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6.1.2 Overview

      DES is a block cipher, as shown in Figure 6.1.

                 Figure 6.1 Encryption and decryption with DES




6.1
6-2 DES STRUCTURE

      The encryption process is made of two permutations (P-
      boxes), which we call initial and final permutations, and
      sixteen Feistel rounds.




      Topics discussed in this section:
  6.2.1   Initial and Final Permutations
  6.2.2   Rounds
  6.2.3   Cipher and Reverse Cipher
  6.2.4   Examples
6.2
6-2 Continue

               Figure 6.2 General structure of DES




6.3
6.2.1 Initial and Final Permutations

      Figure 6.3 Initial and final permutation steps in DES




6.4
6.2.1 Continue


         Table 6.1 Initial and final permutation tables




6.5
6.2.1 Continued

      Example 6.1

      Find the output of the initial permutation box when the input is
      given in hexadecimal as:



      Solution
      Only bit 25 and bit 63 are 1s; the other bits are 0s. In the final
      permutation, bit 25 becomes bit 64 and bit 63 becomes bit 15. The
      result is




6.6
6.2.1 Continued

       Example 6.2

      Prove that the initial and final permutations are the inverse of each
      other by finding the output of the final permutation if the input is



      Solution
      The input has only two 1s; the output must also have only two 1s.
      Using Table 6.1, we can find the output related to these two bits.
      Bit 15 in the input becomes bit 63 in the output. Bit 64 in the input
      becomes bit 25 in the output. So the output has only two 1s, bit 25
      and bit 63. The result in hexadecimal is


6.7
6.2.1   Continued




      Note

      The initial and final permutations are straight P-
                   boxes that are inverses
                        of each other.
        They have no cryptography significance in
                             DES.


6.8
6.2.2 Rounds

      DES uses 16 rounds. Each round of DES is a Feistel
      cipher.




      Figure 6.4
      A round in DES
      (encryption site)




6.9
6.2.2 Continued
             DES Function
   The heart of DES is the DES function. The DES function
   applies a 48-bit key to the rightmost 32 bits to produce a
   32-bit output.


       Figure 6.5
       DES function




6.10
6.2.2 Continue

   Expansion P-box
   Since RI−1 is a 32-bit input and KI is a 48-bit key, we first
   need to expand RI−1 to 48 bits.


                       Figure 6.6 Expansion permutation




6.11
6.2.2 Continue

   Although the relationship between the input and output can
   be defined mathematically, DES uses Table 6.2 to define
   this P-box.
                Table 6.6 Expansion P-box table




6.12
6.2.2 Continue

   Whitener (XOR)
   After the expansion permutation, DES uses the XOR
   operation on the expanded right section and the round key.
   Note that both the right section and the key are 48-bits in
   length. Also note that the round key is used only in this
   operation.




6.13
6.2.2 Continue

   S-Boxes
   The S-boxes do the real mixing (confusion). DES uses 8 S-
   boxes, each with a 6-bit input and a 4-bit output. See
   Figure 6.7.

                     Figure 6.7 S-boxes




6.14
6.2.2 Continue

                 Figure 6.8 S-box rule




6.15
6.2.2 Continue
   Table 6.3 shows the permutation for S-box 1. For the rest
   of the boxes see the textbook.


                     Table 6.3 S-box 1




6.16
6.2.2 Continued
              Example 6.3

   The input to S-box 1 is 100011. What is the output?




   Solution
   If we write the first and the sixth bits together, we get 11 in binary,
   which is 3 in decimal. The remaining bits are 0001 in binary,
   which is 1 in decimal. We look for the value in row 3, column 1, in
   Table 6.3 (S-box 1). The result is 12 in decimal, which in binary is
   1100. So the input 100011 yields the output 1100.



6.17
6.2.2 Continue

   Straight Permutation

                 Table 6.11 Straight permutation table




6.18

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DES Cipher

  • 1. 6.1.2 Overview DES is a block cipher, as shown in Figure 6.1. Figure 6.1 Encryption and decryption with DES 6.1
  • 2. 6-2 DES STRUCTURE The encryption process is made of two permutations (P- boxes), which we call initial and final permutations, and sixteen Feistel rounds. Topics discussed in this section: 6.2.1 Initial and Final Permutations 6.2.2 Rounds 6.2.3 Cipher and Reverse Cipher 6.2.4 Examples 6.2
  • 3. 6-2 Continue Figure 6.2 General structure of DES 6.3
  • 4. 6.2.1 Initial and Final Permutations Figure 6.3 Initial and final permutation steps in DES 6.4
  • 5. 6.2.1 Continue Table 6.1 Initial and final permutation tables 6.5
  • 6. 6.2.1 Continued Example 6.1 Find the output of the initial permutation box when the input is given in hexadecimal as: Solution Only bit 25 and bit 63 are 1s; the other bits are 0s. In the final permutation, bit 25 becomes bit 64 and bit 63 becomes bit 15. The result is 6.6
  • 7. 6.2.1 Continued Example 6.2 Prove that the initial and final permutations are the inverse of each other by finding the output of the final permutation if the input is Solution The input has only two 1s; the output must also have only two 1s. Using Table 6.1, we can find the output related to these two bits. Bit 15 in the input becomes bit 63 in the output. Bit 64 in the input becomes bit 25 in the output. So the output has only two 1s, bit 25 and bit 63. The result in hexadecimal is 6.7
  • 8. 6.2.1 Continued Note The initial and final permutations are straight P- boxes that are inverses of each other. They have no cryptography significance in DES. 6.8
  • 9. 6.2.2 Rounds DES uses 16 rounds. Each round of DES is a Feistel cipher. Figure 6.4 A round in DES (encryption site) 6.9
  • 10. 6.2.2 Continued DES Function The heart of DES is the DES function. The DES function applies a 48-bit key to the rightmost 32 bits to produce a 32-bit output. Figure 6.5 DES function 6.10
  • 11. 6.2.2 Continue Expansion P-box Since RI−1 is a 32-bit input and KI is a 48-bit key, we first need to expand RI−1 to 48 bits. Figure 6.6 Expansion permutation 6.11
  • 12. 6.2.2 Continue Although the relationship between the input and output can be defined mathematically, DES uses Table 6.2 to define this P-box. Table 6.6 Expansion P-box table 6.12
  • 13. 6.2.2 Continue Whitener (XOR) After the expansion permutation, DES uses the XOR operation on the expanded right section and the round key. Note that both the right section and the key are 48-bits in length. Also note that the round key is used only in this operation. 6.13
  • 14. 6.2.2 Continue S-Boxes The S-boxes do the real mixing (confusion). DES uses 8 S- boxes, each with a 6-bit input and a 4-bit output. See Figure 6.7. Figure 6.7 S-boxes 6.14
  • 15. 6.2.2 Continue Figure 6.8 S-box rule 6.15
  • 16. 6.2.2 Continue Table 6.3 shows the permutation for S-box 1. For the rest of the boxes see the textbook. Table 6.3 S-box 1 6.16
  • 17. 6.2.2 Continued Example 6.3 The input to S-box 1 is 100011. What is the output? Solution If we write the first and the sixth bits together, we get 11 in binary, which is 3 in decimal. The remaining bits are 0001 in binary, which is 1 in decimal. We look for the value in row 3, column 1, in Table 6.3 (S-box 1). The result is 12 in decimal, which in binary is 1100. So the input 100011 yields the output 1100. 6.17
  • 18. 6.2.2 Continue Straight Permutation Table 6.11 Straight permutation table 6.18