The Chaocipher and the Sliding Tile Equivalent

This cipher machine and it's resulting cipher, called the Chaocipher, was originally implemented by J. F. Byrne in 1918 and not cracked until 2010 when the blueprints were finally made public. His original model was made with tiles cut from cardboard and placed on wooden wheels. A complete description can be found here.

A primitive mechanical model of the Chaocipher device
Photo courtesy of National Cryptologic Museum

Here is the same cipher with the sliding tiles laid out in a flat row rather than a circle. The top row is the ciphertext alphabet and the bottom row is the plaintext.

The Chaocipher device implemented with sliding tiles

The cipher shuffles both alphabets by shifting and then moving a single tile from one location to another. Note the "race tracks" in the illustration which make it easier to move the tiles to their correct place in the alphabet row. Also notice the two index marks, one for each alphabet, which Byrne called the "zenith". Lacking the race tracks of the sliding tile model, Byrne also used another index mark he called "nadir" to show where to insert the two moved tiles into the alphabet row. Byrne also placed the two wheels side by side instead of concentricly. They were connected by gear-like teeth so that they would move together. Since the wheels will thus move in opposite directions, this requires that in the flat row version we arrange the ciphertext alphabet in the reverse order of the arrangement in Byrne's version.

In operation, whereas with the flat row we would look for the plaintext letter in the bottom row and then find the ciphertext letter in the row above it, in Byrne's version we would turn plaintext wheel until the desired plaintext letter touched the ciphertext wheel, at which time the ciphertext letter would be the tile where the two wheels touch. The net effect, however, is identical in every respect to the flat row version. (See also my discussion of sliding tile ciphers in general)

The sliding tile equivalent works like this: In the ciphertext alphabet take the tile to the right of the last used ciphertext letter and move it 12 slots to the right (or 12 slots clockwise if the rows are arranged in a circular track). With the plaintext alphabet, take the tile second to the right from the last plaintext letter used and move it to a slot 11 tiles to the right. Then shift the plaintext row one tile to the left. (Or we could say shift the ciphertext row one tile to the right since the net result is the same.)

Byrne's actual operating instructions of the Chaocipher device are considerably more complicated than that, but if you actually perform the operations described above and the operations described by Byrne you will see that the end result is identical, and that the same message will be encrypted the same way by both systems.

The fact that this sliding tile machine is equivalent to Byrne's wheel machine is best demonstrated by using the sliding tiles to decrypt one of Byrne's own messages, his "Exhibit One". Here are the first couple line of that ciphertext:

      CLYTZPNZKLDDQGFBOOTYSNEPUAGKIUNKNCRINRCVKJNHTOAFQPDPNCV
      LTVFICOTSSLWYYIHBICFUTHXNUVKGIMVEZYWSTHEPIEWXNNGFTOGHSR
    

We begin by setting the tiles up with the initial alphabets used by Byrne to encrypt that exhibit:

       CPEDQRSTIXYLMOZABFVGUHWJKN
      xayznbqdsefghlwikcmoprtuvj
    

Notice that I have shown the two alphabets offset from each other. This is so that the leftmost letter of each row corresponds to the letter under the index in the illustrations above.

As an aside, "james" on the The Crypto Forum has discovered how Byrne arrived at this starting alphabet using the keyword THINK. Read an account of his rather brilliant discovery here on the forum.

Now we begin the process of decrypting the exhibit. We see that the first ciphertext letter C is above the plaintext letter a, so a becomes the first letter of the plaintext:

      CLYTZPNZKLDDQGFBOOTYSNEPUAGKIUNKNCRINRCVKJNHTOAFQPDPNCV
      a
      
      LTVFICOTSSLWYYIHBICFUTHXNUVKGIMVEZYWSTHEPIEWXNNGFTOGHSR
    

Next we perform the first shuffling operation:

1. Slide the ciphertext row left to put c under the index.
2. Slide the P tile up and to the right, in the manner shown in the above illustrations, and into place after betwen the O and Z tiles, sliding E through O left to make room.
3. Slide the plaintext alphabet left to put a under the index. (x wraps around to the other end.)
4. Slide the n tile down and around and insert it between the i and k tiles, again sliding tiles to the left ot make room.

