A silly RSA implementation

A while ago I had a homework to implement RSA and each letter is raised to the e-th power where e is the public key, modulo N=pq. Decryption is by raise each integer in cipher text C to the d-th power where d is the secret key. The problem? Since we have only 256 ascii characters and if each char is mapped to a distinct integer, then you do NOT need e or d or whatever key to decrypt, you only need a mapping from char to integer.

One remedy approach is to group adjacent char into blocks so you will need a mapping of 256^10 = 2^80 if you group letters in block of 10, and this is much harder to keep a mapping.