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 andbig 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.

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 SoftwareEngineering 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.

1. Introduction.- 2. Background and Preliminaries.- 3. Homomorphic Encryption.- 4. Searchable Encryption.