The resulting alphabet rows now look like this:

       CEDQRSTIXYLMOPZABFVGUHWJKN
      ayzbqdsefghlwinkcmoprtuvjx
    

The next ciphertext letter is L. We find it in the ciphertext row just above the plaintext l, so that is our next plaintext letter:

      CLYTZPNZKLDDQGFBOOTYSNEPUAGKIUNKNCRINRCVKJNHTOAFQPDPNCV
      al
      
      LTVFICOTSSLWYYIHBICFUTHXNUVKGIMVEZYWSTHEPIEWXNNGFTOGHSR
    

Repeating the shuffle as above, and cranking out the next few plaintext letters we get the following alphabet rows and their plaintext solutions:

      

      
       LOPZABFVGUHWJMKNCEDQRSTIXY
      lwikcmoprtuvjxnayzbqdsefgh    plaintext l for ciphertext Y (Note wrap-around)

       YOPZABFVGUHWJLMKNCEDQRSTIX
      lwicmoprtuvjxnkayzbqdsefgh    plaintext g for ciphertext T

       TXYOPZABFVGUHIWJLMKNCEDQRS
      ghlicmoprtuvjxwnkayzbqdsef    plaintext o for ciphertext Z

       ZBFVGUHIWJLMKANCEDQRSTXYOP
      opruvjxwnkayzbtqdsefghlicm    plaintext o for ciphertext P

       PBFVGUHIWJLMKZANCEDQRSTXYO
      oprvjxwnkayzbtuqdsefghlicm    plaintext d for ciphertext N

      CLY TZPNZKLDDQGFBOOTYSNEPUAGKIUNKNCRINRCVKJNHTOAFQPDPNCV
      all good
      
      LTVFICOTSSLWYYIHBICFUTHXNUVKGIMVEZYWSTHEPIEWXNNGFTOGHSR

    

And for further verification, a few more letters are decrypted. And so that you can follow along and verify the result, here are the alphabet rows after each:

