Week 1:Outline. Notation. Background.
Week 2:GCD. Chinese remaindering. Fast polynomial multiplication.
Week 3: Fast integer multiplication. Fast integer division. Fast gcd.
Week 4:Fast matrix multiplication. Tensor rank.
Week 5:Factorization over finite fields.
Week 6:Berlekamp, Cantor-Zassenhaus factoring algorithms.
Week 7: Reed-Solomon code. List decoding. Bivariate polynomial factoring.
Week 8:Kaltofen's blackbox multivariate factoring.
Week 9:Integral polynomial factoring. LLL algo. Shortest vector in lattice.
Week 10:Lattice-based cryptography.
Week 11: Primality testing. RSA cryptosystem. Diffie-Hellman. Discrete Log.
Week 12:Integer factoring. Pollard, Fermat, Morrison-Brillhart, Quadratic sieve methods.
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