I got introduced to the ADFGVX cipher, and it seems very tedious to decipher such ciphertexts. If I do not have access to the key square and the keyword, and I am just given the ciphertext and a string of numbers, how do you decipher it? The columnar transposition is another thing that makes it even more difficult to break. (I am assuming that ADFGVX comes with a columnar transposition). I am planning on making a code that can break it. A complete brute force seems possible, just too tiresome.
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$\begingroup$ This was a general question. It's weird how people can down vote it but not write a reason in the comment section below. Also I don't see a reason for the down-vote. $\endgroup$– tomtomtomCommented Mar 14, 2020 at 6:10
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$\begingroup$ Classical crypto like this is trivially breakable by computer. web.archive.org/web/20100503103848/http://www.vectorsite.net/… talks about how it was broken in 1918. $\endgroup$– SAI PeregrinusCommented Mar 14, 2020 at 16:09
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$\begingroup$ @tomtomtom This cipher has been broken for some time. You are asking for a general method to break the cipher, without going into detail what you've tried or even what search terms you have used to try and find out what techniques are out there. $\endgroup$– Maarten Bodewes ♦Commented Mar 15, 2020 at 17:40
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$\begingroup$ @tomtomtom As one of the moderators just said, please go into detail and show the effort that you have made. Then we can help you more. $\endgroup$– PatriotCommented Mar 16, 2020 at 12:57
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2 Answers
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As you must know, ADFGVX is a German cipher from World War I. It was broken by the French (Painvin) during that war, but not without a major effort, and only on certain days.
It uses fractionation and a Polybius square, followed by a columnar transposition based on a keyword.
In Milton F. Friedman's Military Cryptanalysis, Part IV, pp. 103-149, he goes into detail about how to break this cipher.
There is also a useful paper from 1984, Konheim, A. G. (n.d.). Cryptanalysis of Adfgvx Encipherment Systems. Lecture Notes in Computer Science, 339–341. doi:10.1007/3-540-39568-7_26 (an extended abstract)
Konheim presents a four-step cryptanalytic technique to break ADFGVX.
- Determine which column vectors are adjacent in the array.
- Determine the relative order of the pairs of column vectors.
- Recover the substitution.
- Recover the transposition order of the columns in the array.
One thing that could be looked at first is this: perhaps the Polybius square is not a mixed alphabet after all, but alphabetical.
Edit:
The cryptanalysis of ADFGVX is given extensive step-by-step treatment in a fascinating book called Secret History: The Story of Cryptology, by Craig T. Bauer, CRC Press, 2021. pp. 168-182.
Further reading:
Childs, J. Rives, General Solution of the ADFGVX Cipher System, War Department, Office of the Chief Signal Officer, United States Government Printing Office, Washington, DC, 1934.
Hitt, Parker, Manual for the Solution of Military Ciphers, Army Service Schools Press, Fort Leavenworth, Kansas, 1916, second edition 1918, reprinted by Aegean Park Press, Laguna Hills, California, 1976. Can be found here.
Lasry, George, Ingo Niebel, Nils Kopal, and Arno Wacker, “Deciphering ADFGVX Messages from the Eastern Front of World War I,” Cryptologia, Vol. 41, No. 2, March 2017, pp. 101–136.
Pergent, Jacques, “Une figure extraordinaire du chiffre français de 1914 à 1918: le capitaine Georges Painvin,” Armée et Défense, Vol. 47, No. 4, April 1968, pp. 4–8.
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There is also more modern research in order to attack complete ADFGVX ciphertexts (both partly-known-plaintext attacks and ciphertext-only-attacks).
See chapter 6 of the following PhD thesis: Lasry, G.: A Methodology for the Cryptanalysis of Classical Ciphers with Search Metaheuristics, Kassel University Press. kassel university press (2018) at https://d-nb.info/1153797542/34.
These new results are implemented e.g. in the free, open-source e-learning program CrypTool 2. In ready-to-run templates you can try an ADFGVX dictionary attack or an ADFGVX heuristic analysis with simulated annealing. See the two attached screenshots:
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As you said -- if you plan writing code that can break ADFGVX, you might even try to improve the results from Lasry and in CrypTool and share your findings again with the open-source community.
