Computational Number Theory and Algebra B302611ZXW
| URI | m2://res/B302611ZXW |
|---|---|
| Kind | course |
| Creators | Nitin Saxena (instructor) |
| Date | 2020-08-31 |
| Scope | in |
| Ids | course 05pjsgx75:111104138 |
Expressions
e1: edition
| Language | en |
|---|---|
| Date | 2020-08-31 |
- m1: page, IIT Kanpur (record). nptel 111104138
- m2: page, 2020-08-31 (record). nptel 111104138
Contents
- part 1: Week 1: Outline. Notation. Background.
- session 1: Lecture 1: Introduction: Computation and Algebra
- session 2: Lecture 2: Background
- part 2: Week 2: GCD. Chinese Remaindering. Fast polynomial multiplication.
- session 3: Lecture 3: GCD algorithm and Chinese Remainder Theorem
- session 4: Lecture 4: Fast polynomial multiplication
- part 3: Week 3: Fast integer multiplication. Fast integer division. Fast gcd.
- session 5: Lecture 5: Fast polynomial multiplication (contd.)
- session 6: Lecture 6: Fast integer multiplication and division
- part 4: Week 4: Fast matrix multiplication. Tensor rank.
- session 7: Lecture 7: Fast integer arithmetic and matrix multiplication
- session 8: Lecture 8: Matrix Multiplication Tensor.
- part 5: Week 5: Factorization over finite fields.
- session 9: Lecture 9: Polynomial factoring over finite fields: Irreducibility testing
- session 10: Lecture 10: Equi-degree factorization and idea of Berlekamp's algorithm
- part 6: Week 6: Berlekamp, Cantor-Zassenhaus factoring algorithms.
- session 11: Lecture 11: Berlekamp's algorithm as a reduction method
- session 12: Lecture 12: Factoring over finite fields: Cantor-Zassenhaus algorithm
- part 7: Week 7
- session 13: Lecture 5: Fast polynomial multiplication (contd.)
- session 14: Lecture 6: Fast integer multiplication and division
- session 15: Lecture 13: Reed Solomon Error Correcting Codes
- session 16: Lecture 14: List Decoding
- session 17: Lecture 15: Bivariate Factorization - Hensel Lifting
- part 8: Week 8: Kaltofen's blackbox multivariate factoring.
- session 18: Lecture 16: Bivariate polynomial factoring (continued)
- session 19: Lecture 17: Multivariate Polynomial Factorization
- session 20: Lecture 18: Multivariate Factoring - Hilbert's Irreducibility Theorem
- part 9: Week 9: Integral polynomial factoring. LLL algo. Shortest vector in lattice.
- session 21: Lecture 19: Multivariate factoring (continued)
- session 22: Lecture 20: Analysis of LLL algorithm.
- session 23: Lecture 21: Analysis of LLL algorithm (continued)
- part 10: Week 10: Lattice-based cryptography.
- session 24: Lecture 22: Analysis of LLL-reduced basis algorithm and Introduction to NTRU cryptosystem
- session 25: Lecture 23: NTRU cryptosystem (continued) and Introduction to Primality testing
- part 11: Week 11: Primality testing. RSA cryptosystem. Diffie-Hellman. Discrete Log.
- session 26: Lecture 24: Randomized Primality testing: Solovay-Strassen and Miller-Rabin tests
- session 27: Lecture 25: Deterministic primality test (AKS) and RSA cryptosystem
- part 12: Week 12: Integer factoring. Pollard, Fermat, Morrison-Brillhart, Quadratic sieve methods.
- session 28: Lecture 26: Integer factoring: Smooth numbers and Pollard's rho method
- session 29: Lecture 27: Pollard's p-1, Fermat, Morrison-Brillhart, Quadratic and Number field sieve methods
Catalogue records
- nptel: 111104138 (manifestation)
- nptel_video: 111104138 (manifestation)