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Home Page Hebern's machines The 5 rotors machine home page
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IntroductionI created a program based on the Hill Climbing algorithm to find the rotor wiring in position V. As we have observed, this step is essential because it allows to start deciphering the messages and reconstructing the wiring of the other rotors. AlgorithmThe algorithm is classic (cf. HC for Hebern 1-rotor). On the other hand, we use a single fitness function based on the IC (Index of Coincidence). In addition, I was inspired by the Deavours & Kruh approach to find the rotor (the wiring being known) which is in position V. Indeed, I break down the cryptogram (after removing the Lampboard action) into slices of 26 letters and I calculate the IC for each slice. The fitness function returns the average of the ICs. Example, we know the external key- Start of the plain text message (it is approximately 1000 characters long). C:\H5_TOOLS> more tmp\clair.pln THEWASHINGTONNAVALCONFERENCEWASADISARMAMENTCONFERENCECALLED BYTHEUNITEDSTATESANDHELDINWASHINGTONDCCOMMAFROMNOVEMBER TWENTIETHONENIVETWOONECOMMATOFEBRUARYSIXTHONENIVETWOTWOZDOTZITWAS ... - Create the cryptogram (we use an offset of 5 [RAW=S]) C:\H5_TOOLS> python hebern5_tui.py -E ZZAAAZS ^ < tmp\clair.pln > tmp\clair_DS.cry - We remove the action of the Lampboard (RFS)
C:\H5_TOOLS> python striplamp.py TYOEUMXDFJQVKWBNSHCILRZAGP ^
tmp\clair_DS.cry > tmp\clair_DS.stripped
- We are looking for the rotor wiring in position V.
C:\H5_TOOLS> python hc_h5.py usage: -h Help -c crypto The cryptogram -t tries Number of tries, default: 15 -o offset Offset, 0 by default notes: 1. The cryptogram must be 'stripped', i.e. without the action of the lampboard 2. Offset is relied to RAW (position of right ratchel wheel) ALPHA[ (13 + (N - offset)) % N ], N == 26 C:\HC_TOOLS> python hc_h5.py -c tmp\clair_DS.stripped -o 5 -t 50 0 0.05756708407871199 HTSNXYUJICVOPMLEAGFQWKRBDZ 1 0.05590339892665474 CHGQVIKLWDJEMSZPONTRXBUYFA 2 0.05783542039355991 VUDNXKGIBLRZHPWAJYFCOSETQM ... 49 0.05477638640429336 IVHYPOXAKSGMRZDECJUNBWFLTQ Key: ZRDUEKMPBXVGJLSWANFIOHYTQC Score: 0.06544090056285176 IDJQSRDUCWIKCCSHSTVKCXHLHEJHUCDCPGDCLTCTHENJREXAEAYZAZXIIAUJK GRAWYQGAUNGXTEJIKGAEZGMKHIJAMKVTWKGFFWNNODQVNAVEHNBHQPIHAPKHP MVADMJADQESSMDOSUUZQSKDPFRZFCWZSACQXFXZMFALQALQIOQAIZALVMPHLQ CPXUQHCXM...- We check that the result corresponds to a sequence of mono-substitutions isomorphic to the plain text. m 012345678901234567890----5----0----5----0----5- c' IDJQSRDUCWIKCCSHSTVKCXHLHEJHUCDCPGDCLTCTHENJREX plain THEWASHINGTONNAVALCONFERENCEWASADISARMAMENTCONF e J h h h h t I I n a S S S c c c c n C CC C e e e o K K r h D D p We don't know the external keyIf we do not know the external key, it is always possible to try all possible offsets (from 0 to 25). Here is a test based on the previous example (offset, IC):
- We take a cryptogram of approximately 1000 characters:
0 0.0577 6 0.0672 12 0.0558 18 0.0564
1 0.0581 7 0.0596 13 0.0550 19 0.0565
2 0.0584 8 0.0568 14 0.0566 20 0.0569
3 0.0589 9 0.0566 15 0.0555 21 0.0569
4 0.0629 10 0.0556 16 0.0552 22 0.0565
5 0.0672 11 0.0558 17 0.0550 23 0.0567
24 0.0567 25 0.0560
- Here, we take a cryptogram of around 2000 characters:
0 0.0510 3 0.0611 6 0.0631 9 0.0507 1 0.0532 4 0.0624 7 0.0606 ... 2 0.0520 5 0.0654 8 0.0530 In conclusion, offset 5 corresponds to the correct configuration although this is more obvious with a cryptogram long enough. Relationship between my solution and the authentic wiringMy solution to the Army V rotor wiring seems correct (I can get simple substitutions). Question: Does my rotor have the same wiring as the army machine? 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 the genuine wiring to mine. The signatures are equal. Conclusion, my solution is correct.
C:\H1_TOOLS> python signature.py ^ -R =FQTGXANWCJOIVZPHYBDRKUSLEM -a PI direct PI : FQTGXANWCJOIVZPHYBDRKUSLEM Type : 1.2.10.13. Cycles : (J),(AF),(BQYEXLICTR),(DGNZMVUKOPHWS), Signature: [1, 13, 18, 9, 23, 18, 18, 7, 18, 10] PI reverse PI : FRISYADPLJUXZGKOBTWCVMHEQN Type : 1.2.10.13. Cycles : (J),(AF),(BRTCILXEYQ),(DSWHPOKUVMZNG), Signature: [1, 2, 11, 21, 23, 10, 2, 1, 6, 3] C:\H1_TOOLS> python signature.py ^ -R =ZRDUEKMPBXVGJLSWANFIOHYTQC -c -S Type : 1.10.15. Cycles : (E),(BRNLGMJXTI),(AZCDUOSFKVHPWYQ), Signature: [1, 2, 11, 21, 23, 10, 2, 1, 6, 3]Conclusion : My solution is correct but I obtain the wiring in the reverse mode (also called decipherment mode). How do I get from genuine wiring to mine? All I had to do was inspect the cipher tables for each rotor. Here is the answer : Here is the PI table which identifies the genuine rotor V in reverse mode with the key O. As we can see, it corresponds to the my rotor shifted by 11 positions to the right.
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