Course Introduction

• Prerequisite：Algebra
• Recommended for： graduate students
• Introduction：

In this course, students will learn the mathematical tools used in cryptography which are mainly coming from algebra and algorithmic number theory. Equipped with these tools, classical public key cryptosystems such as the Diffie-Hellman system, RSA, Elliptic Curve Method, etc. will be investigated. Morever, deterministic and probabilistic methods for generating primes and pseudoprimes will be discussed. The course is suitable for upper-level undergraduates and graduate students in mathematics or other fields with an interest in number theory and its applications.

• Syllabus：

1. Some Topics in Algebra and Algorithmic Number Theory
2. Some Topics in Complexity Theory
3. Substitution and Block Ciphers
4. Public-Key Cryptosystems
5. Primality and Prime Number Generation
6. Factoring
7. Elliptic Curves and Applications

• Reference：

1. Johannes A. Buchmann, Introduction to Cryptography, 2n Edition, Springer-Verlag, 2001.
2. Neal Koblitz, A Course in Number Theory and Cryptography, 2nd Edition, Springer-Verlag, 1994.