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Home Page Hebern's machines The 5 rotors machine home page
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IntroductionThere are essentially two works that deal with cryptanalysis of Hebern's 5-rotor ciphering machine:
In this page, we will deal with all the methods described in the two previous works as well as other methods from other sources. Cryptanalysis with known plain textFriedman's approach, deciphering a poemIn his secret report, Friedman does not deal exclusively to find the solution to the Navy's challenge. He gives an example of reconstitution of the wiring of the rotors of a Hebern machine from a couple plain text, cryptogram. (link). The Deavours & Kruh approachDeavours & Kruh also offers a method for finding the wiring of the rotors from a cryptogram/plain text couple. Their method is similar to that of Dawson which I presented in the study of the Hebern 1 rotor machine. Cryptanalysis knowing the wiring of the rotorsFind the fast rotor using statisticsDevours & Kruh try to decipher the messages using in turn each rotor whose wiring is known. The rotor actually used is the one which gives the higher IC value ... (link).Finding the fast rotor using isomorphsDeavours & Kruh offers an alternative using isomorphs: The previous method (based on the IC) to find the rotor in position V uses statistics. A faster method is based on isomorphs. For example, if we assume that the cryptogram begins with "CONFIDENTIAL", we can verify this hypothesis by try each rotor in turn and for each, check if the decipherment gives a simple isomorphic substitution of the probable word. Find the medium rotor (in position I)In their book, Deavours & Kruh outline their method for finding the rotor in position I and its starting position when the wiring of rotors I and V are known (link).Cryptanalysis from the cryptogram aloneObjectives: find at least the wiring of the rotor in position V, decipher the messages, and at best, reconstruct the machine, i.e. find the wiring of all the rotors. The Deavours & Kruh methodDeavours & Kruh presents a complex method based on the fact that every 26 letters, only the fast rotor advances. Concretely their method tries to amalgamate distributions of shifted lines, thanks to a Chi2. Finally, if the fast rotor wiring is found, decryption of encrypted messages seems possible although very complex.Friedman's methodIn his secret report, the key stages of which are described (link). Friedman manages to find the wiring of the rotors and the plain text of 10 messages ( all 10 messages made about 3000 characters). Friedman claims that his statistical method works from 2000 characters. Note: Friedman knows the input and output permutations (Keyboard and Lampboard), as well as the external key of the 10 messages. On the other hand he ignores the wiring of the rotors. Finding plain text from simple substitutionsAs soon as we know the wiring of the rotor in position V (fast rotor), it is possible to start trying to decipher cryptograms. Indeed if we eliminate the action of the Lampboard and the rotor V, the problem comes down to deciphering simple substitutions... but limited to only 26 letters! It's a real feat if you can do it. It is simpler to first reconstruct the wiring of the rotor in position I, but to do so, you need to know a few plain text lines!
Messages in-depthDeavours & Kruh affirm: "... With the Hebern machine even 10 to 15 messages, whose individual lengths may not be more than 50 or so letters, can be solved and the rotor wirings reconstructed to some degree if the texts are identically keyed". I completely disagree with this statement. Through experience that the Challenges that I published gave me, you need at least 100 messages to find the solution. Friedman agrees with me in part by stating in his secret report (paragraph 86) that it takes more than 50 messages to have almost certainty to reconstruct the plain text messages and then be able to reconstruct the fast rotor (the V rotor). Game tree algorithmCarl M. Ellison, proposed in 1988 a method for attacking the Vth rotor by using a “Game tree algorithm”. The latter uses:
Note: In Carl Ellison's article on his solution to the 1924 Navy challenge, Carl only gives his solution for the fast rotor (the rotor in the V position):
U Z X D R Q C E L N H V A K J Y G T B P M O F I S W
I developed a signature program which allows me to identify a rotor independently of whether it has undergone a rotation or a twist effect. This program is described in my page rotor. Using this program, I compared Ellison's solution to Friedman's. The signatures are different. Conclusion, it seems that the solution published by Ellison is incorrect. C:\H1_TOOLS> python signature.py -R =UZXDRQCELNHVAKJYGTBPMOFISW -c -S Type : 1.3.22. Cycles : (D),(AUM),(BZWFQGCXILVOJNKHERTPYS), Signature: [1, 6, 1, 19, 13, 4, 9, 24, 14, 7] C:\H1_TOOLS> python signature.py -R =DPGTBZOHRYMSLAJIWCKUQFNVXE -a PI direct PI : DPGTBZOHRYMSLAJIWCKUQFNVXE Type : 1.4.7.14. Cycles : (H),(KMLS),(ADTUQWN),(BPIRCGOJYXVFZE), Signature: [1, 6, 24, 11, 16, 12, 7, 23, 14, 18] PI reverse PI : NERAZVCHPOSMKWGBUILDTXQYJF Type : 1.4.7.14. Cycles : (H),(KSLM),(ANWQUTD),(BEZFVXYJOGCRIP), Signature: [2, 17, 15, 3, 18, 7, 10, 21, 7, 16] Hill ClimbingTaking inspiration from Deavours & Kruh's approach to finding the rotor in position V (if we know the wiring of the rotors), I created a program using Hill Climbing approach to find the wiring of the rotor in position V from 1000 characters (link). MiscellaneousKnowledge (or not) of Lampboard permutationFriedman succeeds in his feat of deciphering the 10 messages of the Navy challenge because he knew the Lampboard permutation (RFS), which was identical on army machines and on navy machines. Friedman notes that if we put ourselves in real conditions, in short if we respect the principles of Kerckhoff (not quoted by Friedman), we can assume that the enemy knows the details of the machine: either because he bought it (for a commercial machine like this of Hebern), or because he captured it. Nevertheless, Friedman indicates that thanks to his first statistical method (which requires nearly 200,000 letters), the reconstruction of the Lampboard permutation is possible. Analysis in case REVERSE mode is usedFriedman, in his report concerning the analysis of the HCM (Hebern Cipher Machine), asks the question of the difficulty of deciphering messages encrypted by the machine configured in REVERSE mode (decryption mode). It does not deal with a complete example, but concludes with possibility of finding the solution but with a lot more data than in the case where the machine is configured in DIRECT mode. References
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