       NEDQRSTXYOPBFCVGUHIWJLMKZA
      dseghlicmoprvjfxwnkayzbtuq   Z:q
      
       ZNEDQRSTXYOPBAFCVGUHIWJLMK
      qdsghlicmoprvjefxwnkayzbtu   K:q
      
       KNEDQRSTXYOPBZAFCVGUHIWJLM
      qdshlicmoprvjegfxwnkayzbtu   L:u
      
       LKNEDQRSTXYOPMBZAFCVGUHIWJ
      uqdhlicmoprvjesgfxwnkayzbt   D:i
      
       DRSTXYOPMBZAFQCVGUHIWJLKNE
      icmprvjesgfxwnokayzbtuqdhl   D:c
      
       DSTXYOPMBZAFQRCVGUHIWJLKNE
      cmpvjesgfxwnokrayzbtuqdhli   Q:k
      
       QCVGUHIWJLKNERDSTXYOPMBZAF
      krazbtuqdhlicmypvjesgfxwno   G:b
      
       GHIWJLKNERDSTUXYOPMBZAFQCV
      btudhlicmypvjeqsgfxwnokraz   F:r
      
       FCVGHIWJLKNERQDSTUXYOPMBZA
      raztudhlicmypvbjeqsgfxwnok   B:o
      
       BAFCVGHIWJLKNZERQDSTUXYOPM
      okrztudhlicmypavbjeqsgfxwn   O:w
      
       OMBAFCVGHIWJLPKNZERQDSTUXY
      wnorztudhlicmykpavbjeqsgfx   O:n
      
       OBAFCVGHIWJLPMKNZERQDSTUXY
      nortudhlicmykpzavbjeqsgfxw   T:f
      
       TXYOBAFCVGHIWUJLPMKNZERQDS
      fxwortudhlicmynkpzavbjeqsg   Y:o
      
       YBAFCVGHIWUJLOPMKNZERQDSTX
      ortdhlicmynkpzuavbjeqsgfxw   S:x
      
       SXYBAFCVGHIWUTJLOPMKNZERQD
      xwotdhlicmynkprzuavbjeqsgf   N:e
      
       NERQDSXYBAFCVZGHIWUTJLOPMK
      eqsfxwotdhlicmgynkprzuavbj   E:s
      
       EQDSXYBAFCVZGRHIWUTJLOPMKN
      sfxotdhlicmgynwkprzuavbjeq   P:j
      
       PKNEQDSXYBAFCMVZGRHIWUTJLO
      jeqfxotdhlicmgsynwkprzuavb   U:u
      
       UJLOPKNEQDSXYTBAFCMVZGRHIW
      uavjeqfxotdhlibcmgsynwkprz   A:m
      
       ACMVZGRHIWUJLFOPKNEQDSXYTB
      mgsnwkprzuavjeyqfxotdhlibc   G:p
      
       GHIWUJLFOPKNERQDSXYTBACMVZ
      przavjeyqfxotduhlibcmgsnwk   K:o
      
       KERQDSXYTBACMNVZGHIWUJLFOP
      otdhlibcmgsnwkuprzavjeyqfx   I:v
      
       IUJLFOPKERQDSWXYTBACMNVZGH
      vjeqfxotdhlibcymgsnwkuprza   U:e
      
       ULFOPKERQDSWXJYTBACMNVZGHI
      eqfotdhlibcymgxsnwkuprzavj   N:r
      
       NZGHIULFOPKERVQDSWXJYTBACM
      rzajeqfotdhlibvcymgxsnwkup   K:l
      
       KRVQDSWXJYTBAECMNZGHIULFOP
      libcymgxsnwkupvrzajeqfotdh   N:a
      
       NGHIULFOPKRVQZDSWXJYTBAECM
      ajefotdhlibcymqgxsnwkupvrz   C:z
      
       CNGHIULFOPKRVMQZDSWXJYTBAE
      zajfotdhlibcymeqgxsnwkupvr   R:y
      
       RMQZDSWXJYTBAVECNGHIULFOPK
      ymegxsnwkupvrzqajfotdhlibc   I:d
      
       ILFOPKRMQZDSWUXJYTBAVECNGH
      dhlbcymegxsnwkiupvrzqajfot   N:o
      
       NHILFOPKRMQZDGSWUXJYTBAVEC
      otdlbcymegxsnwhkiupvrzqajf   R:g
      
       RQZDGSWUXJYTBMAVECNHILFOPK
      gxswhkiupvrzqanjfotdlbcyme   C:t
      
       CHILFOPKRQZDGNSWUXJYTBMAVE
      tdlcymegxswhkibupvrzqanjfo   V:o
      
       VCHILFOPKRQZDEGNSWUXJYTBMA
      otdcymegxswhkilbupvrzqanjf   K:s
      
       KQZDEGNSWUXJYRTBMAVCHILFOP
      swhilbupvrzqankjfotdcymegx   J:a
      
       JRTBMAVCHILFOYPKQZDEGNSWUX
      ankfotdcymegxsjwhilbupvrzq   N:v
      
       NWUXJRTBMAVCHSILFOYPKQZDEG
      vrzankfotdcymeqgxsjwhilbup   H:e
      
       HILFOYPKQZDEGSNWUXJRTBMAVC
      eqgsjwhilbupvrxzankfotdcym   T:t
      
       TMAVCHILFOYPKBQZDEGSNWUXJR
      tdcmeqgsjwhilbyupvrxzankfo   O:h
      
       OPKBQZDEGSNWUYXJRTMAVCHILF
      hilyupvrxzankfbotdcmeqgsjw   A:e
      
       ACHILFOPKBQZDVEGSNWUYXJRTM
      eqgjwhilyupvrxszankfbotdcm   F:i
      
       FPKBQZDVEGSNWOUYXJRTMACHIL
      ilypvrxszankfbuotdcmeqgjwh   Q:r
      
       QDVEGSNWOUYXJZRTMACHILFPKB
      rxsankfbuotdcmzeqgjwhilypv  .. etc.
      
