BOPE: Boundary Order-Preserving Encryption Scheme in Relational Database System

Recently, researchers are being more interested in performing operations directly on the encrypted database with the help of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O$ </tex-math></inline-formula> rder- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> reserving <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E$ </tex-math></inline-formula> ncryption (OPE) scheme. This mechanism enables executing many types of queries efficiently, such as range query and comparison, since it can preserve the relative order of underlying plaintext on ciphertexts. However, traditional OPE schemes cannot achieve ideal security against IND-OCPA ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IND</i> istinguishability under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O$ </tex-math></inline-formula> rdered <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> hosen- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> laintext <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> ttack) in a linear length of static encoding. Popa’s mutable scheme (namely, mOPE) is an effective solution to perform the range query in the database environment. In this paper, we propose a novel scheme, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$B$ </tex-math></inline-formula> oundary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O$ </tex-math></inline-formula> rder- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> reserving <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E$ </tex-math></inline-formula> ncryption (BOPE), to achieve high performance under ideal security. BOPE comprises two algorithms. One is a searching algorithm in which we propose a data structure, the boundary tree, to optimize the algorithm by cutting the scope of each iteration and reducing the rounds of interaction. The second algorithm is an updating algorithm for stale encoding, which determines whether to update the lookup table according to the type of each query, in order to avoid the time cost of redundant updates. We implemented and evaluated BOPE on a practical environment where we have achieved a performance increase of more than 10% from mOPE.