Optimal Average-Complexity Ideal-Security Order-Preserving Encryption

Order-preserving encryption enables performing many classes of queries -- including range queries -- on encrypted databases. Popa et al. recently presented an ideal-secure order-preserving encryption (or encoding) scheme, but their cost of insertions (encryption) is very high. In this paper we present an also ideal-secure, but significantly more efficient order-preserving encryption scheme. Our scheme is inspired by Reed's referenced work on the average height of random binary search trees. We show that our scheme improves the average communication complexity from O(n log n) to O(n) under uniform distribution. Our scheme also integrates efficiently with adjustable encryption as used in CryptDB. In our experiments for database inserts we achieve a performance increase of up to 81% in LANs and 95% in WANs.