Enhanced Secure Data Encryption Standard (ES-DES ...DES algorithm is improved against cryptanalytic attacks and confusion makes the use of the key so complex, it is still difficult

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 21 (2017) pp.11365-11373

© Research India Publications. http://www.ripublication.com

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Enhanced Secure Data Encryption Standard (ES-DES) Algorithm Using

Extended Substitution Box (S-Box)

T.K.Sivakumar

Research Scholar, Research and Development Centre, Bharathiar University, Coimbatore – 641 046, Tamil Nadu, India.

Assistant Professor (Sr.Gr), Department of Master of Computer Applications, SRM University, Chennai, Tamil Nadu, India.

Orcid: 0000-0002-6166-2695

Dr. T.Sheela Professor & Head, Department of Information Technology, Sri Sai Ram Engineering College, Chennai, Tamil Nadu, India.

Dr. R.Kumar Professor, Department of Electronics and Communication Engineering, SRM University, Chennai, Tamil Nadu, India.

Orcid: 0000-0001-6745-5214

Dr. K.Ganesan Professor, Department of Mathematics, SRM University, Chennai, Tamil Nadu, India.

Orcid: 0000-0002-4532-0222

Abstract

In general, the strength of any cryptographic algorithm

depends on the key size, number of rounds, and robustness of

S-Boxes against cryptanalytic attack. The Data Encryption

Standard (DES) is a block cipher cryptographic system, which

provides the security in the banking sector, cloud computing

but nowadays the development in DES calculation power

seems weak against brute-force attacks. DES algorithm it

accepts an only 64-bit block of plaintext and key. So the

cryptanalysis they can easily find out the original value of the

key using brute-force attacks. In this paper, we proposed the

Enhanced Secure Data Encryption Standard (ES-DES)

Algorithm Using Extended Substitution Box (S-Box) is to

support and improve the security of DES algorithm. To

improve the security of the DES by increasing a size of the

key as well as creating and extending the robust S-Boxes

before the ES-DES algorithm to complete the process using

Enhanced Secure DES (ES-DES) algorithm. While extending

S-Boxes and increasing the key size, the security of the ES-

DES algorithm is improved against cryptanalytic attacks and

confusion makes the use of the key so complex, it is still

difficult to deduce the key.

Keywords: DES, S-BOX, Avalanche effect, hamming

weights

INTRODUCTION ABOUT CRYPTOGRAPHY

Cryptography comes from the Greek words κρυπτο ("hidden

or secret") and γραφη ("writing"). It is the one the techniques

used for secret writing. Normally, cryptography as the art of

translate from one format to another format and it is mainly

used to transfer the information from one participant to others

in a secure manner, otherwise during the transformation the

intruders or hackers can capture the data and understand the

original contents[1]. Cryptography system provide different

types services other than encryption and decryption, such as

• Checking integrity—recipient check that the original

message has not altered during transformation.

• Authentication — verifies the uniqueness of a user or

process.

A readable message is called plaintext. The scrambled or

unreadable information is called cipher text[2]. The process of

converting from readable message to unreadable message is

known as encryption. The process of converting from

unreadable message to readable message is known as

decryption. In Fig. 1 illustrates the overall process of

encryption and decryption.

Figure 1: Encryption and decryption process

Cryptanalysts(from the Greek kryptós, "hidden," and analýein,

"to loosen" or "to untie) attempt to capture ciphertext during

transformation to find the original plaintext without

knowledge of key or the algorithm.

The algorithm and a secret value are involved in the

cryptographic systems. The secret value is known as a key.

The strength any algorithm is based on the key size or secret

value. With a good cryptographic system is perfectly

acceptable for everyone, including the poor (and cryptanalyst)

know the algorithm because anyone can use the algorithm.

But the algorithm does not allow disassembling information

without knowledge of the key. The concept is similar to a

combination of keys for a combination lock.



