Secure Ordered Bucketization

This study examines the ordered bucketization (OB) as a cryptographic object. In OB, plaintextspace is divided into $p$ disjoint buckets, numbered from $1$ to $p$, based on the order of the ranges that they cover. OB is quite useful in that a range query can be performed over encrypted data without the need to decrypt by attaching a bucket number to each ciphertext. Unfortunately, no research has been carried out on the security of OB in a cryptographic sense. This paper defines an encryption scheme with OB (EOB) and suggests a new security model for EOB, IND-OCPA-P, which assumes an adversary has reasonable power. Previous constructions proposed for efficient range queries were not secure in this model. Finally, an OB construction, in which the EOB implementation is secure on the IND-OCPA-P model, is proposed. In the proposed OB, $p$ - $1$ points are selected on the uniform distribution in the plaintext-space and the plaintext-space is divided based on the selected points. A bucket number is assigned to each divided range in ascending range order. With regard to the efficiency of a range query, the proposed OB guarantees reasonably good efficiency on range queries by showing that the distribution of a bucket size is not skewed.