Haskell RSA encryption

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for an assignment I need to write two function, one to RSA encrypt and one to decrypt. These functions take the key pair and modulo as parameters.

rsaencrypt :: (Integer, Integer) -> Integer -> Integer
rsaencrypt (e, m) x = x^e `mod` m

rsadecrypt :: (Integer, Integer) -> Integer -> Integer
rsadecrypt (d, m) x = x^d `mod` m

Let's suppose we have the key pair (5, 29) with a modulo of 91. if we want to encrypt the number 75 we get cyphertext 17, if we decrypt 17 we get the 75 back. All good so far. But when i try a different number, lets say 97. We get cyphertext 41, if we decrypt 41 we get 6. Why does my function only work on certain numbers?

rsa encryption haskell
1 Answers

Looking at the definition of rsadecrypt:

rsadecrypt (d, m) x = x^d `mod` m

It should be clear that all outputs will be between 0 and m-1 (inclusive). Since decryption definitely sits in that range, you cannot create an encryption for any message outside that range that will exactly round-trip.

...and, to connect the final two dots, 97 is outside the range of 0 to 91-1, so it cannot be correctly encrypted (for this definition of "correct").

user_7916040
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