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It is important that the encryption algorithms are reasonably

efficient that the asset can calculate. The good ones are those

who have knowledge of the keys. Without knowledge of the

key is it very difficult to break cryptographic algorithms. The

hackers or intruders can try all possible keys until finding the

original plaintext or key is known as brute-force attacks. The

security of a cryptographic system based on key size and

algorithm[3]. If the large key size and more complicated

algorithm are there, which take more than 10 million years to

break then, it can be considered reasonably safe all the

computers in the world.

With the help of encryption device or computers can be used

for an exhaustive key search. Computers they do not get tired

and are much faster than people, even if encryptor tried with

large key size. Parallel processor is used to solving the

complex problem; it can split into smaller modules, which is

to used to save the time. Some cryptographic algorithm to use

variable length[4]. Whenever the implement more key size,

which provides more safer than other algorithms. Increasing

the length of the key a bit works good guy a little more

complicated, but does the job twice as hard as the bad guy.

DATA ENCRYPTION STANDARD

Publication of the DES algorithm in 1977 by National Bureau

of Standards (NBS) in USA has been surrounded by

controversies First, there were complaints about the key, only

56-bit key length was too short to perform the exhaustive

search attack key well-funded opponents[5]. Second, while

details of the algorithm were published, it was revealed that

some of the design criteria, which leads to the assumption that

the DES contains a hidden security weakness or loophole. In

1993, Wiener showed an efficient design for a machine

costing 1 million. Rec. The United States, which can recover a

DES key in 3.5 hours[6], which makes it likely that the US

government could recover a DES key by exhaustive search in

the 1970s. In 1989 godu Biham and Shamir[7] represented In

DES attack in 1989, using a method called differential

cryptanalysis; In response, IBM stated that the attack was

known to DES designers, and facilitated the protection of this

technique based on the design criteria for the S-box.

In 1994 one of the developers DES Boilermaker listed the

eight criteria for the design of S-boxes[8], and these criteria

were used to create the original eight DES S-boxes. This

seems to solve the problem of hospitals. Despite this, NSA's

role in DES design and, in particular, are not quite clear S-

boxes, as public statements by IBM and the NSA on this issue

seem inconsistent.

In 1982, Meyer and Mathias, two other members of the DES

project team at IBM, discussed the implementation of the S-

boxes, and more precisely, the number of minterms needed for

their implementation. They argue that the early development

of the production of S-Boxes with several minternm between

40 and 48. When you add design criteria, this distribution

evolved in a range of 52 to 59. The left tail of the distribution

was chosen To minimize the size of the DES implementation

in the hardware. The goal is to check this statement in the

hope that it can shed light on the generation of S-DES blocks.

First, we generated a large number of S-blocks that meet

IBM's design criteria published in 1994 godu; This was more

difficult than expected.

ENHANCED SECURE DATA ENCRYPTION

STANDARD (ES-DES)

Nowadays DES is used in different applications like banking,

online trading, and online transactions, etc., as well as unsafe,

because the 56-bit key size is small compared to the other

cryptographic algorithms, and possible to a hacker can attack

using brute-force techniques with a modern processor. So, the

new Enhanced Secure DES (ES-DES) scheme of a symmetric

key algorithm with a DES 128-bit key is proposed. In any

cryptographic algorithm, if the size of the key is very small

then it won't provide more security because the intruder can

easily find the original information duration the

transformation between the sender and receiver. Hence,

proposed algorithm ES-DES algorithm might be protected

from the intruders and others. Therefore, improving the

security of the DES algorithm to increase the size of the key

as well as expanding and creating robust S- boxes before the

ES-DES algorithm to complete the process using an Enhanced

Secure DES (ES-DES) algorithm.While extending S-Boxes

and increasing the key size, the security of the ES-DES

algorithm is improved against cryptanalytic attacks as well as

the user maintain the different services (i.e., confidentiality,

message integrity, and authentication) and confusion is

approximately doubled compared with a DES algorithm.

ES-DES Encryption and Decryption

The ES-DES is a symmetric block cipher algorithm, the

length of the plaintext and key size is 128-bit (i.e., ES-DES

algorithm, which receives 128-bit blocks of plaintext and 128-

bit key(112-bit) as the input to operate successive operation).

