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So if Beaufort was encrypted with two keys, say k1 and k2, then
C_i= (k2_i – (k1_i – [text_i]))%26 = ((k2_i – k1_i) + [text_i])%26 which is by definition using the Vigenère encryption
So the decryption would just be the single Vigenère key (k2 – k1)%26 ?
I haven’t studied dihedral groups yet, but I do look forward to doing some reading on them!