Beijing Institute of Mathematical Sciences and Applications

This course provides a comprehensive introduction to cryptography, balancing theoretical foundations with practical applications. The full course is divided into three parts: Part I - Symmetric-key Cryptography, Part II - Public-Key Cryptography, Part III - Protocols. In this semester, we focus on Part I - Symmetric-key Cryptography. We examine how two parties, Alice and Bob, can securely exchange information when they share a secret key unknown to the adversary. Core topics include data confidentiality, data integrity, and authenticated encryption. Students will study the design principles and security models of symmetric primitives, formal adversarial definitions (e.g., IND-CPA), and constructions that achieve provable security. Emphasis is placed on both rigorous theory and practical deployment, including widely used standards such as ChaCha, AES, HMAC, and GCM.
By the end of this semester, students will acquire a solid understanding of the principles and practice of symmetric cryptography, providing the foundation for subsequent study of public-key cryptography and advanced cryptographic protocols.