I was reading on a site about the Zodiac Killer and how he used a basic substitu

Question

I was reading on a site about the Zodiac Killer and how he used a basic substitution cipher, but instead of substituting english letters and characters he substituted symbols.

I was wondering, if you had a large enough subset of symbols to use for commonly repeating letters like E,T,S ... then by what means could someone decipher the cipher. This is also referring to the fact that no one has yet to decipher his last message. Obviously this type of system of cryptography would not withstand in modern computing.

I am more interested in other techniques that could be used, I also found this site '340 Cipher', which includes frequency counts.

Explanation / Answer

If I understand your cipher idea right, you would have a larger ciphertext alphabet than the plaintext alphabet, where each plaintext symbol maps to multiple ciphertext symbols (and the number is dependent on the frequency of the plaintext symbol), one of which is used randomly.

This is known as a Homophonic substitution, and with it the single-symbol frequency analysis usable for simple substitution ciphers is thwarted, since all symbols now have similar frequencies.

But as soon as we start to look at frequencies of letter-pairs (and triplets), we will observe enough structures to break this, too. For example, q is almost always followed by u, and thus the ciphertexts of q will almost always be followed by one of the ciphertexts of u. (I don't know enough about the statistic properties of the English language to give more examples, but you can be sure that an attacker would know.)

Some examples from German:

- As in English, q is almost always followed by u.
- A c is almost always followed by either k or h.
- ei has about same frequency as ie (and i is the only letter who has this property related to e).

Some more details are given in David's answer.

Of course, if the ciphertext is so short (or the translation table so large) that each symbol is only used once or twice (or not at all), cryptanalysis is more difficult (or even impossible).

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