Caesar Cipher #

Ceaser Substitute the plaintext with a different character.

\[ C = E(k, p) = (p + k) \ mod \ 26 \] \[ p = D(k, C) = (C - k) \ mod \ 26 \]

Key space #

For Caesar cipher, the key is just a number.

There are only 25 possible keys because there are only 25 ways to shift the alphabets.

Brute Force #

The small key space leaves caesar ciphers vulnerable to brute-force attacks. The attacker just needs to try all (only) 25 keys to get the plaintext.

Generalized Monoalphabetic Cipher #

Instead of shifting characters by one, make random pairings to improve key space. E.g. pair a with d, b with e, c with f, etc.

Key space #

Here key is the way we can arrange the 26 alphabets.

Example Key: vfqhloytkzrwgjaixbpmcnseud

There are 26 characters in the alphabet, so there are 26! possible keys.

Frequency Attack #

The frequencies of characters used in the cipher text will match up with the frequencies of characters in the English language. We can use this semantic knowledge to guess the plaintext.

Polyalphabetic ciphers are also susceptible to frequency attacks as the frequency of bigrams or trigrams in the cipher text can still provide clues to the underlying plaintext.