Being symmetric, the same key and same algorithm are used

for both encryption as well as decryption time, and ES-DES

also uses the same key, and the same algorithm is used for

both encryption as well as decryption time but was used in

reverse order.

Introduction about S-BOX

An S-Box is a substitution technique for convert of R input

bits to S output bits, where R is needed not be essentially

equal to S as shown in the following Fig. 2. Each output bit of

S corresponds to the output of a Boolean function of the R



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input bits[9].

Figure : 2 Basic architecture of S-Box

ES-DES S-BOXes

After expanding from R(64) bits to 96 bits using

E(Expansion), which is XORed with corresponding subkey

96-bit for that round. The output of the XOR operation (i.e.,

96 bits), which is equally split into eight 12 bits from left to

the right. So, an each S-Box accept the 12 bits, and it produces

the 8 bits output, but simple DES algorithm, which generates

the 4-bits as an output from 6-bits input. In Fig. 3 shows the

ES-DES calculation of F(R, K).

Figure 3: ES-DES calculation of F(R, K).

In the ES-DES algorithm, Tables 1 - 8 shows the eight ES-

DES S-Boxes, each S-Box consist of 256 values (i.e., 16 × 16;

16 rows and 16 columns). However, DES algorithm, each S-

Box consist of 64 values (i.e., 4 × 16; 4 rows and 16

columns)[10]. So, there are 2048 total number element

available in the ES-DES S-Boxes.(i.e. 8 × 256=2048)

Table 1: ES-DES S-BOX 1

S-BOX 1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 125 66 18 88 132 38 13 204 58 39 139 128 156 68 162 28

1 189 235 222 148 75 253 183 254 4 47 133 94 164 87 114 86

2 35 207 77 157 168 171 163 41 63 11 190 221 43 64 25 137

3 50 145 167 232 101 109 53 146 206 131 95 225 161 227 37 116

4 7 195 71 16 80 165 115 141 202 54 32 56 201 218 149 138

5 113 22 252 23 117 172 209 178 76 255 105 120 174 122 185 83

6 107 233 179 84 118 98 79 215 74 192 144 160 89 45 170 247

7 181 250 142 97 93 176 180 82 246 147 158 193 6 15 103 26

8 70 249 110 237 85 52 14 49 72 123 217 239 17 91 188 177

9 211 124 20 216 92 236 143 210 213 69 243 127 223 248 90 111

10 242 130 9 108 104 44 55 229 166 196 106 173 126 208 81 42

11 226 99 121 186 200 96 150 245 238 152 112 61 134 140 19 228

12 36 5 199 155 197 24 102 205 31 129 34 100 198 240 175 136

13 119 151 219 244 194 67 184 234 203 182 231 251 154 214 12 1

14 187 29 33 8 27 59 51 3 230 169 60 21 10 30 153 65

15 62 241 135 57 159 46 191 40 73 212 220 2 224 48 78 0


S-BOX 2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 186 67 56 171 87 86 12 242 122 85 204 210 196 152 55 83

1 14 250 160 53 142 182 181 236 16 50 41 187 101 25 146 118

2 105 158 128 92 176 135 164 109 151 38 163 111 30 106 59 58

3 126 159 218 183 197 24 147 132 154 29 133 65 177 91 6 179

4 15 194 155 34 116 203 120 74 191 119 23 96 248 233 61 165

5 192 60 150 40 26 97 18 169 157 241 72 145 215 107 220 27

6 93 189 121 98 202 123 144 110 84 188 232 17 129 9 214 124

7 166 201 62 102 117 190 205 90 75 170 35 246 19 28 45 63

8 33 255 48 240 82 37 36 54 130 211 247 224 49 115 225 52

9 184 88 7 51 5 253 199 239 103 161 46 217 153 231 140 43

10 80 143 11 207 185 81 127 208 180 136 198 95 73 69 68 20

11 162 113 31 149 200 173 193 178 213 234 89 100 112 174 44 243

12 76 13 222 125 168 39 114 237 64 167 99 141 230 252 227 172

13 108 104 212 249 221 66 138 226 209 206 229 238 175 251 8 2

14 235 10 32 21 78 3 70 1 216 244 79 42 22 47 195 0

15 186 67 56 171 87 86 12 242 122 85 204 210 196 152 55 83



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S-BOX 3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 1 53 13 118 186 249 226 48 43 63 22 153 182 161 80 179

