Introduction to Cryptography with Open-Source Software

Block ciphers and the data encryption st andard 187

The S- boxes (“S” stands for “substitution”) are defined by the tables:

0 1 2 3

0 1 0 3 2

1 3 2 1 0

2 0 2 1 3

3 3 1 3 2

S-box S

0

0 1 2 3

0 0 1 2 3

1 2 0 1 3

2 3 0 1 0

3 2 1 0 3

S-box S

1

To apply an S-box, say S

0

, suppose the 4 input bits are x

0

x

1

x

2

x

3

. The outer

two bits give the row number; the inner two bits the column number. So for

example, 1011 has row 11, or 3, and column 01, or 1. At row 3 and column 1

is the value 1, or 01 in binary. Another example: 0001. The row value is 01,

or 1, and the column value 00, or 0. At row 1 and column 0 of S

0

is the value

3, or 11 in binary.

The entire mixing function is