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jdege
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I'm not sure where you're seeing a polyalphabetic substitution. Looks to me like you have two monoalphabetic substitutions, one of letters to binary tetragraphs, and one of individual bits to individual letters. The result is a homophonic substitution.

The thing is - the output of the first stage is easily identified. If you have properly partitioned the second-stage bit assignments correctly, the result will have at most 26 unique values out of the 32 possible, and the values will match a normal frequency distribution. The index of coincidence will be that of plain text.

So, how hard is it to partition your bit assignments? Your sample ciphertext has 52 distinct letters. That means that there are 2^52 possible partitions. That's within the range of exhaustive search. But that overstates it. An almost-correct partition assignment will give a IC that's closer to that of plaintext than a not-quite-as-correct assignment. And that means that a hill-climber would be able to crack it very quickly. (Simple substitution ciphers have 26! keys, more than 80 billion more than your second-stage has, and hill-climbers routinely break them in minutes.)

When cryptography is outlawed, bayl bhgynjf jvyy unir cevinpl.
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