1. Complexity. Basics from group theory. Chinese remainder theorem.Public key cryptosystems with an emphasis on RSA.2. Modular quadratic equations, Rabin cryptosystem.3. Pseudoprimes and probabilistic prime number tests.4. Factoring algorithms by Fermat, Dixon, Pollard. Quadratic sieve.

1. Complexity. Basics from group theory. Chinese remainder theorem. Public key cryptosystems with an emphasis on RSA.2. Modular quadratic equations, Rabin cryptosystem.3. Probabilistic and deterministic prime number tests.4. Factoring algorithms by Fermat, Dixon, Pollard. Quadratic sieve, elliptic curve factorization.

A. Diophantine approximation and continued fractions.Public key cryptosystems, RSA and Merkle-Hellman. Continued fraction factoring method.B. Basics about lattices. Minkowski's results on shortest vectors. Reduction theory. LLL-algorithm.C. Applications of lattice theory: Diophantine approximation, knapsack problem,CVP, the theory of Coppersmith and applications to RSA.

Factoring algorithms by Fermat and related ones ( Lehman, Dixon, Morrison-Brillhart, quadratic sieve). Smooth numbers. Factoring with quadratic form representations. Ideal theory in number fields. Number field sieve. Applications to the discrete logarithm problem. (Deterministic primality tests.)