This course covers divisibility; congruences and residues, including the Chinese Remainder Theorem; primes and their distribution; the Euler-phi function; quadratic reciprocity; public-key cryptography, particularly the RSA cryptosystem; elliptic curves and their group structure.
- Understand the importance of prime numbers.
- Analyze the algebraic and arithmetical structure of a group of finite residues of a given prime number.
- Solve some diophantine equations.
- Generate a public-key cryptosystem.
- Find rational points in an elliptic curve.