COMPUTATIONAL NUMBER THEORY (2/1 Credits)

Learning Outcomes:

On successful completion of this course, students will be able to: solve the problems related to the concept of divisibility and prime number and its implementation using SAGE software; solve the problems related to the concept of congruence theoretically and practically in SAGE software; explain the fundamental principles and application of Public-key Cryptography and its computation using SAGE software; solve the problem of quadratic residue using the Law of Quadratic Reciprocity and its implementation using SAGE software; explain the concepts of continued fraction and its computation using SAGE software.

Topics:

1. Prime Numbers;
2. The Ring of Integers Modulo n;
3. Public-Key Cryptography;
4. Quadratic Reciprocity;
5. Continued Fractions;
6. Elliptic Curves.