The book Modern Cryptography Volume 2 by Zhiyong Zheng, Kun Tian, and Fengxia Liu offers a comprehensive exploration of post-quantum cryptography with a focus on theoretical foundations and computational complexity. Below is a summary of its key topics and contributions:
Key Focus Areas:
- Post-Quantum Cryptography:
- The book addresses the forefront of post-quantum cryptographic research, emphasizing theoretical underpinnings to complement practical algorithm implementation.
- Lattice-Based Cryptography:
- Explores lattice ciphers with a particular focus on the computational complexity theory, including Ajtai’s reduction principle, which connects lattice problems to cryptographic security.
- Learning with Errors (LWE):
- Chapters 3, 4, and 6 delve into the Learning with Errors (LWE) distribution, its associated ciphers, and its application to homomorphic encryption.
- Discusses ambiguities in definitions and algorithms when employing random analysis tools, addressing these with rigorous mathematical frameworks.
- Mathematical Rigor:
- One of the book’s distinguishing features is its use of probability distributions for rigorous mathematical definitions and demonstrations, refining imprecise or unclear concepts into a robust theoretical system.
- Advanced Lattice Theories:
- Chapters 5 and 7 extend and refine theories of:
- Cyclic lattices
- Ideal lattices
- Generalized NTRU cryptography
- These concepts are critical for advancing cryptographic techniques in a post-quantum landscape.
- Chapters 5 and 7 extend and refine theories of:
Audience:
- Designed for graduate students in mathematics and cryptography, serving as a professional academic resource.
- Acts as a reference guide for researchers and practitioners in cryptography, focusing on the theoretical aspects of post-quantum cryptographic systems.
Significance:
- Fills a gap in the cryptography literature by providing robust theoretical proofs for post-quantum encryption and decryption schemes.
- Supports classroom teaching and research dissemination with a mathematically rigorous approach to cryptographic theories.
This book is an essential resource for those seeking to understand and contribute to the theoretical development of post-quantum cryptography, bridging the gap between practical applications and foundational theory.