Lecture 1: Introduction: Computation and Algebra

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Lecture 2: Background

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Lecture 3: GCD algorithm and Chinese Remainder Theorem

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Lecture 4: Fast polynomial multiplication

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Lecture 5: Fast polynomial multiplication (contd.)

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Lecture 6: Fast integer multiplication and division

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Lecture 7: Fast integer arithmetic and matrix multiplication

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Lecture 8: Matrix Multiplication Tensor.

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Polynomial factoring over finite fields: Irreducibility testing

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Equi-degree factorization and idea of Berlekamp's algorithm

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Lecture 11: Berlekamp's algorithm as a reduction method

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Lecture 12: Factoring over finite fields: Cantor-Zassenhaus algorithm

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Lecture 13: Reed Solomon Error Correcting Codes

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Lecture 14: List Decoding

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Lecture 15: Bivariate Factorization - Hensel Lifting

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Lecture 16: Bivariate polynomial factoring (continued)

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Lecture 17: Multivariate Polynomial Factorization

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Lecture 18: Multivariate Factoring - Hilbert's Irreducibility Theorem

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Lecture 19: Multivariate factoring (continued)

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Lecture 20: Analysis of LLL algorithm.

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Lecture 21: Analysis of LLL algorithm (continued)

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Lecture 22: Analysis of LLL-reduced basis algorithm and Introduction to NTRU cryptosystem

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Lecture 23: NTRU cryptosystem (continued) and Introduction to Primality testing

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Lecture 24: Randomized Primality testing: Solovay-Strassen and Miller-Rabin tests

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Lecture 25: Deterministic primality test (AKS) and RSA cryptosystem

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Lecture 26: Integer factoring: Smooth numbers and Pollard's rho method

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Lecture 27: Pollard's p-1, Fermat, Morrison-Brillhart, Quadratic and Number field sieve methods

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