DES (Data Encryption Standard) Cipher Algorithm

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∟DES (Data Encryption Standard) Cipher Algorithm

This section describes DES (Data Encryption Standard) algorithm - A 16-round Feistel cipher with block size of 64 bits.

DES Cipher - A 16-round Feistel cipher with block size of 64 bits. DES stands for Data Encryption Standard.

DES was developed by IBM in 1974 in response to a federal government public invitation for data encryption algorithms. In 977, DES was published as a federal standard, FIPS PUB 46.

DES algorithm:

Input: 
   T: 64 bits of clear text
   k1, k2, ..., k16: 16 round keys
   IP: Initial permutation
   FP: Final permutation
   f(): Round function
   
Output: 
   C: 64 bits of cipher text

Algorithm:
   T' = IP(T), applying initial permutation
   (L0, R0) = T', dividing T' into two 32-bit parts
   (L1, R1) = (R0, L0 ^ f(R0, k1))
   (L2, R2) = (R1, L1 ^ f(R1, k2))
   ......
   C' = (R16, L16), swapping the two parts
   C = FP(C'), applying final permutation

where ^ is the XOR operation.

The round function f(R,k) is defined as:

Input: 
   R: 32-bit input data
   k: 48-bit round key
   E: Expansion permutation
   P: Round permutation
   s(): S boxes function
   
Output
   R' = f(R,k): 32-bit output data

Algorithm
   X = E(R), applying expansion permutation and returning 48-bit data
   X' = X ^ k, XOR with the round key
   X" = s(X'), applying S boxes function and returning 32-bit data
   R' = P(X"), applying the round permutation

The S boxes function s(X) is defined as:

Input: 
   X: 48-bit input data
   S1, S2, ..., S8: 8 S boxes - 4 x 16 tables

Output: 
   X' = s(X): 32-bit output data

Algorithm: 
   (X1, X2, ..., X8) = X, dividing X into 8 6-bit parts
   X' = (S1(X1), S2(X2), ..., S8(X8))
      where Si(Xi) is the value at row r and column c of S box i with
         r = 2*b1 + b6 
         c = 8*b2 + 4*b3 + 2*b3 + b4 
         b1, b2, b3, b4, b5, b6 are the 6 bits of the Xi

DES cipher algorithm supporting tables:

Initial Permutation - IP:

58    50   42    34    26   18    10    2
60    52   44    36    28   20    12    4
62    54   46    38    30   22    14    6
64    56   48    40    32   24    16    8
57    49   41    33    25   17     9    1
59    51   43    35    27   19    11    3
61    53   45    37    29   21    13    5
63    55   47    39    31   23    15    7

Final Permutation - FP:

40     8   48    16    56   24    64   32
39     7   47    15    55   23    63   31
38     6   46    14    54   22    62   30
37     5   45    13    53   21    61   29
36     4   44    12    52   20    60   28
35     3   43    11    51   19    59   27
34     2   42    10    50   18    58   26
33     1   41     9    49   17    57   25

Expansion permutation - E:

32     1    2     3     4    5
 4     5    6     7     8    9
 8     9   10    11    12   13
12    13   14    15    16   17
16    17   18    19    20   21
20    21   22    23    24   25
24    25   26    27    28   29
28    29   30    31    32    1

Round permutation - P:

16   7  20  21
29  12  28  17
 1  15  23  26
 5  18  31  10
 2   8  24  14
32  27   3   9
19  13  30   6
22  11   4  25

S boxes - S1, S2, ..., S8:

                        S1

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

                        S2

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

                        S3

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

                        S4

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

                        S5

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

                        S6

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

                        S7

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

                        S8

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