How to implement the Data Encryption Standard (DES)

 

A step by step tutorial

Version 1.24

 

 

The Data Encryption Standard (DES) algorithm, adopted by the U.S.

government in 1977, is a block cipher that transforms 64-bit data

blocks under a 56-bit secret key, by means of permutation and

substitution. It is officially described in FIPS PUB 46. The DES

algorithm is widely used and is still considered reasonably secure.

 

This is a tutorial designed to be clear and compact, and to provide a

newcomer to the DES with all the necessary information to implement it

himself, without having to track down printed works or wade through C

source code. I welcome any comments.

Matthew Fischer <mfischer@heinous.music.uiowa.edu>

 

 

Here's how to do it, step by step:

 

  1. Process the key.

    2.  

    1. Get a 64-bit key from the user. (Every 8th bit (the least significant bit of each byte) is considered a parity bit. For a key to have correct parity, each byte should contain an odd number of "1" bits.) This key can be entered directly, or it can be the result of hashing something else. There is no standard hashing algorithm for this purpose.

      2.  

    2. Calculate the key schedule.

      3.  

      1. Perform the following permutation on the 64-bit key. (The parity bits are discarded, reducing the key to 56 bits. Bit 1 (the most significant bit) of the permuted block is bit 57 of the original key, bit 2 is bit 49, and so on with bit 56 being bit 4 of the original key.)

        2.  

        Permuted Choice 1 (PC-1)

         

        57 49 41 33 25 17 9

        1 58 50 42 34 26 18

        10 2 59 51 43 35 27

        19 11 3 60 52 44 36

        63 55 47 39 31 23 15

        7 62 54 46 38 30 22

        14 6 61 53 45 37 29

        21 13 5 28 20 12 4

         

      2. Split the permuted key into two halves. The first 28 bits are called C[0] and the last 28 bits are called D[0].

        3.  

      3. Calculate the 16 subkeys. Start with i = 1.

        4.  

        1. Perform one or two circular left shifts on both C[i-1] and D[i-1] to get C[i] and D[i], respectively. The number of shifts periteration are given in the table below.

          2.  

          Iteration # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

          Left Shifts 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1

           

        2. Permute the concatenation C[i]D[i] as indicated below. This will yield K[i], which is 48 bits long.

          3.  

          Permuted Choice 2 (PC-2)

           

          14 17 11 24 1 5

          3 28 15 6 21 10

          23 19 12 4 26 8

          16 7 27 20 13 2

          41 52 31 37 47 55

          30 40 51 45 33 48

          44 49 39 56 34 53

          46 42 50 36 29 32

           

        3. Loop back to 1.2.3.1 until K[16] has been calculated.

     

  2. Process a 64-bit data block.

    3.  

    1. Get a 64-bit data block. If the block is shorter than 64 bits, it should be padded as appropriate for the application.

      2.  

    2. Perform the following permutation on the data block.

      3.  

      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

       

    3. Split the block into two halves. The first 32 bits are called L[0], and the last 32 bits are called R[0].

      4.  

    4. Apply the 16 subkeys to the data block. Start with i = 1.

      5.  

      1. Expand the 32-bit R[i-1] into 48 bits according to the bit-selection function below.

        2.  

        Expansion (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

         

      2. Exclusive-or E(R[i-1]) with K[i].

        3.  

      3. Break E(R[i-1]) xor K[i] into eight 6-bit blocks. Bits 1-6 are B[1], bits 7-12 are B[2], and so on with bits 43-48 being B[8].

        4.  

      4. Substitute the values found in the S-boxes for all B[j]. Start with j = 1. All values in the S-boxes should be considered 4 bits wide.

        5.  

        1. Take the 1st and 6th bits of B[j] together as a 2-bit value (call it m) indicating the row in S[j] to look in for the substitution.

          2.  

        2. Take the 2nd through 5th bits of B[j] together as a 4-bit value (call it n) indicating the column in S[j] to find the substitution.

          3.  

        3. Replace B[j] with S[j][m][n].

          4.  

          Substitution Box 1 (S[1])

           

          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

           

          S[2]

           

          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

           

          S[3]

           

          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

           

          S[4]

           

          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

           

          S[5]

           

          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

           

          S[6]

           

          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

           

          S[7]

           

          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

           

          S[8]

           

          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

           

        4. Loop back to 2.4.4.1 until all 8 blocks have been replaced.

         

      5. Permute the concatenation of B[1] through B[8] as indicated below.

        6.  

        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

         

      6. Exclusive-or the resulting value with L[i-1]. Thus, all together, your R[i] = L[i-1] xor P(S[1](B[1])...S[8](B[8])), where B[j] is a 6-bit block of E(R[i-1]) xor K[i]. (The function for R[i] is more concisely written as, R[i] = L[i-1] xor f(R[i-1], K[i]).)

        7.  

      7. L[i] = R[i-1].

        8.  

      8. Loop back to 2.4.1 until K[16] has been applied.

       

    5. Perform the following permutation on the block R[16]L[16]. (Note that block R precedes block L this time.)

 

Final Permutation (IP**-1)

 

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

 

 

This has been a description of how to use the DES algorithm to encrypt one 64-bit block. To decrypt, use the same process, but just use the keys K[i] in reverse order. That is, instead of applying K[1] for the first iteration, apply K[16], and then K[15] for the second, on down to K[1].

 

Summaries:

 

Key schedule:

C[0]D[0] = PC1(key)

for 1 <= i <= 16

C[i] = LS[i](C[i-1])

D[i] = LS[i](D[i-1])

K[i] = PC2(C[i]D[i])

 

Encipherment:

L[0]R[0] = IP(plain block)

for 1 <= i <= 16

L[i] = R[i-1]

R[i] = L[i-1] xor f(R[i-1], K[i])

cipher block = FP(R[16]L[16])

 

Decipherment:

R[16]L[16] = IP(cipher block)

for 1 <= i <= 16

R[i-1] = L[i]

L[i-1] = R[i] xor f(L[i], K[i])

plain block = FP(L[0]R[0])

 

 

To encrypt or decrypt more than 64 bits there are four official modes (defined in FIPS PUB 81). One is to go through the above-described process for each block in succession. This is called Electronic Codebook (ECB) mode. A stronger method is to exclusive-or each plaintext block with the preceding ciphertext block prior to encryption. (The first block is exclusive-or'ed with a secret 64-bit initialization vector (IV). This IV is generally a random value that is kept with the key.) This is called Cipher Block Chaining (CBC) mode. The other two modes are Output Feedback (OFB) and Cipher Feedback (CFB).

 

When it comes to padding the data block, there are several options. One is to simply append zeros. Two suggested by FIPS PUB 81 are, if the data is binary data, fill up the block with bits that are the opposite of the last bit of data, or, if the data is ASCII data, fill up the block with random characters and put the ASCII character for the number of pad characters in the last byte of the block.

 

The DES algorithm can also be used to calculate cryptographic checksums up to 64 bits long (see FIPS PUB 113). If the number of data bits to be checksummed is not a multiple of 64, the last data block should be padded with zeros. If the data is ASCII data, the most significant bit of each byte should be set to 0. The data is then encrypted in CBC mode with IV = 0. The most significant n bits (where 16 <= n <= 64, and n is a multiple of 8) of the final ciphertext block are an n-bit checksum.

 

(Matthew Fischer November 1995)