To encrypt messages I propose the formula C = (3P + 1) mod 27, where P is the "plain text" (the original letter value) and C is the "cipher text" (the encrypted letter value). For example, if P = 2 (the letter 'c'), C would be 7 (the letter 'h') since (3 (2) + 1) mod 27 = 7. There is a problem though: When I send the message 'c' to my friend, encrypted as 'h', they don't know whether the original message was 'c' or another letter that also encrypts to 'h'. What other letter (s) would also encrypt to 'h' besides 'c' in this system?

Question

Computers and Technology

Makayla Day

17 June, 16:13

To encrypt messages I propose the formula C = (3P + 1) mod 27, where P is the "plain text" (the original letter value) and C is the "cipher text" (the encrypted letter value). For example, if P = 2 (the letter 'c'), C would be 7 (the letter 'h') since (3 (2) + 1) mod 27 = 7. There is a problem though: When I send the message 'c' to my friend, encrypted as 'h', they don't know whether the original message was 'c' or another letter that also encrypts to 'h'. What other letter (s) would also encrypt to 'h' besides 'c' in this system?

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Answers (1)

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Skylar Hammond · Answer 1

C = (3P+1) % 27

so when P will be max 26, when P is 26 the (3P+1) = 79. And 79/27 = 2 so let's give name n = 2.

Now doing reverse process

We get,

P = ((27*n) + C-1) / 3

Where n can be 0,1,2

So substituting value of n one by one and the C=7 (corresponding index of h)

For n = 0, we get P=2, corresponding char is 'c'

For n=1, we get P=11, corresponding char is 'l'

For n=2, we get P = 20, corresponding cahr is 'u'.

So beside 'c', the system will generate 'h' for 'l' and 'u' also.