Actually, CryptDB does (or at least did originally) use homomorphic encryption (HE) for evaluating SQL arithmetic expressions. While the earliest suggestions f

Actually, CryptDB does (or at least did originally) use homomorphic encryption (HE) for evaluating SQL arithmetic expressions. While the earliest suggestions for HE were terribly slow, CryptDB found one that was practical. If memory serves, there have since been HE improvements claimed by IBM and/or Google. But as michwill states (and CryptDB acknowledges), their approach either leaks information or precludes classes of expressions. For example, their order-preserving encryption could be susceptible to a brute-force attack via 'a > b' ... '(a+1) > b' ... '(a+2) > b'