6 Countermeasures
This chapter covers
- Double encipherment
- Null characters and null bits
- Homophones
- Hiding messages within images or computer files
To recap section 5.9, polyalphabetic ciphers can be solved by a two-step process. First, the period or the key length is determined using the Kasiski Method or the Index of Coincidence. This separates the ciphertext into several smaller texts, each enciphered by just one letter of the key. Second, these individual texts are deciphered using the standard methods for simple substitution ciphers, frequency and contacts.
Let's turn it around. What can the cryptologist do to prevent a polyalphabetic cipher from being cracked by this two-step process? We will look at a few countermeasures.
6.1 Double Encipherment
If a message is enciphered with one polyalphabetic cipher whose period is P, and the resulting intermediate text is enciphered with a second polyalphabetic cipher whose period is Q, the result is equivalent to a polyalphabetic cipher whose period is the least common multiple of P and Q, denoted lcm(P,Q). That is, the period is the smallest integer which is a multiple of both P and Q. For example, if P is 10 and Q is 11, then the double encipherment will have a period of 110, but if P is 10 and Q is 12 the double encipherment will have a period of 60 because 60 is a multiple of both 10 and 12.