |
Skipjack S-box [21] | 105.7 | 0.4980 | 0.499 | 104.1 | 0.0468 | 0.109 |
Xyi S-box [19] | 105 | 0.5048 | 0.503 | 103.7 | 0.0468 | 0.156 |
Residue Prime [8] | 99.5 | 0.5012 | 0.502 | 101.7 | 0.2810 | 0.132 |
Proposed S-box 1 | 103.25 | 0.501221 | 0.498117 | 103.5 | 0.046875 | 0.140625 |
Proposed S-box 2 | 103.375 | 0.503906 | 0.503278 | 103.179 | 0.015625 | 0.144531 |
Proposed S-box 3 | 103.875 | 0.506592 | 0.501744 | 103.464 | 0.0390625 | 0.136719 |
Proposed S-box 4 | 102.875 | 0.501709 | 0.503418 | 103.393 | 0.046875 | 0.144531 |
Proposed S-box 5 | 103.625 | 0.505615 | 0.506836 | 103.393 | 0.0390625 | 0.132813 |
Proposed S-box 6 | 102.375 | 0.502686 | 0.504534 | 102.964 | 0.046875 | 0.140625 |
Proposed S-box 7 | 103.625 | 0.505859 | 0.501395 | 104.75 | 0.0390625 | 0.136719 |
Proposed S-box 8 | 104.125 | 0.499756 | 0.503976 | 103.464 | 0.046875 | 0.144531 |
Proposed S-box 9 | 104.375 | 0.501221 | 0.504534 | 103.536 | 0.046875 | 0.13281 |
Proposed S-box 10 | 103.875 | 0.499023 | 0.50007 | 103.75 | 0.046875 | 0.125 |
Average proposed results | 103.538 | 0.502759 | 0.50279 | 103.539 | 0.041406 | 0.13789 |