Cryptography Reference
In-Depth Information
This means each letter in an English message contains only slightly more than a single
bit of information. If we express the redundancy of a language as its absolute rate minus its
rate, i.e.,
D = R r
then clearly English is a very redundant language, for we have in this case
D = R r 4.7 1.3 = 3.4.
This means that on the average, English messages are only about 28 percent real infor-
mation, and 72 percent wasted space. Such a low value is beneficial to a cryptanalyst, since,
conceivably, it means the analyst only has to determine around a single bit for each letter
in a message to determine the message. If we encode characters in bytes (as we usually do),
the analyst would only need to determine 1 out of every 8 bits to successfully recover a
plaintext message. (Of course, finding these bits, and making them hard to find is the con-
tinuing battle between cryptanalyst and cryptographer!)
If we want to measure the entropy of a cipher, we can simply measure the entropy of its
key space K . If each key in a key space K is equally likely for a 64-bit cipher, then, since
there are 2 64 possible keys to use, the entropy of the cipher is
) = log 2 2 64 = 64
Of course, for a cryptographer, the higher the entropy of a cipher, the better.
E
(
K
AII.3
CRYPTOGRAPHIC TECHNIQUES
In general, a cryptographer wants to decrease the redundancy in messages (likewise, increase
the entropy), since as we have seen, the more redundant a language is, the easier messages
are to cryptanalyze. This is done using techniques that can be separated into categories:
confusion, and diffusion.
AII.4
CONFUSION
This technique is intended to make statistical analysis more difficult by replacing plaintext
items with ciphertext items possessing less redundancy (hence, greater entropy).
This is commonly done through simple substitution. For example, the Caesar cipher
substitutes letters with other letters, though, as we have seen, the substituted letters contain
as much redundancy as the plaintext letters, so do little to protect the information. Other sub-
stitution methods replace entire blocks of characters with other blocks. If, on the average,
half of the bits of a substituted block change with every bit change in a plaintext block, and
if one is unable to predict which bits will change, we have ciphertext that appears to have
greater entropy than the plaintext.
In practice, however, the conditions required for a successful substitution are often not
met; that is, sometimes the analyst is able to predict how many bits of ciphertext will change
for some bit change in the plaintext, and can even know which ciphertext bits will change.
They can do this with careful study of the ciphertext, and of the mathematical transforma-
tion used.
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