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This message has been encoded by a monoalphabetic function $f(p)=p+b~ \pmod{26}: APHUO~ EGEHP~ PEXOV~ FKEUH~ CKVUE~ CHKVE~ APHUO,$ where we digitize the alphabet by letting $A = 00, B = 01, . . . , Z = 25.$

I want to find the original message. For this purpose, I tried to identify $b$ by finding the most occurring letter in the ciphertext which is E, so E=E+b gives us b=0 and encoding is $f(p)=p$ and decoding function is $f^{-1} (p)= p$. I can not find the original message with my decoding function. Can you please tell me where is my mistake?

amWhy
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Nil
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  • Obviously $E$ does not correspond to $E$. So $b\neq 0$ – Stéphane Jaouen Mar 31 '24 at 17:37
  • The left hand side E is the most letter in ciphertext and its corresponding digit is 4, right? – Nil Mar 31 '24 at 17:40
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    What you’re describing sounds like a shift cipher. I just brute forced all the possible shifts and got gibberish for all of them. Am I misreading your explanation? – Isaac Cheng Mar 31 '24 at 17:42
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    The most common letter in all English is E, but that doesn't mean it is the most common letter in the unencoded message. The message is a very small sample of all of English. – Thomas Andrews Mar 31 '24 at 17:45
  • Finding the most common letter in a cyphered English message by first assuming E is the most common letter in the message is a "heuristic" method, a place to start when brute forcing a question like this. Obviously, if the message is in English, $f(p)=p$ is not the encoding. – Thomas Andrews Mar 31 '24 at 17:48
  • @SiongThyeGoh yes, exactly, but I can not understand the solution, where are lower case letters in the given ciphertext? – Nil Mar 31 '24 at 17:58
  • I've tried $f(p)=p+b$ and $f(p)=p-b$ and $f(p)=pb$, it is all gibberish – Masd Mar 31 '24 at 17:59
  • @IsaacCheng This is shift cipher – Nil Mar 31 '24 at 18:01
  • You said up front it was $f(p)=p+b\bmod 26.$ We are assuming that it was of this form. If you don't know that, as indicated by you trying $f(p)=bp\bmod26,$ then change the question. – Thomas Andrews Mar 31 '24 at 18:15

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