### Course Information

** Course Slot: S** (Tue 4:00-5:30 pm, Fri 2:30-4:00 pm),

** Classroom: ** A-117

**List of topics:**
Euclid's algorithm, Bezout's lemma, prime numbers, fundamental theorem of arithmetic, congruences,
Fermat's little theorem, the rings Z

_{n} and Z

_{p}, Lagrange's theorem, roots of unity,
quadratic residues, quadratic equations in Z

_{p}, finite fields, applications of finite fields,
univariate polynomial factorization in Z

_{p}, linear equations over Z, lattices,
Hermite Normal Form, the LLL algorithm, polynomial factorization over Z, primality testing,
integer factoring, the RSA cryptosystem, binary quadratic forms.

** References: **
1. Victor Shoup:

A computational introduction to number theory and algebra
2. Neal Koblitz: A course in number theory and cryptography

3. Crandall and Pomerance: Prime numbers - A computational perspective

Other recommended books on Number Theory:

4. The Higher Arithmetic by Henry Davenport,
5. A Concise Introduction to the Theory of Numbers by Alan Baker,
6. An Introduction to the Theory of Numbers by Hardy and Wright
7. A course in number theory by H.E. Rose