Haskell RSA encryption-CodePudding

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?

CodePudding user response：

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").