Introduction to Cryptographic Definitions

Cryptographic definitions are often abstract and complex, making them challenging for beginners to understand and apply.

This concise textbook/resource provides a structured introduction to cryptographic definitions, explaining the syntax definitions and security definitions of cryptographic primitives. It builds foundational knowledge by covering essential mathematical concepts and formal definitions in cryptology. Through a carefully designed learning curve, readers will grasp key elements, why they are defined this way, and how new definitions are developed. The book's presentation enables readers to validate and propose cryptographic definitions, offering a step-by-step guide to understanding them.

Topics and features:

- Covers all essential components of cryptographic definitions from sets and functions, making the subject accessible to beginners

- Introduces intermediate concepts to smooth the transition from basic principles to formal definitions

- Equips readers with the skills to validate and propose cryptographic definitions, linking theory with research

- Minimizes unnecessary complexity while retaining depth, thereby ensuring a smooth learning experience

Advanced undergraduate students, security engineers, and professionals interested in the formal foundations of cryptographic definitions will find the work an invaluable guide. The text is also an ideal reference for graduate students and early-stage researchers in cryptology and computer security.

Fuchun Guo received his Ph.D. degree in Computer Science from the University of Wollongong, Australia. He is an Associate Professor at the School of Computing and Information Technology at the University of Wollongong. He has been recognized as an ARC DECRA Fellow and an ARC Future Fellow by the Australian Research Council (ARC) for his significant contributions to cryptography. His main research interests include security proofs and research philosophy in modern cryptography. His work has been widely published, with peer-reviewed research papers appearing in international conferences and journals such as CRYPTO, EUROCRYPT, and ASIACRYPT, as well as two books: Introduction to Security Reduction (Springer) and Cryptologic Research History of Digital Signatures: From 1976 to 2020 (in Chinese)

Willy Susilo received his Ph.D. degree in Computer Science from University of Wollongong, Australia. He is a Distinguished Professor and the Head of School of Computing and Information Technology and the director of Institute of Cybersecurity and Cryptology (iC2) at the University of Wollongong. Recently, he was awarded an Australian Laureate Fellowship due to his contribution in cloud computing security. He was previously awarded a prestigious ARC Future Fellow by the Australian Research Council (ARC) and the Researcher of the Year award in 2016 by the University of Wollongong. He is a Fellow of IEEE, Australian Computer Society (ACS), IET and AAAI. His main research interests include cybersecurity, cryptography and information security.

Khoa Nguyen received his Ph.D. degree in Cryptography from Nanyang Technological University, Singapore, in 2014. He is a Senior Lecturer at the Institute of Cybersecurity and Cryptology at the University of Wollongong, Australia. Previously, he held prestigious positions including Presidential Postdoctoral Fellow and Senior Research Fellow at Nanyang Technological University. His contributions to cryptography have been recognized through awards such as the Singapore International Graduate Award and his selection as an Invited Participant at the Second Commonwealth Science Conference in 2017. His main research interests include cryptography, cybersecurity, and information security. Nguyen is an emerging leader in the cryptography research community, having served as Program Committee Co-Chair for ProvSec 2020 and ACISP 2022, Area Chair for ASIACRYPT 2023, and Workshop Chair for AsiaCCS 2025.

Xiaofeng Chen received his B.S. and M.S. degrees in Mathematics from Northwest University, China, in 1998 and 2000, respectively, and his Ph.D. degree in Cryptography from Xidian University in 2003. He is currently a HUASHAN Leading Professor at Xidian University. His research interests include applied cryptography, cloud computing security, and AI security. He serves on the editorial boards of several prestigious journals, including IEEE Transactions on Dependable and Secure Computing andthe International Journal of Foundations of Computer Science. He has also served as a program or general chair or program committee member for over 30 international conferences. He is a Fellow of IEEE and AAIA.

Zhen Zhao received her Ph.D. degree in Cryptography from Xidian University, China. She is currently an Associate Professor at the School of Cyber Engineering, Xidian University. Her research focuses on public-key cryptography, with an emphasis on security proofs, digital signatures, and encryption schemes. She has led and participated in several national research projects on public-key encryption techniques. She actively serves as a program committee member for numerous international conferences and contributes to the advancement of cryptographic research through her publications and projects.