Computational Number Theory and Algebra

Lecturer - Prof. Nitin Saxena

1. Preliminaries and Notations

2. Euclid's algorithm and Chinese Remainder Thoerem

3. Fast polynomial multiplication

4. Fast Integer multiplication

5. Fast Integer Division

6. Matrix Multiplication

7. Polynomial factoring over finite fields - Berlakamp's algorithm

8. PFFF - Resultant. Berlekamp as a reduction method

9. PFFF - Cantor-Zassenhaus algorithm

10. PFFF - Coding Theory

11. PFFF - Bivariate polynomials

12. Blackbox multivariate factoring

13. Integral polynomial factoring

14. Primality testing (Randomized)

15. Primality testing (Deterministic) and RSA

16. Integer factoring