if you want the users of the program to know the output, but you want to keep the input a secret, you could use functional encryption (another special case of i

if you want the users of the program to know the output, but you want to keep the input a secret, you could use functional encryption (another special case of iO.) users can compute a function of the input without being able to decrypt the input or learn anything else about it. if you want the output to be encrypted too (even potentially with a different key), you can use vanilla FHE.