Partially Homomorphic Encryption

This monograph provides a comprehensive examination of known partially homomorphic encryption algorithms, exploring their formulation, arithmetic, efficiency, and security. It is valuable for researchers and graduate students in Computer Science, Engineering, and Mathematics engaged with Cryptology.

Format: Paperback / softback
Length: 146 pages
Publication date: 01 October 2022
Publisher: Springer Nature Switzerland AG

This monograph presents a comprehensive exploration of partially homomorphic encryption (PHE) functions, employing a unified notation. After providing the necessary mathematical foundations, the authors delve into a systematic examination of several well-known algorithms, including Rivest-Shamir-Adleman, Goldwasser-Micali, ElGamal, Benaloh, Naccache-Stern, Okamoto-Uchiyama, Paillier, Damgaard-Jurik, Boneh-Goh-Nissim, and Sander-Young-Yung. Over the past few years, researchers have proposed and studied various partially and fully homomorphic encryption algorithms, addressing concerns such as their formulation, arithmetic, efficiency, and security. While formidable efficiency barriers persist, a diverse range of algorithms has emerged that can be applied to diverse private computation problems in healthcare, finance, and national security. By studying these functions, we can gain insights into the challenges that lie ahead. This book holds immense value for researchers and graduate students in the fields of Computer Science, Engineering, and Mathematics who are actively engaged in the study of Cryptology.

Introduction:
Partially homomorphic encryption (PHE) is a cryptographic technique that enables secure computation on encrypted data. It allows users to perform operations on encrypted data without revealing its actual contents. PHE has gained significant attention in recent years due to its potential applications in various fields, such as healthcare, finance, and national security.
Mathematical Background:
Before delving into the algorithms, it is essential to understand the mathematical foundations of PHE. This monograph provides a comprehensive introduction to the necessary mathematical concepts, including linear algebra, group theory, and number theory. The authors explain these concepts in a clear and concise manner, making it accessible to readers with a background in computer science or mathematics.
Algorithms:
The book then presents a systematic examination of several well-known PHE algorithms. Each algorithm is discussed in detail, including its formulation, arithmetic, efficiency, and security considerations. The authors provide examples and illustrations to help readers understand the practical applications of these algorithms.
Efficiency Barriers:
One of the major challenges in PHE is the efficiency barrier. Homomorphic encryption is computationally expensive, as it requires performing computations on encrypted data. However, the authors highlight the progress that has been made in improving the efficiency of PHE algorithms. They discuss various techniques, such as code-based encryption, multi-party computation, and optimized implementations, that have been developed to enhance the performance of PHE.
Applications:
The book also explores the potential applications of PHE in various fields. It discusses how PHE can be used to protect patient data in healthcare, perform secure financial transactions, and enable secure communication in national security. The authors provide real-world examples and case studies to demonstrate the practical benefits of PHE.
Conclusion:
In conclusion, this monograph provides a comprehensive and up-to-date introduction to partially homomorphic encryption functions. It covers the necessary mathematical background, presents a systematic examination of several well-known algorithms, and discusses the challenges and opportunities associated with PHE. The book is valuable for researchers and graduate students in Computer Science, Engineering, and Mathematics who are interested in the study of Cryptology.

Weight: 250g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030876319
Edition number: 1st ed. 2021