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Nonetheless, I have been thinking about Chaocipher at odd moments, and am becoming more convinced that the method is akin to Terry Ritter's Dynamic Substitution (http://www.ciphersbyritter.com/GLOSSARY.HTM#DynamicSubstitutionCombiner). I recently read through my entire set of Cryptologia issues, both to rejuvenate the neurons, but with an eye towards Chaocipher-related ideas. While doing it I chanced upon Ritter's article (see also http://www.ciphersbyritter.com/index.html#DynSubTech for the original article as published in Cryptologia). It is actually related to the hypothetical system I proposed in TCCH Progress Report #2 (http://www.mountainvistasoft.com/chaocipher/chaocipher-002.htm).

Ritter's patented idea is that the substitution table(s) can be dynamically changed after each enciphered letter. He recommends permuting the substitution alphabet by swapping the last-enciphered letter with another one. In this way, a sequence of two identical pt letters will result in non-identical ct letters, just what we see in Chaocipher.

I was thinking specifically about the characteristic that pt/ct identities not repeating for a minimum of nine steps. Supposing the following:

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• A system of two disks, one for keying, the other for substituting (e.g., Jeff Hill's C98A)
  
• The keying disk has 26 removable/detachable tabs around its circumference, allowing the operator to permute the letters at any time
  
• The operator uses a key letter to set up the substitution disk
  
• The operator performs the substitution
  
• The operator advances the keying disk one position
  
• After enciphering one letter, the operator removes the key tab just used (which has shifted one position) and swaps it with another tab at least nine places ahead (by 'ahead' I mean that it would take nine position shifts for that key letter to be used again). Because we're swapping with the last key tab which has already shifted one position, we will never swap a just-swapped key letter back as the next key letter.
  
• [Open question: what is the method to determine the swapping distance? This is the crux, and I believe it is related to the plaintext and/or ciphertext letter.]
  
• As time goes on, the keying alphabet will become well-mixed. The keying sequence would thus be truly aperiodic, supporting Byrne's claim that it would never, ever repeat.
  

I'm aware that no one intimates permuting the keying disk, but no one rules it out, either. This could explain why Friedman found it error prone: if the shift is off by one, the keying sequence slowly (!) propagates the error.

BTW, I believe the substitution disk is _not_ being permuted because I have a hunch we would not get the pt/ct identity phenomenon.

The more I think about it, the more I lean towards such a system. It is the only type of system that could explain how 100 encipherments of the same ALLGOOD sentence can result in non-identical, non-isomorphic forms.

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After some thought and experimentation I've reluctantly come to the conclusion that Ritter's system is too good at scrambling to be able to produce the incidence wave that is such a strong feature of Chaocipher.

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• Chaocipher is duplicated by a Markov Model
  
• The stepping vector of (1, 1, 2, 4) is the correct one
  
• The absence of intervals of 7 and 8 is not significant; the fact that they did not occur is a statistical 'fluke'