1 7 17 162 46 77 200 92 24 76 29 121 109 131 236 209 151

2 234 218 175 67 133 165 62 31 195 8 93 59 184 86 127 240

3 9 88 10 216 98 243 83 26 155 50 70 130 213 188 189 203

4 2 225 232 248 25 65 123 108 115 244 219 107 137 78 241 143

5 32 207 233 12 167 204 119 112 237 177 66 56 89 30 132 235

6 152 52 247 223 224 251 117 231 101 239 54 85 185 159 227 58

7 238 202 124 64 94 21 33 190 158 164 23 149 208 100 41 82

8 122 199 180 214 5 103 212 75 68 87 84 126 228 141 37 176

9 61 36 96 99 125 16 136 140 135 19 11 181 97 128 138 139

10 47 20 217 42 129 3 250 168 90 221 173 242 148 150 157 254

11 51 15 18 57 91 14 27 145 102 71 105 111 95 206 245 198

12 60 81 255 72 183 166 134 116 222 220 252 104 197 35 154 193

13 4 120 40 196 110 49 39 246 191 171 45 106 201 187 113 192

14 253 69 163 205 170 44 79 160 210 55 178 142 194 74 229 174

15 114 34 38 73 6 28 156 147 211 169 144 146 230 215 172 0


S-BOX 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 205 75 124 210 70 146 46 238 165 140 225 236 198 196 34 160

1 7 245 120 31 175 142 166 208 58 56 2 231 74 72 144 128

2 35 116 153 62 161 102 151 176 202 87 133 67 26 134 106 36

3 184 152 222 149 237 66 206 107 113 13 139 33 170 51 6 200

4 45 103 96 84 131 203 109 50 172 145 21 129 250 214 48 163

5 226 122 211 61 17 65 8 147 138 218 57 137 213 90 216 14

6 85 154 132 169 180 188 168 173 91 79 246 20 143 12 227 71

7 159 167 39 100 121 181 195 97 37 164 16 248 47 49 28 114

8 23 255 32 228 82 30 80 60 158 239 242 194 93 117 224 29

9 157 69 3 25 11 252 209 234 59 220 19 240 104 201 156 22

10 42 130 24 243 221 118 126 182 177 94 235 27 54 38 63 53

11 119 112 18 111 183 207 197 136 185 244 78 127 92 179 83 232

12 125 40 162 99 135 55 110 233 105 174 155 148 223 249 230 178

13 95 77 189 241 212 68 101 123 190 199 204 215 171 253 1 15

14 76 5 41 44 150 4 89 9 187 251 98 73 43 64 219 0

15 191 254 247 186 229 141 217 115 52 86 88 10 108 192 193 81


S-BOX 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 1 58 8 154 191 79 67 43 129 42 38 223 226 226 178 151

1 2 37 105 109 112 101 49 51 47 119 64 134 156 156 118 189

2 252 240 235 90 209 89 13 184 33 113 44 145 98 98 181 146

3 7 84 25 249 177 121 54 61 114 30 175 244 148 148 231 167

4 5 107 52 250 22 215 24 192 187 214 194 206 142 142 246 104

5 28 75 144 21 230 196 164 218 139 68 140 116 57 57 133 245

6 19 110 241 123 85 149 253 137 205 97 122 198 161 161 236 141

7 34 39 99 82 31 88 128 211 179 77 169 76 94 94 87 159

8 32 219 233 238 16 71 131 29 111 56 138 186 190 190 102 127

9 59 14 147 126 27 153 225 73 41 40 74 125 158 158 199 210

10 124 10 220 15 96 227 208 150 195 48 234 229 232 232 213 176

11 3 26 9 93 100 66 204 132 135 160 172 117 247 247 254 237

12 4 115 163 23 91 193 80 152 173 168 63 171 86 86 217 182

13 6 174 11 78 166 55 188 162 242 36 202 216 228 228 180 170

14 255 70 65 20 62 143 222 251 72 243 212 224 83 83 106 203

15 157 18 35 60 17 130 165 185 197 155 207 108 248 248 200 0


S-BOX 6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 234 44 195 243 117 185 72 132 217 219 253 255 173 116 48 171

