Abstract—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 descrypt 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, < Final Year Projects > 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.
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