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I have been told that one of the keys in an affine cipher is 33. The Mod is 37 - the set being the alphabet + numbers + space. So the affine function is

$ax + b$ $(mod$ $37)$ with $a$ and $b$ being the keys. I cannot figure out if $33$ is $a$ or $b$.

Is there a definitive way to figure that out? I thought there might be a relationship between $a$ or $b$ and the $mod$, but all I can recall is that $gcd(a,mod)=1$. This is satisfied by $33$ and $37$, but I do not confirm this to mean $a$ is $33$.

Any help is appreciated.

Rob Bor
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  • Do you also have some ciphertext or something related to this? In general both a = 33 and b = 33 seem possible. If you have some data to go along with this, then that should be very helpful. For example, the most frequent character should be the "space" character, and you could try the two cases: a = 33 or b = 33, and in both cases try to figure out the other unknown variable by looking at the value you think corresponds to "space". (PS. I don't think affine-varieties is an appropriate tag... varieties are some geometric objects.) – CJD Mar 16 '19 at 04:39
  • @CJD Yes I do have ciphertext, could you explain a little further what I could do with this? ALSO, using an online decryptor thing, I have found out that a = 17 and b = 33. Is there any way to work backwards to reach this conclusion? (PS. Oh, I have removed the tag. Thanks for letting me know) – Rob Bor Mar 16 '19 at 05:25
  • What I was thinking was: Case 1. Guess "space" is the most common character and that a = 33. Then solve for b. Check if that produces readable plaintext. Case 2. Guess "space" is the most common character and that b = 33. Then solve for a. Check if that produces readable plaintext. You could also try a similar strategy for "e" which should be the second most common character. – CJD Mar 16 '19 at 14:01

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