1 12 247 99 93 165 169 157 155 65 21 5 179 90 138 220 15

2 101 50 39 102 164 110 208 237 100 142 55 8 29 228 198 13

3 11 226 212 216 236 135 60 207 136 36 118 64 224 32 4 34

4 49 148 112 159 205 128 197 94 244 233 53 145 231 202 89 181

5 235 111 131 104 46 54 23 170 124 74 106 210 245 87 203 26

6 184 206 59 150 18 96 240 227 187 107 156 2 211 35 51 91

7 241 125 10 166 204 57 186 144 31 242 37 143 129 73 82 14

8 68 121 25 189 182 30 174 41 127 223 199 209 75 123 214 71

9 88 146 7 47 24 180 248 218 134 77 38 192 6 70 239 40

10 20 194 43 193 45 140 188 201 66 183 250 81 105 97 98 16

11 163 108 52 122 172 221 126 80 225 114 86 196 147 120 27 249

12 113 69 119 22 167 84 154 76 92 246 177 213 229 230 168 215

13 176 85 33 238 175 103 200 63 151 109 137 190 160 251 1 42

14 139 9 83 61 158 3 130 19 178 162 17 133 115 153 232 0

15 141 58 254 222 252 56 67 95 78 152 79 28 62 191 161 149



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S-BOX 7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 1 8 27 32 214 112 74 125 52 71 99 81 249 243 231 191

1 2 36 30 113 95 118 86 53 102 82 108 147 163 187 150 173

2 194 48 140 122 202 217 128 44 177 59 211 104 114 183 222 219

3 6 60 57 197 46 75 186 121 119 87 80 139 254 218 161 239

4 9 67 73 33 40 157 233 41 228 111 155 154 105 142 240 198

5 11 110 92 39 79 251 47 229 93 131 120 174 148 130 195 184

6 13 145 116 50 22 26 63 244 227 212 156 158 127 234 170 179

7 16 7 171 91 24 69 70 90 245 101 132 188 149 182 146 220

8 64 61 210 31 38 89 78 54 68 117 135 141 133 153 166 215

9 85 10 14 51 58 29 175 159 88 84 115 165 199 180 196 213

10 126 20 235 34 136 37 97 205 100 164 109 223 143 137 250 242

11 3 21 15 42 185 45 107 72 151 208 190 230 167 129 237 246

12 4 43 18 62 23 248 232 181 172 201 209 98 206 162 207 238

13 5 19 28 96 192 55 66 224 176 255 103 168 169 193 221 241

14 77 138 144 35 25 94 49 252 204 76 253 200 203 178 189 247

15 152 12 17 106 56 65 83 124 216 134 160 225 123 226 236 0

Table 8 : ES-DES S-BOX 8

S-BOX 8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 243 112 217 251 176 169 94 4 181 250 65 234 223 25 33 195

1 26 146 95 41 131 233 183 136 104 60 3 206 81 229 83 54

2 125 121 99 46 158 113 211 17 155 87 51 14 84 177 212 6

3 36 236 148 235 88 123 58 64 12 106 48 24 74 40 13 63

4 120 96 188 194 210 108 124 42 247 213 61 208 149 196 45 224

5 47 167 150 93 72 80 10 204 128 62 86 164 127 35 244 16

6 240 159 130 29 55 98 245 242 221 157 205 2 230 111 129 187

7 254 8 23 184 215 20 185 168 66 191 90 70 214 132 34 32

8 85 139 50 239 246 75 209 118 172 225 102 182 114 207 170 153

9 7 203 22 57 15 137 226 30 147 156 68 138 21 37 249 71

10 44 166 11 248 103 198 134 186 91 190 255 100 140 192 171 9

11 197 145 73 216 180 222 160 77 200 152 101 238 28 199 78 232

12 107 135 27 39 38 122 219 165 162 218 174 252 220 161 228 179

13 141 178 79 59 241 201 126 144 53 163 82 193 110 227 1 19

14 189 18 69 143 173 5 116 67 105 237 49 133 175 154 31 0

15 119 89 253 231 202 115 151 52 97 142 92 56 76 117 43 109

Algorithm for Mapping 96 bits to 64 bits: F(E,K)

