保留次序加密能夠讓許多查詢在加密資料庫上順利進行，例如範圍查詢。Popa等人首先提出一個達到理想安全性的保留次序加密方案，但是他們的新增成本非常高。Kerschbaum等人接著提出另一個達到理想安全性的保留次序加密方案，能夠有效降低新增資料時與伺服器溝通的成本，但是卻不適用在所有資料形式。本文則是利用平衡二元樹的概念進一步改良，在維持相同溝通成本的同時降低加密成本，並且適用在各種資料形式。
本文提出的保留次序加密方案除了將溝通成本維持在 O(n)，還可以把最差狀況下的加密成本從 O(n^3/log n) 降到 O(n^2)。在本文模擬中，處理有序資料的效能可以大幅提升 90% 以上，至於處理隨機資料的效能則是可以提升平均約11%。

Order-preserving encryption can help perform many kinds of queries such as range queries on encrypted databases. Popa et al. presented the first order-preserving encryption scheme that achieved ideal security, but their insertion cost is very high. Kerschbaum et al. presented another ideal-secure order-preserving encryption scheme, which can effectively reduce the communication cost when inserting ciphertexts into the server. However, their scheme is not applicable to many kinds of data sets.
In this thesis, we proposed a novel order-preserving encryption scheme. Not only can our proposed scheme maintain the communication cost at O(n), but it can also reduce the encryption cost from O(n^3/log⁡n) to O(n^2 ) in the worst case. Simulation shows that the performance of inserting ordered data can be significantly improved at least by 90%, and the performance of inserting random data can be improved by about
11% on average.

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