具常數密文之去中心化內積加密機制

Abstract

隨著近年來科技的興起，分散式的系統架構也越來越多人研究，例如:e 化政府系統。而去中心化架構是分散式系統的其中一種架構，也就是伺服器之間不需任何溝通就能達到分散式的效果，這種架構的優點在於當單點故障發生時，並不會使整個系統被其他攻擊者入侵，讓整個系統更具安全性。\n為了應用在這種去中心化架構上，因此，去中心化的加密機制已被深入地研究數年。不過，大部分都是對於去中心化屬性加密機制的研究，如:Lewko 和 Water [8] 在2011 年所提出的去中心化屬性加密機制。然而，對於去中心化內積加密機制的相關研究並沒有很多，僅有Michalevsky 和Joye [10] 在2018 年所發表的一篇而已。在此篇論文中，密文的長度會與權威機構的個數成正比的成長，這樣會增加系統儲存空間上的負擔。另外，由於此篇去中心化方式是每個權威機構負責將謂詞向量的每個分量產生解密金鑰的一部份，這也就意味著向量的長度必須與權威機構的個數相同，這對於實際的應用情境較不實用，因為在內積加密的機制中，接收者的屬性會被一起編碼成一個向量，而不是一個屬性編碼成一個向量的分量。\n為了解決上述問題，我們基於Attrapadung 等人[1] 在2010 年所發表的一個具常數密文的內積加密機制，提出了具常數密文大小的去中心化內積加密機制，此機制密文大小與權威機構個數和向量長度無關，除此之外，我們也實作了我們的機制與Michalevsky 和Joye 的機制，並對演算法做執行時間的比較，實驗結果顯示大部分的演算法，我們具有較佳的表現，最後，我們也提出相關的安全性證明，證明機制難以被破解。

With the rise of technology in recent years, more people are studying distributed system architecture, such as e-government system. The decentralized architecture is one of the architectures of the distributed system, that is, the decentralization can be achieved without any communication between the servers. The advantage of this architecture is that when a single point of failure occurs, it does not cause the system invaded by other attackers, making the entire system more secure.\nIn order to apply to this decentralized system, therefore, the decentralized encryption has been intensively studied for several years. Nevertheless, most of them are researches on decentralized attribute-based encryption, such as the\ndecentralized attribute-based encryption proposed by Lewko and Waters [8] in 2011. However, there is not much research on decentralized inner product encryption, only a work published by Michalevsky and Joye [10] in 2018. In their construction, the length of the ciphertext is proportional to the number of authorities, which will increase the burden on the system storage space. In addition, since the decentralization method in this work is that each authority is responsible for generating a part of private key for an element of the predicate vector. It means that the length of the vector must be the same as the number of authorities. This is impractical in reality. In the inner product encryption, the receiver’s attributes will be encoded together into a vector, rather than an attribute encoded into an element of a vector.\nIn order to solve the above problems, based on the inner product encryption achieving constant-size ciphertexts published by Attrapadung [1] in 2010, we proposed a decentralized inner product encryption with constant-size ciphertexts. The length of ciphertext of our work is independent of the number of authorities and the length of the vector. Besides, we implement our scheme and the scheme\nof Michalevsky and Joye, and compare the execution time of the algorithms. The experiment result shows that the most of our algorithms have better performance. Finally, we also present related security proof, which proves that our work is difficult to break.