Step 1: Start

Step 2: Read values: plaintext and key

Step 3: Both the input separately converted into 96 bits block

Step 4: Generate 96 bits output after perform Boolean XOR

operation bit by bit

Step 5: Resultant 96 bits, equally divided into eight 12 bits.

Step 6: To convert 12 bits input to 8 bits output from each S-

Box the following procedure to be followed.

Step i: Select the column_value1 and row_value1

Step ii: Using column_value1 and row_value1,

obtain the intersection_value1 from particular S-

BOX.

Step iii: Select the column_value2 and row_value2

Step iv: Using column_value2 and row_value2,

obtain the intersection_value2 from particular S-

BOX.

Step v: Perform binary XOR operation using

intersection_value1 with intersection_value2

Step 7: Repeat the step i to step v.

Step 8: To get the 64 bits output, all the output S-Boxes are

appended from left to right.

Step 9: stop.

To obtain the intersection_value1 from S-Boxi,

For selecting the column_value1, consider the 1,2,11, and 12th

-bit position from 12 bits input then convert 4-bit binary to

decimal value and this value is used to select the particular

column_value1 from particular S-BOXi.(ie.i: 1,2,..,8). Fig. 4

shows the mapping from 12-bit input to 8-bit output from S-

Boxi

For selecting the row_value1, consider the 3,4,5,6th-bit

position from 12 bits input then convert 4-bit binary to

decimal value and this value is used to select to the particular

row_value1 from particular S-BOXi. To obtain the 8-bit

output from each S-Box, computer the binary XOR operation

column_value1 with row_value1,



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Figure 4: Mapping from 12-bit to 8-bit

To obtain the intersection_value2 from S-Boxi,

For selecting the column_value2, consider the 11,12,1, and

2nd-bit position from 12 bits input then convert 4-bit binary to


column_value2 from particular S-BOXi.

For selecting the row_value2, consider the 7,8,9, and 10th-bit

position from 12 bits input then convert 4-bit binary to


row_value2 from particular S-BOXi.

To obtain the 8 bits output from each S-Boxi, compute the

binary XOR operation column_value2 with row_value2, and

finally, to get the 64 bits output, all the output of the S-Boxes

are appended from left to right.

MATHEMATICAL MODELING AND ANALYSIS

The Symmetric group

Perform Mapping N-bit blocks to N-bit blocks with one-to-

one transformation using substitution, and it creates value E

block cipher. Let EK(X) be the encryption process using input

X with secret key K. Then, for any static K using EK(X)

function then perform the permutation of the set of N-bit

blocks and this value is called PK. Let 𝑆2𝑁. Denote the set all

N-bit permutations, and the order of the symmetric group

Ò(𝑆2𝑁) is (2N)!. The sub-set is denoted E(𝑆2𝑁) where

E(𝑆2𝑁) ⫃ (𝑆2𝑁 ). For Example, the DES algorithm needs 64-

bit data blocks under the control of 56-bit key to produce the

ciphertext. Therefore, Ò(𝑆2𝑁) = (264 )!. Whereas Ò(𝐸(𝑆2𝑁)).

Hence, the proposed ES-DES algorithm operates on 128-bit

data blocks under the control of the 112-bit key. Therefore,

Ò(𝑆2𝑁) = (2 128)!. Whereas Ò(𝐸(𝑆2𝑁)).

In general, our aim is to make E a random mapping from

plaintexts to ciphertexts, so that E(𝑆2𝑁) will be as large a

subset of 𝑆2𝑁 as possible

Practical limits on the size of E(𝑺𝟐𝑵)

In practical it is always the case that Ò(𝐸(𝑆2𝑁))≪ Ò(𝑆2𝑁)

otherwise the key would quickly become far too large. This is

illustrated in Table 4.1 which gives the size of the key |𝐾| in

bits if E(𝑆2𝑁) = 𝑆2𝑁, that is, if the key space us large enough

to allow every mapping in the symmetric group to be reached.

