Cryptography Reference
In-Depth Information
2.
Known plaintext.
In this case it suffices that Eve knows a plaintext of just
one letter and its corresponding ciphertext. Indeed, if
Enc
k
(
)
=
i
j
, then
mod 26.
3.
Chosen plaintext.
Eve just chooses 0 as plaintext and computes
k
k
=
(
j
−
i
)
=
Enc
k
(
0
)
.
4.
Chosen ciphertext.
Eve chooses 0 as ciphertext and computes
k
=−
Dec
k
(
0
)
mod 26.
We see that cryptanalysis of the Caesar cipher is so easy that it can be easily carried
out by hand even assuming ciphertext-only. The remaining cases are included just to
illustrate the different situations that might arise. As a curiosity, we can mention a
recent episode that serves to illustrate the pitfalls of using cryptography while being
completely ignorant of the available cryptanalytic techniques. In April 2006 it was
reported that Italian police had arrested the 'boss of bosses' of the Sicilian Mafia,
Bernardo Provenzano. It appears that one of the things that led to his arrest was the
fact that the police found in his hideaway about 350
pizzini
(cryptograms in Sicilian)
which, once deciphered, revealed in some cases the names of his collaborators. These
cryptograms were enciphered by means of the
Binnu code
which encrypts the letter
A as 4, B as 5 and so on up to Z which goes to 24 and hence is essentially the Caesar
cipher with key 3 over a 21-letter alphabet. It is no wonder that the police easily
decrypted these cryptograms. But it is also interesting to note a remark attributed to a
'mathematics expert' in the news report. According to this expert, '
In the Provenzano
code the key is the +3 shift ... the code might have been made more secure by changing
the +3 key with other shift characters (+5, +7, +8) from time to time'
.
Exercise 1.3
Write a brief comment on the 'expert remarks' on the Binnu code.
Exercise 1.4
Suppose that the Caesar cipher, with a randomly chosen key, is used
to encrypt a message which is either 'y' or 'n' (we can interpret these messages as
'yes' and 'no'). An adversary knows this and observes the ciphertext 'q'. Does this
ciphertext give the adversary any additional information about the plaintext?
Example 1.3
We have just seen that cryptanalyzing the Caesar cipher is an easy task
that can be carried out by hand with little effort. Of course, with a computer, the
brute-force attack is carried out almost instantly. For example, a Maple function that
does it (assuming the same alphabet as before) is the following:
> CaesarCryptanalysis := ciphertext ->
table([seq(CaesarDec(k+1, ciphertext), k=0..modulus-1)]):
