I have the following cryptogram:


Of which I only know that it was encrypted with a historical cipher. The original text is in English.

First I tried to hypothesize the algorithm used. I have analyzed entropy, autocorrelation, and histogram.

Since the frequencies of the letters are different from the English language I have excluded the transposition cipher. I have also excluded the ciphers for mono-alphabetic substitution, since there is no substitution that returns the original text.

The most likely cipher remains therefore the polyalphabetic substitution. I used some tools to break the Vigenere cipher, but without success. I also tried to break the Hill cipher by observing the frequency of digram, but without success. I can not recover the original text, does anyone have any suggestions? can someone recover the text?

  • $\begingroup$ In order to encourage suggestions, you should also detail what you have found, not only what has failed. Eg that the length is 1024 which allows it to be organised into blocks or squares, or that it contains only 13 different characters with highly uneven frequencies. It would also be appropriate to explain where the cipher comes from. $\endgroup$ – Einar Rødland Jun 3 '18 at 8:44
  • $\begingroup$ @EinarRødland Thanks for the comment. I had only noticed that there were 13 characters. In addition to the length of 1024 that you said, I have not found other useful considerations. The ciphertext was given to us as a university exercise. $\endgroup$ – Gabriele Picco Jun 3 '18 at 8:55
  • $\begingroup$ Trying out known ciphers, as you have, might give success if you manage to guess the right one, but quickly one should start looking at more general patterns, statistics, etc which might give some clue of what kind of cipher is being used (which may well be one you're not familiar with). I'll place a few observations as an answer: it's not supposed to go as comments. $\endgroup$ – Einar Rødland Jun 3 '18 at 9:55

Here are a few observations.

The length of the cipher text is 1024, ie $2^{10}$. This lends itself well to block ciphers, or ciphers where characters form one or more squares (eg $32\times 32$ or many smaller ones).

Only 13 different characters are used, and these are A, C, E, G, etc: ie every second character from the alphabet. The frequency is far from even giving some indication that letter frequencies somehow influences the cipher:

166*I, 163*A, 108*M, 105*O, 93*C, 90*K, 67*Q, 64*W, 53*G, 39*E, 28*S, 25*U, 23*Y

The 2-gram frequency, ie length 2 substrings, is

51*OI, 43*MO, 33*AA, 31*AM, 26*II, 23*IK, 22*IG, 22*IA, 22*CA, 21*QA, 18*KO, 18*AG, 17*AI, 17*CO, 17*AK, ...

for which it may be noted that eg OI, MO, AM are frequent while the reverse IO, OM, MA are not. However, there does not seem to be a similar different between 2-grams in even positions and odd positions (I start indexing the first character at position 0).

So you should be looking for ciphers that produce these kinds of patterns.


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