(Note that there is some slight redundancy in the results as 22m

is rarely an exact power of 2). These quantities were

computed using Stirling's approximation or |𝐾| = log2(2n)!.

viz Table 9 shows the size of keys.

1 1 1

2 2 ln(2) (2 ) 2 ln(2 )2 12 2

ln(2)

N N N N

k

Which for N>2 is very closely approximated by

1

2 2 ln(2) (2 )2

ln(2)

N N N

k

To produce a good cipher, we require E(𝑆2𝑁) to a small,

apparently ( to the cryptanalyst) randomly chosen subset of

𝑆2𝑁. Thus, it is important that any specific subset of 𝑆2𝑁 from

which E(𝑆2𝑁) is to be chosen be of sufficient order to make a

search of the nongroup to be within an order of magnitude of

that of the symmetric group for security.Table Size of keys if

Ò (E(𝑆2𝑁)) = Ò(𝑆2𝑁)

Table 9: Size of keys

N Ò(𝑆2𝑁) |𝐾|

1 (21)! 1

2 (22)! 5

4 (24)! 45

8 (28)! 1684

16 (216)! 95404

32 (232)! 1.3124 × 1011

64 (264)! 1.1540 × 1021

128 (2128)! 4.3065 × 1040

256 (2256)! 2.9476 × 1079



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Comparison between ES-DES with DES, 3DES and

AES

The following Table 10 shows a comparison between ES-DES

and others algorithms among various factors [11],

Table 10 : Comparison between ES-DES with DES, 3DES,

and AES

Factors DES 3DES AES ES-

DES

Key Length 64

bits

(K1,K2,

and K3)

168 or

112 bits

Variable

length key :

128-

bits,192-

bits, 256-

bits

128 bits

Block Size 64

bits 64 bits

Variable

length key :

128-

bits,192-bits

256-bits

128 bits

Possible Keys 264 2168 or

2112

2128 , 2192 or

2256 2128

Time

Required to

break (50

Billion keys

per Second)

400

Days

For a 112

bits key :

800 days

Key Size :

128-bit 5

x 1021

Years

Key

Size :

128-bit

5 x 1021

Years

So, based on the above table, the proposed ES-DES also

produces the equal protection from intruders like AES.

STRICT AVALANCHE CRITERION (SAC)

The following analysis methods are to be used for SAC,

a. Analysis the hamming weight with various frequency

(Avalanche effect).

b. Analysis the bit position(Strong S-box) with

hamming weights.

a: Analysis the hamming weight with various frequency

Input: m( Where ' m' is no. of bits).

Output: Analysis the 'w' with various frequency (where, w:

hamming weight)

Algorithm:

Step 1: select any two location randomally from particular S-

Box 1(say x1, x2) and find the corresponding output value of

that S-box.

y = S(x1); [Location x1 value ].

y'= S(x2); [Location x2 value ].

Step 2: calculate the ∆Y [Where, ∆Y: differential value

outputs]

∆Y = y ⊕ y'

Step 3: Find 'w' and ∆Y of outputs [Where, w: hamming

weight, ∆Y: differential value]

Step 4: Repeat steps 1 through 3 for the required number of

tests.

Step 5: Analysis of the frequency of 'w'.

Example

1. x = 234, x′ = 89; y = S1(234) = 90, y′ = S1(89) = 52, ∆y1

= 104 = 01101000; w = 3.

2. x = 101, x′ = 99; y = S1(101) = 115, y′ = S1(99) = 163,

∆y2 = 208 = 11010000; w = 3.

3. x = 56, x′ = 61; y = S1(56) = 97, y′ = S1(61) = 155,

∆y3 = 250 = 11111010; w = 6.

4. x = 126, x′ = 82; y = S1(126) = 234, y′ = S1(82) = 253,

∆y4= 23 = 00010111; w = 4.

