d'Agapeyeff Cipher

D'Agapeyeff Cipher - Solution

Encryption thereafter proceeds as already shown.

Conclusion

So - there we have it. An elaborate 'April Fool', masquerading as a 'cryptogram upon which the reader is invited to test his skill'. Based on the recovered plain text above, I'm now totally convinced that the remaining 182 groups are nulls and merit no further analysis. [See next paragraph.]

Null Cipher

In her excellent book 'Cryptanalysis' (originally published in November 1939 as 'Elementary Cryptanalysis'), Helen Fouché Gaines devotes a short section to Concealment Devices. In particular, she mentions the null cipher - the name deriving from the fact that, in any given cryptogram, the greater portion of the letters (or characters) are null, with only a few being significant. These significant letters may be concealed in an infinite variety of ways - eg - ends of words (and although not specifically mentioned, columns would of course be a possibility also). She goes on to say that "a purely concealment cipher may be enveloped in apparent ciphers of other types .......... even more effective would be the device of concealing the message in what appears to be a cryptogram, but is not ......... in this case, it would be hoped that the analyst's full attention is given to the hopeless task of decrypting the dummy".

Re-reading d'Agapeyeff, early in his book he gives a description of Jerome Cardan's Trellis cipher, which is broadly in line with what we have here - including instructions to the encipherer such as 'taking care to put down one sentence only per sheet ........ compose an innocent-looking message to fill in the gaps'. Later, in Chapter III - Ciphers in Literature, he mentions a leg-pull uncovered by Bazeries in a cryptogram from a much earlier book by Balzac and also a mystery parchment in Jules Verne's A Journey to the Centre of the Earth, where the message is contained in the 'finals of the lines read backwards'.

Cipher Messages and Reversibility

Ordinarily, a Plain message is enciphered by (let's say) person A and is intended solely for person B. Both A and B would be in possession of the message key and hence B is able to reverse the process and recover, with no ambiguity, the underlying Plain. The interceptor (let's say, person C) attempts to recover the Plain by analysing the message(s), hopefully recovering the underlying Plain and perhaps also the key in the process. In the case of 'April Fool', the solution as shown is not fully reversible back to the Plain. Some might reasonably insist this makes the solution invalid (or at least that part from April '39 back to April Fool). I would argue, however, that we are not dealing with the norm - the message is a challenge cipher, where we, the readers of the book, are both the B and C above - ie - intended to receive the message but not in possession of the key and where normal rules may not apply. I firmly believe that d'Agapeyeff intended his challenge cipher to be solved and gave just enough clues, hints etc. to allow the analyst to get back to April '39 (eg - the 92 inserted twice to steer the analyst into thinking date, the six groups not re-ciphered through Porta, allied to the three successive key words and the almost identical example solution) and, from there, take the short step back to April Fool. Of course, the 2nd edition in 1949 (minus LONDON and April 1939) made solving nigh impossible - hence, the withdrawal of the puzzle in 1952. [It is perhaps worth noting that, in the example solution, the Keyword used for both the Polybius and Transposition is MANCHESTR, with the repeated E omitted. This would not be considered (by some) normal Keyword usage for the Transposition stage.]

Polybius Square - Swaps Explained

In the recovered Polybius Square, three pairs of letters were swapped: E with F, P with Y and R with U. Considering the latter 2 swaps first, recall that the letters P and R (from April) are enciphered as 71 04. After substitution to letters, these digits become U Q P R - which are then transposed to give R U P Q and finally transformed into 2-digit groups using the Polybius Square again, yielding 04 94 71 93. All ok. BUT - if P hadn't been swapped with Y, the result would have been 61 04, which becomes Y Q P R, transposing to R Y P Q becoming 04 71 61 93. This means we have lost the 'U' (94 or 04). So P must swap with Y. Similarly, if R hadn't been swapped with U, the result would have been 71 94, which becomes U Q O R, then R U O Q then 94 04 92 93. This means we have lost the 'P' (61 or 71). So R must swap with U.

Looking at E with F, if the swap hadn't taken place, letter F would be 73 - which would defeat the argument that FOOL reduces to just 39. [And of course we know that 73 is a non-occurring group and should therefore be E.]

Q & A (anticipated)

Why so long a cryptogram for just 9 letters of Plain text?

In order to decipher the message, the analyst has to be able to determine what normal cipher looks like - hence, a reasonably long message, from which the analyst is able to separate the regularly-occurring groups from the low-scoring/non-occurring groups

Why, if they are mainly nulls, do the regularly-occurring cipher groups have such a rough frequency distribution?

To sow the seeds of doubt in the mind of the analyst as to the type of system (or, as mentioned above, to steer the analyst to "the hopeless task of decrypting the dummy")

Why make all the low-scoring groups occur in a single column?

To assist with diagnosing the system (ie - the method of encipherment) and the recovery of the Polybius Square and (later) Porta table

Why introduce two null groups into that same column?

To steer the analyst in the direction of thinking 'April 1939', especially the '1939' bit

Why use consecutive words as Keywords?

To assist with recovery generally and (in the case of LONDON) the eventual identification and recovery of the RailFence Transposition, the Transposition rules and the Porta encipherment. As already mentioned, this backfired when the 2nd edition was published in 1949.

Comparison with D'Agapeyeff's worked example of a Combination Substitution-Transposition Cipher

In Chapter VI, entitled Types of Codes and Ciphers, d'Agapeyeff includes a worked example of a Combination Substitution-Transposition cipher. It is worth comparing this with the system I have described above (changes and/or additions to his worked example are in red):

encipherment begins with a keyword-based mixed alphabet inscribed into a Polybius Square (as does my solution)

row/column coordinates are letters [ABCDE] [ABCDE] (as opposed to digits [67890] [12345], transformed to letters)

eg - M enciphers as AA (as opposed to M = 83, which then becomes IE)

the cipher digraphs (AA etc) are transposed according to a Keyword (the same deduped Keyword as for the Polybius)

(as opposed to the Transpositions I describe, which are:

Rail Fence, where keyword LONDON, immediately following d'Agapeyeff, is used to provide a blank template

rule-based - eg - Left shift 1st letter of each top row pair etc)

fractionation (although not specifically mentioned) takes place during the Transposition (and also in my solution)

mention is made of the Chinese fill Transposition (as opposed to actually used)

mention is made of the simplified Porta with indicator letter for each word (as opposed to actually used)

since there is only one Porta table involved, it is reasonable to argue that no indicator letter is required

an optional 3rd stage re-encipherment using the same Polybius Square is described (as opposed to actually used)

using a reverse operation to return to a monoliteral state (as opposed to a repeat of the opening stage, yielding dinomes)

Message length: same number of Cipher letters as Plain (as opposed to twice the number of Cipher dinomes as Plain)

In the worked example, d'Agapeyeff is able to reverse the encipherment process, since his example cipher comprises solely the letters ABCDE

(as opposed to cipher consisting of 13 letters, which are forward enciphered to dinomes)

Thank you for taking the time to read thus far.

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