Let A=1, B=2,... Z=26, etc. Consider a message, a sequence of letters, as terms in a continued fraction. Form an infinite continued fraction by repeating the message. Convert this repeating continued fraction into an expression for quadratic irrational (quadratic surd): (a+sqrt(b))/c.
As a cipher (one step of a cipher) I suspect this achieves good diffusion. Investigate how small changes in the input message affect output.
The continued fraction can have an initial prefix before the repeating section. Not sure what to do with it. Maybe chaff to confuse cryptanalysis.
Put the message in the prefix, then append infinite ones repeating, making it irrational, essentially appending the golden ratio. This is probably a bad idea.
Instead assigning letters to numbers in order, one could use letter frequency. This will result in smaller output.
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