Cryptography Reference
In-Depth Information
Analysis of S-DES and Comparison to DES
Schaefer relabeled S-DES as babyDES since it is a much simpler block cipher
than the full-blown DES. S-DES will encipher one block at a time and there are
2 8 possible plaintext blocks since we are dealing with 8-bit plaintext bitstrings.
In terms of composition of functions, all of the above discussion of S-DES can
be encapsulated in the following (see Definition A.5 on page 467 in Appendix
A).
( IP 1
IP )( m )= IP 1 ( f k 2 ( SW ( f k 1 ( IP ( m )))) = c.
f k 2
SW
f k 1
Full DES takes 64-bit plaintext blocks, a 56-bit key, from which sixteen 48-bit
subkeys are generated, and sixteen round functions, which we will label f k j for
j =1 , 2 ,..., 16. Hence, we may specify (full) DES now as a single composition
of functions.
( IP 1
f k 16
SW
f k 15
SW
◦···◦
f k 1
IP )( m )= c.
Moreover, in DES, we have eight S-Boxes S j for j =1 , 2 ,..., 8, each having 4
rows and 16 columns, where
S j ( m 1 m 2 m 3 m 4 m 5 m 6 )
picks out the entry in row ( m 1 m 6 ) and column ( m 2 m 3 m 4 m 5 ), which represents
16 possible entries, in binary, for each such row. Also, P 4 in S-DES, is replaced
by P 32 in DES, which is half the bitlength of the input in either case.
One of the weaknesses of DES that makes it unsuitable for use, and ranks it
as below standard for the modern day are its weak keys , which are keys k such
that
M
.
DES has four of these as follows, where an exponent means the repetition of
that bitstring the number of times the exponent dictates.
E k ( E k ( m )) = m for all m
(0 28 , 0 28 ) , (1 28 , 1 28 ) , (0 28 , 1 28 ) , (1 28 , 0 28 )
28
28
k
∈{
Z
× Z
}
.
With these keys, encryption is the same function as decryption, so these keys
must be avoided. There are also semiweak keys , which are key pairs ( k 1 ,k 2 )
such that
E k 1 ( E k 2 ( m )) = m for all
M
.
There are six of them. They are listed as follows:
((01) 14 (01) 14 , (10) 14 (10) 14 ) ,
((01) 14 (10) 14 , (10) 14 (01) 14 ) ,
((01) 14 (0) 28 , (10) 14 (0) 28 ) ,
((01) 14 (1) 28 , (10) 14 (1) 28 ) ,
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