This book provides a comprehensive overview of the development history and research achievements in provable security, divided into five chapters. Chapter 1 introduces some mathematical knowledge and basic tools used in provable security. Chapter 2 discusses the definition of semantic security in public key cryptographic systems. Chapter 3 presents several commonly used semantic secure public key cryptosystems. Chapter 4 delves into identity-based cryptographic systems, while Chapter 5 covers attribute-based cryptographic systems. The book offers novel insights by not only introducing the foundational theories and practical algorithms of provable security but also including the latest research findings in cryptographic provable security. It aims to help readers understand the most recent directions in this field through studying the book. This book can serve as a textbook for undergraduate and graduate students in relevant majors at higher education institutions, as well as a reference for communication engineers and computer network engineers.