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With the ADFGX cipher, each "side" letter or "top" letter is associated with five plaintext letters.In the example above, the "side" letter "D" is associated with the plaintext letters "d h o z k", and the "top" letter "D" is associated with the plaintext letters "t h f j r".(Considerable statistical analysis was required after that step had been reached, all done by hand.) It was thus effective only during times of very high traffic, but fortunately for the cryptanalysts, that was also when the most important messages were sent.However, that was not the only trick that Painvin used to crack the ADFGX cipher.Since the two groups of five letters have different cumulative frequency distributions, a frequency analysis of the "D" letter in columns consisting of "side" letters has a distinctively different result from those of the "D" letter in columns consisting of "top" letters.That trick allowed Painvin to guess which columns consisted of "side" letters and which columns consisted of "top" letters.He also used repeating sections of ciphertext to derive information about the likely length of the key that was being used.
ADFGVX was in fact an extension of an earlier cipher called ADFGX.Also, after substitution but before transposition, the columns would alternately consist entirely of "top" and "side" letters.One of the characteristics of frequency analysis of letters is that while the distributions of individual letters may vary widely from the norm, the law of averages dictates that groups of letters vary less.He could then pair them up and perform a frequency analysis on the pairings to see if the pairings were only noise or corresponding to plaintext letters.Once he had the proper pairings, he could then use frequency analysis to figure out the actual plaintext letters.