Prerequisite – Simplified Data Encryption Standard | Set 1
Simplified Data Encryption Standard is a simple version of Data Encryption Standard having a 10-bit key and 8-bit plain text. It is much smaller than the DES algorithm as it takes only 8-bit plain text whereas DES takes 64-bit plain text. It was developed for educational purpose so that understanding DES can become easy. It is a block cipher algorithm and uses a symmetric key for its algorithm i.e. they use the same key for both encryption and decryption. It has 2 rounds for encryption which use two different keys.
First, we need to generate 2 keys before encryption. After generating keys we pass them to each individual round for s-des encryption. The below diagram shows the steps involved in the s-des algorithm.
Components :
S-DES encryption involves four functions –
1. Initial permutation(IP) –
2. Complex function (fk) –
It is the combination of permutation and substitution functions. The below image represents a round of encryption and decryption. This round is repeated twice in each encryption and decryption.
Components in fk are –
a. Expanded Permutation (EP) –
It takes a 4-bit input and converts it into an 8-bit output.
b. S-boxes (S0 and S1) –
It is a basic component of a symmetric key algorithm that performs substitution.
c. Permutation P4 –
3. Switch (SW) –
4. Inverse of Initial Permutation (IP-1) –
First, we need to generate 2 keys before encryption.
Consider, the entered 10-bit key is - 1 0 1 0 0 0 0 0 1 0
Therefore,
Key-1 is - 1 0 1 0 0 1 0 0
Key-2 is - 0 1 0 0 0 0 1 1
Encryption –
Entered 8-bit plaintext is - 1 0 0 1 0 1 1 1
Step-1:
We perform initial permutation on our 8-bit plain text using the IP table. The initial permutation is defined as –
IP(k1, k2, k3, k4, k5, k6, k7, k8) = (k2, k6, k3, k1, k4, k8, k5, k7)
After ip = 0 1 0 1 1 1 0 1
Step-2:
After the initial permutation, we get an 8-bit block of text which we divide into 2 halves of 4 bit each.
l = 0 1 0 1 and r = 1 1 0 1
On the right half, we perform expanded permutation using EP table which converts 4 bits into 8 bits. Expand permutation is defined as –
EP(k1, k2, k3, k4) = (k4, k1, k2, k3, k2, k3, k4, k1)
After ep = 1 1 1 0 1 0 1 1
We perform XOR operation using the first key K1 with the output of expanded permutation.
Key-1 is - 1 0 1 0 0 1 0 0
(1 0 1 0 0 1 0 0) XOR (1 1 1 0 1 0 1 1) = 0 1 0 0 1 1 1 1
After XOR operation with 1st Key = 0 1 0 0 1 1 1 1
Again we divide the output of XOR into 2 halves of 4 bit each.
l = 0 1 0 0 and r = 1 1 1 1
We take the first and fourth bit as row and the second and third bit as a column for our S boxes.
S0 = [1,0,3,2
3,2,1,0
0,2,1,3
3,1,3,2]
S1= [0,1,2,3
2,0,1,3
3,0,1,0
2,1,0,3]
For l = 0 1 0 0
row = 00 = 0, column = 10 = 2
S0 = 3 = 11
For r = 1 1 1 1
row = 11 = 3, column = 11 = 3
S1 = 3 = 11
After first S-Boxes combining S0 and S1 = 1 1 1 1
S boxes gives a 2-bit output which we combine to get 4 bits and then perform permutation using the P4 table. P4 is defined as –
P4(k1, k2, k3, k4) = (k2, k4, k3, k1)
After P4 = 1 1 1 1
We XOR the output of the P4 table with the left half of the initial permutation table i.e. IP table.
(0 1 0 1) XOR (1 1 1 1) = 1 0 1 0
After XOR operation with left nibble of after ip = 1 0 1 0
We combine both halves i.e. right half of initial permutation and output of ip.
Combine 1 1 0 1 and 1 0 1 0
After combine = 1 0 1 0 1 1 0 1
Step-3:
Now, divide the output into two halves of 4 bit each. Combine them again, but now the left part should become right and the right part should become left.
After step 3 = 1 1 0 1 1 0 1 0
Step-4:
Again perform step 2, but this time while doing XOR operation after expanded permutation use key 2 instead of key 1.
Expand permutation is defined as - 4 1 2 3 2 3 4 1
After second ep = 0 1 0 1 0 1 0 1
After XOR operation with 2nd Key = 0 0 0 1 0 1 1 0
After second S-Boxes = 1 1 1 1
P4 is defined as - 2 4 3 1
After P4 = 1 1 1 1
After XOR operation with left nibble of after first part = 0 0 1 0
After second part = 0 0 1 0 1 0 1 0
l = 1 1 0 1 and r = 1 0 1 0
On the right half, we perform expanded permutation using EP table which converts 4 bits into 8 bits. Expand permutation is defined as –
EP(k1, k2, k3, k4) = (k4, k1, k2, k3, k2, k3, k4, k1)
After second ep = 0 1 0 1 0 1 0 1
We perform XOR operation using second key K2 with the output of expanded permutation.
