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I try to use the function $$C_i=E(M_{2i}, M_{2i+1}) = (M_{2i} + M_{2i+1})\bmod 26.$$ to encode English text.

For example,

Plaintext: The quick brown fox jumps over the lazy dog.
Regrouped Text: TH EQ UI CK BR OW NF OX JU MP SO VE RT HE LA ZY DO G. $$ T = 19, H = 7, (T + H) \bmod 26 = 26 \bmod 26 = 0 = A.\\ \cdots\\ (D + O) \bmod 26 = R. $$ Ciphertext: AUCMSKSLDBGZKLLXRG.

Then I'm trying to decode the cipher. Frequency analysis doesn't work, maybe Kasiski examination's variant works.

There might be many sentences that satisfy the English grammar and can be encoded as the cipher text. It's okay to get only some of them.

Alex-Github-Programmer
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    This cannot be reliably decoded because it loses information. For instance AA, BZ, CY, etc all encode to A, so when deciding A it's ambiguous what the corresponding plaintext is. – Gordon Davisson Feb 20 '22 at 19:00
  • @GordonDavisson I'm encoding English text, therefore the text must satisfy the English grammar. – Alex-Github-Programmer Feb 21 '22 at 10:46
  • This seems more like a (lossy) encoding method than a cipher, as the latter (usually) involve a key. Given each letter of ciphertext decodes to one of 26 digraphs, it seems plausible that one could use a model trained on natural languages to recover likely plaintexts. That is not really part of the field of cryptography though, rather you might want to check existing work in natural language processing. I can imagine that e.g. OCR techniques face related issues. – Morrolan Feb 21 '22 at 15:22

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