Let's say I have a PIC and an EEPROM memory IC. I store sensitive data in the EEPROM. If I want to encrypt the data what is a good encryption algorithm? It should be executed by the PIC but that does have time for that. So I want to store ~100 bytes and the encryption shouldn't take longer than ~5s on 40MHz.
Microchip provides ready made encryption library. Typically AES is the most commonly used and available, and I see no reason to use anything else.
Due to export restrictions, you will need to contact them directly to obtain the source code.