Key-2 is - 0 1 0 0 0 0 1 1
(0 1 0 0 0 0 1 1) XOR (0 1 0 1 0 1 0 1) = 0 0 0 1 0 1 1 0
After XOR operation with 2nd Key = 0 0 0 1 0 1 1 0
Again we divide the output of XOR into 2 halves of 4 bit each.
l = 0 0 0 1 and r = 0 1 1 0
We take the first and fourth bit as row and the second and third bit as a column for our S boxes.
S0 = [1,0,3,2
3,2,1,0
0,2,1,3
3,1,3,2]
S1 = [0,1,2,3
2,0,1,3
3,0,1,0
2,1,0,3]
For l = 0 0 0 1
row = 01 = 1 , column = 00 = 0
S0 = 3 = 11
For r = 0 1 1 0
row = 00 = 0 , column = 11 = 3
S1 = 3 = 11
After first S-Boxes combining S0 and S1 = 1 1 1 1
S boxes gives a 2-bit output which we combine to get 4 bits and then perform permutation using the P4 table. P4 is defined as –
P4(k1, k2, k3, k4) = (k2, k4, k3, k1)
After P4 = 1 1 1 1
We XOR the output of the P4 table with the left half of the initial permutation table i.e. IP table.
(1 1 0 1) XOR (1 1 1 1) = 0 0 1 0
After XOR operation with left nibble of after first part = 0 0 1 0
We combine both halves i.e. right half of initial permutation and output of ip.
Combine 1 0 1 0 and 0 0 1 0
After combine = 0 0 1 0 1 0 1 0
After second part = 0 0 1 0 1 0 1 0
Step-5:
Perform inverse initial permutation. The output of this table is the cipher text of 8 bit.
Output of step 4 : 0 0 1 0 1 0 1 0
Inverse Initial permutation is defined as –
IP-1(k1, k2, k3, k4, k5, k6, k7, k8) = (k4, k1, k3, k5, k7, k2, k8, k6)
8-bit Cipher Text will be = 0 0 1 1 1 0 0 0
Java
import java.io.*;
public class GFG {
int key[] = {
1 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 1 , 0
};
int P10[] = { 3 , 5 , 2 , 7 , 4 , 10 , 1 , 9 , 8 , 6 };
int P8[] = { 6 , 3 , 7 , 4 , 8 , 5 , 10 , 9 };
int key1[] = new int [ 8 ];
int key2[] = new int [ 8 ];
int [] IP = { 2 , 6 , 3 , 1 , 4 , 8 , 5 , 7 };
int [] EP = { 4 , 1 , 2 , 3 , 2 , 3 , 4 , 1 };
int [] P4 = { 2 , 4 , 3 , 1 };
int [] IP_inv = { 4 , 1 , 3 , 5 , 7 , 2 , 8 , 6 };
int [][] S0 = { { 1 , 0 , 3 , 2 },
{ 3 , 2 , 1 , 0 },
{ 0 , 2 , 1 , 3 },
{ 3 , 1 , 3 , 2 } };
int [][] S1 = { { 0 , 1 , 2 , 3 },
{ 2 , 0 , 1 , 3 },
{ 3 , 0 , 1 , 0 },
{ 2 , 1 , 0 , 3 } };
void key_generation()
{
int key_[] = new int [ 10 ];
for ( int i = 0 ; i < 10 ; i++) {
key_[i] = key[P10[i] - 1 ];
}
int Ls[] = new int [ 5 ];
int Rs[] = new int [ 5 ];
for ( int i = 0 ; i < 5 ; i++) {
Ls[i] = key_[i];
Rs[i] = key_[i + 5 ];
}
int [] Ls_1 = shift(Ls, 1 );
int [] Rs_1 = shift(Rs, 1 );
for ( int i = 0 ; i < 5 ; i++) {
key_[i] = Ls_1[i];
key_[i + 5 ] = Rs_1[i];
}
for ( int i = 0 ; i < 8 ; i++) {
key1[i] = key_[P8[i] - 1 ];
}
int [] Ls_2 = shift(Ls, 2 );
int [] Rs_2 = shift(Rs, 2 );
for ( int i = 0 ; i < 5 ; i++) {
key_[i] = Ls_2[i];
key_[i + 5 ] = Rs_2[i];
}
for ( int i = 0 ; i < 8 ; i++) {
key2[i] = key_[P8[i] - 1 ];
}
System.out.println( "Your Key-1 :" );
for ( int i = 0 ; i < 8 ; i++)
System.out.print(key1[i] + " " );
System.out.println();
System.out.println( "Your Key-2 :" );
for ( int i = 0 ; i < 8 ; i++)
System.out.print(key2[i] + " " );
}
int [] shift( int [] ar, int n)
{
while (n > 0 ) {
int temp = ar[ 0 ];
for ( int i = 0 ; i < ar.length - 1 ; i++) {
ar[i] = ar[i + 1 ];
}
ar[ar.length - 1 ] = temp;
n--;
}
return ar;
}
int [] encryption( int [] plaintext)
{
int [] arr = new int [ 8 ];
for ( int i = 0 ; i < 8 ; i++) {
