Foundations of Cryptography Ville Junnila, Arto Lepist¨ o
[email protected],
[email protected] Department of Mathematics and Statistics University of Turku
2017
Ville Junnila, Arto Lepist¨ o
[email protected],
[email protected]
About the course
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Objectives To provide the mathematical background for the cryptography courses Contents Basic number theory: divisibility, congruences, Chinese remainder theorem, quadratic residues etc. Basic abstract algebra: groups, rings, fields etc. Basics of complexity theory: what problems are algorithmically easy or difficult to solve, probability algorithms Warning The course is not applicable for students majoring in mathematics (or statistics.)
Ville Junnila, Arto Lepist¨ o
[email protected],
[email protected]
About the course
2 of 7
Lectures Lectures September 5 – October 18 (2h × 14 = 28h) On Tuesdays at 10-12 in the lecture hall Arc3 (Arcanum) On Wednesdays at 10-12 in the lecture hall M3 (Quantum)
Ville Junnila, Arto Lepist¨ o
[email protected],
[email protected]
About the course
3 of 7
Exercises Exercises on Fridays from September 15 to October 20. In total, 6 exercise lessons (6 × 2h = 12h) There are two groups on Fridays at 8–10 and 10–12 (M4, Quantum). Choose your favourite group in the electronic registration. One of the groups may be cancelled if there are not enough students. Exercise sets will be available in the exercise lessons and webpages of the course at https://www.utu.fi/fi/yksikot/sci/yksikot/ mattil/opiskelu/kurssit/Sivut/ Foundations of cryptography.aspx Solutions to the exercise problems will not be available online.
Ville Junnila, Arto Lepist¨ o
[email protected],
[email protected]
About the course
4 of 7
Exercises (continued) In the exercise lessons, there is a list available for marking down the solved problems. According to these markings, for each problem, a student is chosen to present the solution in the blackboard. You can mark an exercise solved if you think it is correct and you are ready to present it in the blackboard. If you are not able to attend to an exercise lesson (for a good reason), you may give in your exercises in written form before the first group begins. Otherwise, you do not need to give in your solutions in written.
Ville Junnila, Arto Lepist¨ o
[email protected],
[email protected]
About the course
5 of 7
Exam In order to pass the course and attend an exam, one has to solve at least 25% of the problems (achieving class C). Solving 45% (class B) of the problems will give 1 extra point to the exam and solving 70% (Class A) will give 2 extra points. There are 4 problems in the exam and the maximum points for each problem is 8. Hence, the maximum number of points for the exam is 32.
Ville Junnila, Arto Lepist¨ o
[email protected],
[email protected]
About the course
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Course material The main material used in the course are the lecture notes Foundations of Cryptography by Tommi Meskanen (2012) which are sold by the student association Delta located in the first floor of Quantum building. Buy these as soon as possible. For extra material, I will suggest any books on elementary number theory and abstract algebra. In the webpages of the course, there are a couple of freely available online resources listed. Although they might use different notation and they cover lots of material out of scope of the course, they may be of help. However, one should be able to pass the course with the lecture notes and active participation in the lectures and exercise lessons. Exercise sets, lecture slides, news (regarding the course) and other stuff will be published in the webpages of the course. Ville Junnila, Arto Lepist¨ o
[email protected],
[email protected]
About the course
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