| Area of Mathematics: | Algebra and Geometry (EAG) | ||
| Semester: | 6ο | ||
| Course ID: | 62203 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | |||
| Instructors: |
Description
- Elementary number theory over the integers, key elements from ring theory, quotient ring, homomorphisms, ideals.
- The law of quadratic reciprocity, quadratic residues, Gauss sums.
- Field extensions, elements of Galois theory.
- The Frobenius operator, N-th roots of unity.
- Irreducible polynomials over finite fields, the cyclotomic reciprocity law, additive polynomials.
- Simple cryptosystems, Vigenere, Hill, permutation ciphers, stream ciphers. Cryptanalysis.
- Public key cryptosystems, RSA, baby step-giant step.
- Elliptic curves, point order, Mordel’s theorem.
- Elliptic cryptosystems, factorization with elliptic curves.
- Construction of elliptic curves of given order.
Bibliography
- N. Koblitz. A Course in Number Theory and Cryptography, 2nd edition. Springer, 1994.