5. x = 55, x′ = 178; y = S1(55) = 84, y′ = S1(178) = 94,

∆y5 = 10 = 00001010; w = 2.

6. x = 167, x′ = 179; y = S1(167) = 144, y′ =S1(179) = 221,

∆y6 = 77 = 01001101; w = 4.

7. x = 245, x′ = 112; y = S1(245) = 138, y′ =S1(112) = 191,

∆y7 = 173 = 10101101; w = 5.

8. x = 187, x′ = 210; y = S1(187) = 173, y′ = S1(210) = 87,

∆y8= 26 = 00011010; w = 3.

9. x = 179, x′ = 221; y = S1(179) = 221, y′ =S1(212) = 227,

∆y9 = 62 = 00111110; w = 5.

10. x = 7, x′ = 29; y = S1(7) = 107, y′ = S1(29) = 5, ∆y10 =

110 = 01101110; w = 5.



11372

Table 11: Frequency Table for Hamming Weight

Hamming

weights

frequency

1 0

2 1

3 3

4 2

5 3

6 1

Table 11 shows the weight and frequency. Their relationship

can be displayed in the form of a bar graph in Fig. 5 and

shows the result of calculating the correct S-Box from ES-

DES S-Box. This result shows that the S-box has a good strict

avalanche criterion properties.

Figure 5: Frequency relations

a. Analysis the bit position (Strong S-box) with hamming

weights.

Input: m (Where ' m' is no. of bits).

Output: bit position with hamming weights.

Algorithm:

Step 1: select any two location randomally from

particular S-Box (say x1, x2)and findthe corresponding

output value of that S-box.

y = S(x1) ; [Location x1 value ]

y'= S(x2) ; [Location x2 value ]

step 2: calculte the ∆Y [Where, ∆Y : differential value

outputs]

∆Y = y ⊕ y'

Step 3: Find 'w' and ∆Y of outputs [Where, w: hamming

weight, ∆Y: differential value]

Step 4: Analyze the weight of Hamming based on the bit

Position of the resulting differential values∆Y.

Table 12: Hamming Weight with Position

Decimal Binary

104 0 1 1 0 1 0 0 0

208 1 1 0 1 0 0 0 0

250 1 1 1 1 1 0 1 0

23 0 0 0 1 0 1 1 1

10 0 0 0 0 1 0 1 0

77 0 1 0 0 1 1 0 1

173 1 0 1 0 1 1 0 1

26 0 0 0 1 1 0 1 0

62 0 0 1 1 1 1 1 0

110 0 1 1 0 1 1 1 0

Hamming

Weights 3 5 5 5 8 5 6 3

Figure 6: Differential values and their frequency

Table 12 shows the Hamming weight with position and their

relationship can be displayed in the form of a bar graph in Fig.

6, and this shows the result of calculating the good S-Box, and

it's properties by frequency testing and shows strong S-Boxes

against intruders from ES-DES S-Box.

CONCLUSION

The ES-DES system has improved the security of the original

DES by increasing the size of the key from 64-bit to 128-bit

after extending the S-Boxes from (4 × 16 ) to ( 16 × 16 )

values. Then, two intersection values selected from each S-

Box in each round, which makes more confusion against

intruders or brute force attackers. The extended S-boxes has

satisfied a good strict avalanche Criterion properties, and

analyzed the bit position with hamming weight; it's properties



11373

by frequency testing, which shows strong S-Boxes against

intruders from ES-DES S-Box. The only drawback of

Enhanced DES is the need for additional computing, but today

the computer has parallel and high-speed computing power, so

the lack of ES-DES algorithm is neglected because our main

goal is to increase the security of the system. So, the ES-DES

algorithm provides more protection from hackers, and it's

almost impossible to crack and split ES-DES.

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[1] “Introduction to Cryptography” http://www.ggu.ac.in

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[10] Yong Wang, Kwok-Wo, Wong, Changbing Li. Elsevier:

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Documents

Enhanced Secure Data Encryption Standard (ES-DES ...DES algorithm is improved against cryptanalytic attacks and confusion makes the use of the key so complex, it is still difficult