Cryptography Reference
In-Depth Information
efficiency-security tradeoff). However, most homophonic codes have extremely
large keys and involve some degree of message expansion.
LESSON FROM HOMOPHONIC ENCODING
Homophonic encoding defeats single letter frequency analysis by increasing the
size of the ciphertext (but not the plaintext) alphabet, thus enabling a given
plaintext letter to be encrypted to different ciphertext letters. A good homophonic
code arguably provides quite a secure cryptosystem. However, the biggest lesson
fromstudying homophonic encoding is that the price to be paid for strong security
is sometimes not worth paying. Good homophonic encoding comes at a significant
cost in terms of key size and message expansion. It is unlikely that many modern
security applications will be willing to bear these costs when they can get all the
security they need from a much more efficient cryptosystem.
2.2.4
Vigenère Cipher
The last historical cryptosystem that we will look at is the famous
Vigenère Cipher
,
which was for a significant period in history regarded as being such a secure
cryptosystem that it was regularly used for protecting sensitive political and
military information and referred to as the 'indecipherable cipher'. The Vigenère
Cipher is of interest to us because it illustrates the use of positional dependency
to defeat single letter frequency analysis.
ENCRYPTION USING THE VIGENÈRE CIPHER
The Vigenère Cipher is fairly straightforward to understand. The key of the
Vigenère Cipher consists of a string of letters that form a
keyword
. Associating
the letters A, B,
...,
Z with the numbers 0
,
1
,...,
25, respectively, the encryption
process proceeds as follows:
1. write out the keyword repeatedly underneath the plaintext until every plaintext
letter has a keyword letter beneath it;
2. encrypt each plaintext letter using a Caesar Cipher, whose key is the number
associated with the keyword letter written beneath it.
Figure 2.5 provides an example of the Vigenère Cipher with keyword DIG,
where the plaintext appears in the top row and the ciphertext appears in the
bottom row. Thus, for example, the first plaintext letter A is shifted using a Caesar
Cipher with shift 3 (corresponding to keyword letter D) to obtain the ciphertext
letter D. The second plaintext letter, which is also A, is shifted using a Caesar
Cipher with shift 8 (corresponding to keyword letter I) to obtain ciphertext letter I.
The third plaintext letter, which is R, is shifted using a Caesar Cipher with shift
6 (corresponding to keyword letter G) to obtain ciphertext letter X. The rest of
ciphertext is produced in a similar way. Decryption is just the reverse process.
The important point to note is that, for example, the plaintext letter A is
encrypted to three different ciphertext letters (D, G and I). The critical fact that