       PBQDVEGSNWOUYKXJZRTMACHILF
      pvrsankfbuotdcxmzeqgjwhily 
      
       DEGSNWOUYKXJZVRTMACHILFPBQ
      ankbuotdcxmzeqfgjwhilypvrs 
      
       PQDEGSNWOUYKXBJZVRTMACHILF
      rsakbuotdcxmzenqfgjwhilypv 
      
       NOUYKXBJZVRTMWACHILFPQDEGS
      tdcmzenqfgjwhixlypvrsakbuo 
      
       CILFPQDEGSNOUHYKXBJZVRTMWA
      ypvsakbuotdcmzrenqfgjwhixl 
      
       VTMWACILFPQDERGSNOUHYKXBJZ
      whilypvsakbuotxdcmzrenqfgj 
      
       LPQDERGSNOUHYFKXBJZVTMWACI
      akbotxdcmzrenqufgjwhilypvs 
      
       TWACILPQDERGSMNOUHYFKXBJZV
      lypsakbotxdcmzvrenqufgjwhi 
      
       VWACILPQDERGSTMNOUHYFKXBJZ
      lypakbotxdcmzvsrenqufgjwhi 
      
       FXBJZVWACILPQKDERGSTMNOUHY
      gjwilypakbotxdhcmzvsrenquf 
      
       IPQKDERGSTMNOLUHYFXBJZVWAC
      otxhcmzvsrenqudfgjwilypakb 
      
       CPQKDERGSTMNOILUHYFXBJZVWA
      otxcmzvsrenqudhfgjwilypakb 
      
       OLUHYFXBJZVWAICPQKDERGSTMN
      dhfjwilypakbotgxcmzvsrenqu 
      
       TNOLUHYFXBJZVMWAICPQKDERGS
      qudfjwilypakbohtgxcmzvsren 
      
       SNOLUHYFXBJZVTMWAICPQKDERG
      qudjwilypakbohftgxcmzvsren 
      
       SOLUHYFXBJZVTNMWAICPQKDERG
      udjilypakbohftwgxcmzvsrenq 
      
       LHYFXBJZVTNMWUAICPQKDERGSO
      ilyakbohftwgxcpmzvsrenqudj 
      
       WAICPQKDERGSOULHYFXBJZVTNM
      cpmvsrenqudjilzyakbohftwgx 
      
       YXBJZVTNMWAICFPQKDERGSOULH
      kboftwgxcpmvsrhenqudjilzya 
      
       YBJZVTNMWAICFXPQKDERGSOULH
      bofwgxcpmvsrhetnqudjilzyak 
      
       IFXPQKDERGSOUCLHYBJZVTNMWA
      rhenqudjilzyaktbofwgxcpmvs 
      
       HBJZVTNMWAIFXYPQKDERGSOUCL
      ofwxcpmvsrhenqgudjilzyaktb 
      
       BZVTNMWAIFXYPJQKDERGSOUCLH
      wxcmvsrhenqgudpjilzyaktbof 
      
       IXYPJQKDERGSOFUCLHBZVTNMWA
      nqgdpjilzyaktbuofwxcmvsrhe 
      
       CHBZVTNMWAIXYLPJQKDERGSOFU
      fwxmvsrhenqgdpcjilzyaktbuo 
      
       FCHBZVTNMWAIXUYLPJQKDERGSO
      ofwmvsrhenqgdpxcjilzyaktbu 
      
       ULPJQKDERGSOFYCHBZVTNMWAIX
      xcjlzyaktbuofwimvsrhenqgdp 
      
       TMWAIXULPJQKDNERGSOFYCHBZV
      enqdpxcjlzyaktgbuofwimvsrh 
      
       HZVTMWAIXULPJBQKDNERGSOFYC
      srhnqdpxcjlzyaektgbuofwimv 
      
       XLPJBQKDNERGSUOFYCHZVTMWAI
      jlzaektgbuofwiymvsrhnqdpxc 
      
       NRGSUOFYCHZVTEMWAIXLPJBQKD
      uofiymvsrhnqdpwxcjlzaektgb 
      
       UFYCHZVTEMWAIOXLPJBQKDNRGS
      mvshnqdpwxcjlzraektgbuofiy 
      
       VEMWAIOXLPJBQTKDNRGSUFYCHZ
      pwxjlzraektgbucofiymvshnqd 
      
       KNRGSUFYCHZVEDMWAIOXLPJBQT
      ofimvshnqdpwxjylzraektgbuc 
      
       GUFYCHZVEDMWASIOXLPJBQTKNR
      vshqdpwxjylzranektgbucofim 
      
       IXLPJBQTKNRGUOFYCHZVEDMWAS
      ektbucofimvshqgdpwxjylzran 
      
       MASIXLPJBQTKNWRGUOFYCHZVED
      ranktbucofimvsehqgdpwxjylz 
      
      CLY TZPN Z KLDDQ GFBOO TYSNE PUAG KIUN KNCR INR CV KJNH TOAFQ PDPNC V
      all good q quick brown foxes jump over lazy dog to save their party w
      
      LTV FICO T SSLWY YIHBI CFUTH XNUV KGIM VEZYWSTHEPIEWXNNGFTOGHSR
      all good q quick brown foxes jump over ...
    

And so on for as long as we care to continue. This demonstrates that the sliding tile machine produces results equivalent to those of the Choacipher machine.