CipherText only attack, historical cipher

Question

I have the following cryptogram:

AAGYQUCWUAKSOAMMOIKOAKMAKIECAGMQYIAAGQMKIWWAKIECAGMQYICAMOIKEQAICKMOIWOEUWIKKYAIIKOIKAAUCAEUCAOIIOAOAEOIKCOMWOIEOIGKCISAIGAAGMOMMIGKCISAIGSQMOAWWOIIKCIEIMOMMIGKQIKMCACAIKQGIAAGMOIACAMOICMOIIMIWQAMMCYCQIMOIEAIMCOMMOIKQUSOQEKSIIIAMMAEUQAMOIIQAAWWGQIIEMQCAKAAGMOIKOAKMSAKIAQKIGAMAQAAAGKIWWOECAOIIAMOQIGMQYIMOIAAKCOIMOSQMOOIAQWYIAKOIIGCWCSKYQUCWUASAKQAAKOIWMOAMOIECOWGACMUQWWOIIAMCAICWCSKOIKAMCOMOCAISAKKOCOMIGQAMOIEICSGKOIWWKAWWQAAYQAOMIYAMIKMOIIISQWWKCCACIAAIAGCKOIIKAQGAAAGYQIQAMKEIEMAMCIQAMOIEICSGKIMEOAAAUIMCOIIKQAQKOOIICKKKOCOMIGAMOQIGQWWKOCSWCOKMAAGCKKYQUCWUAKEIIAYIGKIAAMQEAWWWOIMOIISGCSAMOIKOAKMKMCCEIGGCSAQAMOIEAIMAAGEQEUIGOEAAQICAEICSCAIWCCUCOMOIKOCOMIGAAGSQMOAWWOQKYQMOMOIGIAWMAKMOAAQAMCWCSAMMOIECCIYAIIMOICWCSKIWWMOIYAIIKMAMMIIIGKAAUCAEUMIQIGMCEOWWCOMMOICAIKIWWAMAQASQMOAKSQAMQAMCWCSCAOIICAEUAAGKOIKIWWCAMOIMICOAGWQUIAWCMKQAQKOOIICKKKOCOMIGYQUCWUAAAGOIWIAEMCIKQGIOQYKIWKCOMCKMOIEAIMKIQIIAWWCOAMYIAAWKCKWOKOIGSQMOGIQAUKIQYIGAAWMOQAMMOIWECOWGECYIAEICKKSOQEKKMQEUKECWIKAAGIAAMCMOIGWQAMYAIIYQUCWUAKMCCGCACAIKQGIAAGCIMAA

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?

Answer 1

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.