Advances to Homomorphic and Searchable Encryption

This book presents the current state of the literature on the fields of homomorphic and searchable encryption, from both theoretical and practical points of view. Homomorphic and searchable encryption are still relatively novel and rapidly evolving areas and face practical constraints in the contexts of large-scale cloud computing and big data.

Both encryption methods can be quantum-resistant if they use the right mathematical techniques. In fact, many fully homomorphic encryption schemes already use quantum-resistant techniques, such as lattices or characteristics of polynomials - which is what motivated the authors to present them in detail.

On the one hand, the book highlights the characteristics of each type of encryption, including methods, security elements, security requirements, and the main types of attacks that can occur. On the other, it includes practical cases and addresses aspects like performance, limitations, etc.

As cloud computing and big data already represent the future in terms of storing, managing, analyzing, and processing data, these processes need to be made as secure as possible, and homomorphic and searchable encryption hold huge potential to secure both the data involved and the processes through which it passes.

This book is intended for graduates, professionals and researchers alike. Homomorphic and searchable encryption involve advanced mathematical techniques; accordingly, readers should have a basic background in number theory, abstract algebra, lattice theory, and polynomial algebra.

本書從理論和實踐的角度介紹了同態加密和可搜索加密領域的最新研究成果。同態加密和可搜索加密仍然是相對新穎且快速發展的領域，在大規模雲計算和大數據的背景下面臨實際限制。

如果使用正確的數學技術，這兩種加密方法都可以抵抗量子攻擊。事實上，許多完全同態加密方案已經使用了抵抗量子攻擊的技術，例如格和多項式的特性，這也是作者詳細介紹它們的原因。

一方面，本書突出了每種加密類型的特點，包括方法、安全元素、安全要求以及可能發生的主要攻擊類型。另一方面，它還包括實際案例，並討論性能、限制等方面的問題。

由於雲計算和大數據已經代表了存儲、管理、分析和處理數據的未來，這些過程需要盡可能地保護安全，同態加密和可搜索加密具有巨大的潛力，可以保護涉及的數據以及其通過的過程。

本書適用於研究生、專業人士和研究人員。同態加密和可搜索加密涉及高級數學技術，因此讀者應具備基本的數論、抽象代數、格理論和多項式代數背景知識。

Stefania Loredana Nita, Ph.D., is Senior Lecturer at the Faculty of Information Systems and Cybernetic Security of "Ferdinand I" Military Technical Academy, Bucharest, Romania, where she teaches courses on Formal Languages and Translators, Management and Development of Database Applications, and Data Structures and Algorithms. Also, she is Software Developer at the Institute for Computers, Bucharest, Romania. She received her Ph.D. degree in 2021, and her Ph.D. thesis is on advanced cryptographic schemes using searchable encryption and homomorphic encryption. She has worked for more than two years as Assistant Lecturer at the University of Bucharest where she taught courses on subjects such as Advanced Programming Techniques, Simulation Methods, and Operating Systems. She has authored and co-authored more than 32 work papers published in international conferences proceedings and journals and 7 books on functional programming and cryptography. She holds an M.Sc. in Software Engineering and two B.Sc. in Computer Science and Mathematics.
Marius Iulian Mihailescu, Ph.D., is Associate Professor at the Faculty of Engineering and Informatics of "Spiru Haret" University, Bucharest, Romania, and Software IT Project Manager at the Institute for Computers, Bucharest, Romania. He is also CEO of Dapyx Solution Ltd., a company based in Bucharest, Romania, where he is involved in information security and cryptography-related research projects. He authored and co-authored more than 40 articles in conference proceedings and journals, and 8 books. For more than six years he has served as Lecturer at well-known national and international universities (the University of Bucharest, "Titu Maiorescu" University of Bucharest, and Kadir Has University in Istanbul, Turkey). He served for three years as IT Officer at Royal Caribbean Cruises Ltd. where he dealt with IT infrastructure, data security, and satellite communications systems. He received his Ph.D. degree in 2014, and his thesis was on applied cryptography over biometrics data.

Stefania Loredana Nita博士是羅馬尼亞布加勒斯特'Ferdinand I'軍事技術學院資訊系統和網絡安全學院的高級講師，教授形式語言和翻譯器、數據庫應用管理和開發以及數據結構和算法等課程。同時，她還是布加勒斯特計算機研究所的軟件開發人員。她於2021年獲得博士學位，其博士論文研究了使用可搜索加密和同態加密的先進加密方案。她曾在布加勒斯特大學擔任助理講師超過兩年，教授高級編程技術、模擬方法和操作系統等課程。她撰寫和合著了32篇以上發表在國際會議論文集和期刊上的論文，以及7本關於函數式編程和密碼學的書籍。她擁有軟件工程碩士學位和計算機科學和數學兩個學士學位。

Marius Iulian Mihailescu博士是羅馬尼亞布加勒斯特'Spiru Haret'大學工程與信息學院的副教授，也是布加勒斯特計算機研究所的軟件IT項目經理。他還是Dapyx Solution Ltd.的首席執行官，該公司位於羅馬尼亞布加勒斯特，從事與信息安全和密碼學相關的研究項目。他撰寫和合著了40篇以上發表在會議論文集和期刊上的文章，以及8本書籍。他在知名國內外大學（布加勒斯特大學、布加勒斯特'Titu Maiorescu'大學和土耳其伊斯坦布爾Kadir Has大學）擔任講師超過六年。他曾在皇家加勒比郵輪有限公司擔任三年的IT官員，負責IT基礎設施、數據安全和衛星通信系統。他於2014年獲得博士學位，其論文研究了應用於生物特徵數據的應用密碼學。