John knows that computational overheads are a concern for cryptographic systems. What can he do to limit the computational needs of his solution?

Elliptic curve encryption schemes allow the use of a shorter key for the same strength that an RSA key would require, reducing the computational overhead required to encrypt and decrypt data. That doesn’t mean you should use a short key; instead, you must select a key length that matches your requirements for resistance to brute force and other attacks. Hashing is nonreversible and is not a form of encryption.