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