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Home Page Hebern's machines The 5 rotors machine home page
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IntroductionIf we know the wiring of the rotors, it is possible to find the right rotor (the fast Rotor or Rotor in position V). When the rotor wirings are known, even a single message of several hundred characters can be solved fairly easily. Making use of Index of coincidence (IC) statistic, we can determine both the identity and starting position of the fast rotor and position of the right ratchet wheel. To determine the identify and starting position of the fast rotor, V, we test the rotors one by one. The procedure
An exampleRemove influence from Lampboard permutationWe start by removing the influence of the RFS wiring which corresponds at the first permutation carried out in decryption mode. Then, we cut the cryptogram into slices of 26 characters. For each slice, we calculate the IC and take the average. If the chosen rotor is the right one, each slice is the result of a simple substitution. The largest IC value gives us the starting position of the rotor in position V. If it is the rotor which has actually been used in position V, this IC value is clearly higher than the maximum value obtained for the other rotors. For the demonstration, we take the message given as an example from the book of Deavours & Kruh, page 49. - Cryptogram: C:\H5_TOOLS> more MSGS\kruh_page_49.cry GEEDN TKVLM TBTFY CYEDV WYZKQ IEQFO GVVUS OJOXP BUHUF RLDLK SDLHY BYUVB TTMZX TIQQO FVTVG PKITT EDXZF HNLMG IBFOV DBHVO PCIRM VRTYI AXOTW OVVVB JCNNT EEBCG JGJUZ DJOWY XXWCQ CKTWL CJSAY NLGIN WHKCG QSEAF CJAGJ NGWFQ WRITY YMVQZ KFICG EXWKQ VQAHU HKZBM OAXIY TMKAP CJHWH WGIPM QKVGR GLNPI- Cryptogram, but without the influence of RFS permutation: C:\H5_TOOLS> python striplamp.py TYOEUMXDFJQVKWBNSHCILRZAGP ^ MSGS\kruh_page_49.cry > MSGS\kruh_page_49.stripped C:\H5_TOOLS> python groupe.py < MSGS/kruh_page_49.stripped YDDHP AMLUF AOAIB SBDHL NBWMK TDKIC YLLEQ CJCGZ OEREI VUHUM QHURB OBELO AAFWG ATKKC ILALY ZMTAA DHGWI RPUFY TOICL HORLC ZSTVF LVABT XGCAN CLLLO JSPPA DDOSY JYJEW HJCNB GGNSK SMANU SJQXB PUYTP NRMSY KQDXI SJXYJ PYNIK NVTAB BFLKW MITSY DGNMK LKXRE RMWOF CXGTB AFMXZ SJRNR NYTZF KMLYV YUPZT Cut the cryptogram into slices of 26 letters...We cut the cryptogram into slices of 26 letters and for each slice, calculate the IC and the final mean IC.
- Calculate IC for the five rotors. H5_TOOLS> python search_rotor.py 1 < MSGS/kruh_page_49.stripped IC max: 0.0471, key: M H5_TOOLS> python search_rotor.py 1 < MSGS/kruh_page_49.stripped IC max: 0.0406, key: V ... In short: First rotor : IC max: 0.0471, key: M First rotor (mirror): IC max: 0.0422, key: P Second rotor : IC max: 0.0406, key: V Second rotor (mirror): IC max: 0.0431, key: F Third rotor : IC max: 0.0449, key: R Third rotor (mirror): IC max: 0.0397, key: D Fourth rotor : IC max: 0.0431, key: Q Fourth rotor (mirror): IC max: 0.0406, key: O Fith rotor : IC max: 0.0514, key: L Fith rotor (mirror): IC max: 0.0418, key: N We can deduce that it is the 5th rotor which was used in the normal direction.
For the rotor considered, we calculate the IC for each positionIt seems that the starting position of the 5th rotor is position L. Let's give the IC values for each position: C:\H5_TOOLS> python search_rotor.py 5 < MSGS\kruh_page_49.stripped ... Starting position Average IC A: 0.0348 B: 0.0332 C: 0.0292 D: 0.0382 E: 0.0311 F: 0.0320 G: 0.0345 H: 0.0305 I: 0.0363 J: 0.0332 K: 0.0360 L: 0.0514 M: 0.0338 N: 0.0351 O: 0.0434 P: 0.0369 Q: 0.0326 R: 0.0369 S: 0.0342 T: 0.0286 U: 0.0409 V: 0.0314 W: 0.0305 X: 0.0372 Y: 0.0332 Z: 0.0388 ... At the correct starting position of the 5th rotor, the 26 consecutive letters will belong to one or two monoalphabetic distributions. This is why the maximum IC value is important but significantly lower than 0.07. If we find the initial position of the right ratchet wheel, we will have only slices of 26 letters belonging to a single distribution monoalphabetic. The example below searches for this position. Note: The following is from the previous program, but at the end.
Starting position Average IC
0 0.0564
1 0.0545
2 0.0566
3 0.0569
4 0.0582
5 0.0582
6 0.0609
7 0.0669
8 0.0615
9 0.0641
10 0.0642
11 0.0666
12 0.0685
13 0.0637
14 0.0593
15 0.0581
16 0.0558
17 0.0536
18 0.0517
19 0.0513
20 0.0521
21 0.0514
22 0.0530
23 0.0533
24 0.0547
25 0.0554
---> ic max: 0.0685, start of ratchet wheel: A
Note: thanks to my programs, I obtained the previous results. They are similar to those obtained by Deavours & Kruh but different. On the other hand, the conclusions are the same: use of 5th rotor at L position and Ratchet right wheel at A position. References
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