Principle and Practice of Computer Algorithms (Summer 2012)/Computational Number Theory
Director: Ziqing Xiang
Members:
- Zhipeng Chen
- Shunning Jiang
- Qinglin Li
- Siliang Shen
- Kai Sun
- Kuan Yang
This course will cover these things.
- Basic elementary number theory.
- Primer of algebraic number theory.
- Primer of analytic number theory.
- Primality test.
- Prime generating.
- Integer factorization.
- Discrete logarithm.
Goal: Factorize an integer about 200bits using whatever you want.
- July 9: Difference. Perfect number. Dirichlet convolution.
- July 11: Modular arithmetic. Congruence Equation. Primitive root.
- July 16: Primitive root. Divisor function. Sieve of Eratosthenes. Euler product. Quadratic residue. Miller-Rabin primality test.
- July 18: Finitely-generated abelian group. Dirichlet character. Dirichlet L-series. Dirichlet's theorem.
- July 23: The p-adic number. Quadratic sieve. Number field sieve.
- July 25: Riemann hypothesis. General number field sieve.
- TODO