Conventional Cryptography - A Classical Introduction to Cryptography: Applications for Communications Security - page 25

The 6-bit input b 1 b 2 b 3 b 4 b 5 b 6 is split into two parts b 1 b 6 and b 2 b 3 b 4 b 5 . The first
part b 1 b 6 indicates which line to read: 00 is the first line, 01 the second, 10 the third,
and 11 the fourth. The second part b 2 b 3 b 4 b 5 indicates which column to read in binary.
For instance, 0101 is column 5. The entry is the 4-bit output in decimal, to be converted
in binary. Hence the image of 001011 by S 3 is 0100 (4).

The DES key schedule is done by the following algorithm. We use two registers C
and D of 28 bits. The 56 key bits from K are first split into C and D following a fixed
bit selection table PC1. Each round then rotates the bits in C and D by r i positions
depending on the round number i . (The r i 's are also defined by a table.) Then another
bit selection table PC2 takes 24 bits from each of the two registers and concatenates
them in order to make a round key.

PC1
−→

1: K ( C , D )

2: for i = 1to16 do

3: C ← ROL r i ( C )

4: D ← ROL r i ( D )

5: K i ← PC2( C , D )

6: end for

Here ROL r is a circular rotation of r bits to the left. The r i 's are defined by

i 123456789 0 1 2 3 4 5 6
r i 112222221 2222221

Note that the sum of all r i 's is 28 so that we can generate the round keys in the decryption
ordering by starting with the same C and D and by running the loop backwards.

2.2 DES Modes of Operation

DES enables the encryption of 64-bit blocks. In order to encrypt plaintexts of arbi-
trary length, we have to use DES in a mode of operation. Several modes have been
standardized for DES (ECB, CBC, OFB, CFB, CTR) in Ref. [6].

2.2.1 Electronic Code Book (ECB)

The plaintext x is split into 64-bit blocks x 1 ,..., x n , and the ciphertext y is the con-

catenation of encrypted blocks.

=

x 1 || x 2 ||···||

x x n

y = C ( x 1 ) || C ( x 2 ) ||···|| C ( x n )

(See Fig. 2.5.) There are a few security problems.