Boneh 在 2004 年提出的具有關鍵字搜索之公開金鑰加密是一個能在公開金鑰加密機制中對加密資料進行搜尋的突破性方法。在這個架構中，資料發送方可以從文檔中提取特定關鍵字來生成可搜索的密文並上傳到伺服器中；而資料接收者可以使用持有的私鑰生成對應的陷門在存放著加密文檔的伺服器當中根據關鍵字進行搜索。

近期，Jiang 基於具有關鍵字搜索之公開金鑰加密機制提出了一種改進的方案，稱為具有授權關鍵字搜索之公鑰加密機制，在他們的機制中允許獲得授權的使用者為特定的關鍵字集合製作陷門，即便這些使用者沒有辦法取得私鑰。然而，在此機制中有關授權的執行不夠靈活，只能仰賴系統當中唯一一個權威機構替所有使用者執行，這個權威機構無法將自己授權的權力委託給已獲得授權的使用者代為執行授權的處理。考量到實際的企業場景中並不適合具有這種限制的機制。

為了解決上述問題，本論文提出了一種新的密碼機制，稱為具有階層式授權關鍵字搜索之公鑰加密機制，與Jiang提出的機制相比，此論文提出的機制中允許獲得授權的使用者能夠進一步階層式地委派授權工作的執行，替未經授權的使用者製作陷門。

此論文根據提出的密碼機制定義了能夠支援一次多個關鍵字搜尋的系統模型，並根據實際情況會面臨到攻擊訂定安全需求。最後，我們採用對偶向量空間技術實際建構了一個可證明安全性的架構，來表明此論文所提出的密碼機制能夠安全地適用在有階層式授權需求的場景中順利運作而不被破解。

Public key encryption with keyword search , which was introduced by Boneh et al. at Eurocrypt'04, is a breakthrough approach to searching encrypted data under a public key setting. Recently, Jiang et al. proposed an improved PEKS scheme called public key encryption with authorized keyword search , which allows authorized users to generate trapdoors for specific sets of keywords even if they do not have access to the private key. Unfortunately, authorized users cannot delegate their own power to other unauthorized users because the authorization in PEAKS is not flexible enough; therefore, this scheme is not suitable for enterprise scenarios in general. In this work, we introduce a novel cryptographic primitive called public key encryption with hierarchical authorized keyword search to solve the above problem. Compared with PEAKS, the proposed primitive allows authorized users to further hierarchically delegate their power to generate trapdoors for unauthorized users. We formally define the system model of PEHAKS under a multi-keyword setting and design the desired security requirements to withstand attacks in a real scenario. Furthermore, we propose a provably secure scheme using the dual pairing vector spaces technique, and show that the scheme is secure under the hardness of the 𝑛-extended decisional Diffie-Hellman assumption. Therefore, the proposed scheme can work securely in scenarios that require hierarchical authorization. To the best of the authors' knowledge, no PEKS variant schemes have discussed for this property.

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