temario
Contents
The planned syllabus is the following
- Historical introduction.
Motivation and examples. Elementary group theory and number theory.
Finite fields. Simple encryption algorithms.
- Discrete logarithm problem.
Statement and examples. Basic attacks. Diffie-Hellman key exchange. The
ElGamal cryptosystem.
- The RSA cryptosystem.
Algorithm, examples and cautions. Primality tests and factorization
algorithms. Introduction to the number field sieve.
- Elliptic curve
cryptography.
Elliptic curves and group law. Elliptic curves and factorization. The
elliptic version of the discrete logarithm problem.
- Complementary topics.
Digital signatures. The algorithm DES. Knapsack cryptosystems. Lattices
and cryptography.
This syllabus, the scope, aims
and background are included in the
proposal
of the course.
It was written long time ago and may suffer some (non substantial)
changes.
This is the
presentation
of the course delivered the first day.
The
schedule of the lectures is Tuesday and Thursday from 5:30 pm to 7:00
pm. The classroom is 320 in the Math Department
"módulo
17" (formerly C-XV).
There is a
web
page
for general reference about master courses in the Math Department. This
is the
Moodle server at
Math Department.
examenes
Grading
You can consult your grades in the
Moodle server at
Math Department using your email address and the password of your computer account.
1) Home assignments: 40%.
2) Final exam or challenges:
40%.
3) Quizzes, in-class exercises,
participation: 20%
You have to get
at least 50% to pass the course.
Examples: Suppose that there are 5 assignments sheets and 8 challenges
along the course.
A student solving 4/5 of the exercises and one half of the challenges
gets 40*4/5+40*1/2=52 plus the grade coming from 3).
Another student solving one half of the exercises and zero challenges
accumulates 40*1/2+0=20 and (even with a high participation in class)
should pass a final exam.
In other words, the final examination is not mandatory. It is reserved
for students who did not get enough points from other sources.