arr[i] = plaintext[IP[i] - 1 ];
}
int [] arr1 = function_(arr, key1);
int [] after_swap = swap(arr1, arr1.length / 2 );
int [] arr2 = function_(after_swap, key2);
int [] ciphertext = new int [ 8 ];
for ( int i = 0 ; i < 8 ; i++) {
ciphertext[i] = arr2[IP_inv[i] - 1 ];
}
return ciphertext;
}
String binary_( int val)
{
if (val == 0 )
return "00" ;
else if (val == 1 )
return "01" ;
else if (val == 2 )
return "10" ;
else
return "11" ;
}
int [] function_( int [] ar, int [] key_)
{
int [] l = new int [ 4 ];
int [] r = new int [ 4 ];
for ( int i = 0 ; i < 4 ; i++) {
l[i] = ar[i];
r[i] = ar[i + 4 ];
}
int [] ep = new int [ 8 ];
for ( int i = 0 ; i < 8 ; i++) {
ep[i] = r[EP[i] - 1 ];
}
for ( int i = 0 ; i < 8 ; i++) {
ar[i] = key_[i] ^ ep[i];
}
int [] l_1 = new int [ 4 ];
int [] r_1 = new int [ 4 ];
for ( int i = 0 ; i < 4 ; i++) {
l_1[i] = ar[i];
r_1[i] = ar[i + 4 ];
}
int row, col, val;
row = Integer.parseInt( "" + l_1[ 0 ] + l_1[ 3 ], 2 );
col = Integer.parseInt( "" + l_1[ 1 ] + l_1[ 2 ], 2 );
val = S0[row][col];
String str_l = binary_(val);
row = Integer.parseInt( "" + r_1[ 0 ] + r_1[ 3 ], 2 );
col = Integer.parseInt( "" + r_1[ 1 ] + r_1[ 2 ], 2 );
val = S1[row][col];
String str_r = binary_(val);
int [] r_ = new int [ 4 ];
for ( int i = 0 ; i < 2 ; i++) {
char c1 = str_l.charAt(i);
char c2 = str_r.charAt(i);
r_[i] = Character.getNumericValue(c1);
r_[i + 2 ] = Character.getNumericValue(c2);
}
int [] r_p4 = new int [ 4 ];
for ( int i = 0 ; i < 4 ; i++) {
r_p4[i] = r_[P4[i] - 1 ];
}
for ( int i = 0 ; i < 4 ; i++) {
l[i] = l[i] ^ r_p4[i];
}
int [] output = new int [ 8 ];
for ( int i = 0 ; i < 4 ; i++) {
output[i] = l[i];
output[i + 4 ] = r[i];
}
return output;
}
int [] swap( int [] array, int n)
{
int [] l = new int [n];
int [] r = new int [n];
for ( int i = 0 ; i < n; i++) {
l[i] = array[i];
r[i] = array[i + n];
}
int [] output = new int [ 2 * n];
for ( int i = 0 ; i < n; i++) {
output[i] = r[i];
output[i + n] = l[i];
}
return output;
}
int [] decryption( int [] ar)
{
int [] arr = new int [ 8 ];
for ( int i = 0 ; i < 8 ; i++) {
arr[i] = ar[IP[i] - 1 ];
}
int [] arr1 = function_(arr, key2);
int [] after_swap = swap(arr1, arr1.length / 2 );
int [] arr2 = function_(after_swap, key1);
int [] decrypted = new int [ 8 ];
for ( int i = 0 ; i < 8 ; i++) {
decrypted[i] = arr2[IP_inv[i] - 1 ];
}
return decrypted;
}
public static void main(String[] args)
{
GFG obj = new GFG();
obj.key_generation();
int [] plaintext = {
1 , 0 , 0 , 1 , 0 , 1 , 1 , 1
};
System.out.println();
System.out.println( "Your plain Text is :" );
for ( int i = 0 ; i < 8 ; i++)
System.out.print(plaintext[i] + " " );
int [] ciphertext = obj.encryption(plaintext);
System.out.println();
System.out.println(
"Your cipher Text is :" );
for ( int i = 0 ; i < 8 ; i++)
System.out.print(ciphertext[i] + " " );
int [] decrypted = obj.decryption(ciphertext);
System.out.println();
System.out.println(
"Your decrypted Text is :" );
for ( int i = 0 ; i < 8 ; i++)
System.out.print(decrypted[i] + " " );
}
}
|
Output
Your Key-1 :
1 0 1 0 0 1 0 0
Your Key-2 :
0 1 0 0 0 0 1 1
Your plain Text is :
1 0 0 1 0 1 1 1
Your cipher Text is :
0 0 1 1 1 0 0 0
Your decrypted Text is :
1 0 0 1 0 1 1 1
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