Math 474/574-Cryptography
Section 002, Fall 2008.

Course notes | Exams | Grading | Homework | Old Tests

Professor: Martyn Dixon
Office: 312B Gordon Palmer
Telephone: 348-5154
e-mail: mdixon at gp dot as dot ua dot edu
Office Hours: Monday-Thursday 12:30-2:00 pm, or by appointment.
Lecture: Monday, Wednesday, Friday, 9:00-9:50 am, 154 GP

COURSE PREREQUISITES: MA 307, MA 470/570 or consent of the department.

COURSE DESCRIPTION: Fundamental aspects of cryptography are covered. Topics include: Finite Fields and Quadratic Residues, Public Key Cryptography, Primality and Factoring, Elliptic Curve Cryptography.

COURSE OBJECTIVES: This course is an introduction to a rapidly growing area of cryptography, an application of algebra, especially number theory. The material covers the basic technique of the cryptography theory including public key cryptography. Then, some fundamental techniques of primality and factoring of natural numbers including the elliptic curve method is discussed. It is expected that the student knows the elementary properties of groups, rings and vector spaces. The theory will be supplemented by numerous examples. There may also be some use of computer software.

Text: A Course in Number Theory and Cryptography. 2nd ed. by Neal Koblitz, published by Springer Verlag.

CHAPTERS COVERED:
The following material will be covered.
Chapter I: Topics in Elementary Number Theory
Chapter II: Finite Fields and Quadratic Residues
Chapter III: Cryptography
Chapter IV: Public Key
Chapter V: Primality and Factoring
Chapter VI: Elliptic Curves

Exams and Presentations:

Exam DATE
midterm take-home test Due Monday, October 13
midterm take-home test Due Monday, November 17
Student Presentations November 21-December 5
FINAL EXAM Tuesday, December 9, 8:00-10:30 am (Comprehensive)

Attendance Policy and Grading:

Attendance is required at the lectures. Students are solely responsible for any work missed during an absence.

Your grade for the course will be based on take-home tests/final exam and presentation as follows:

2 midterm (take-home) tests: 30%
Presentation: 10%
Comprehensive Final Exam: 30%

Your grade for the course will be based on the following scale:

A+ [97,100) A [92,97) A- [90,92)
B+ [87,90) B [82,87) B- [80,82)
C+ [77,80) C [72,77) C- [70,72)
D+ [67,70) D [62,67) D- [60,62)
F [0,60)

Course Notes

 Each class period I shall assign some problems (typically from the book). These problems are not to be handed in, but you should make sure that you write out neat solutions to the problems, since at some stage I may ask you to give me a dossier of such assigned problems or I may ask you to present such problems at the board. You are encouraged to consult with other students concerning these. During the semester there will be two midterm take-home tests each of which will count 30% of your course grade. You will have one week to do each of these tests and they should be done independently, although you will have access to class notes and books. Also all students will be required to give a 20 minute presentation on a cryptography topic of his/her choice, which will be worth 10% of the final course grade. These presentations will take place in the final two weeks of class and may be a topic that we have not covered in class or may be a deeper treatment of some topic that we have covered. All students should discuss their topic with me prior to deciding what topic to cover. The final exam will be an in-class comprehensive final and will also count 30% to your final course grade. The percentages announced for tests are meant to be rough guides to you, but I may not adhere to them strictly. For example, a student who has been doing poorly throughout the semester but who performs really well on the final exam may have more weight put on the final exam. Student participation is also a facter here. Please note that the exams for graduate students will be more involved than those for undergraduates. At various places in the lectures I may also leave proofs for you to complete or skip details of proofs that you should fill in. This is all part of being an advanced student-developing the ability to think for yourself. Your grade depends upon you and how much time and effort you are prepared to put in.

CODE OF ACADEMIC CONDUCT STATEMENT

All acts of dishonesty in any work constitute academic misconduct. This includes, but is not limited to, cheating, plagiarism, fabrication of information, misrepresentation, and abetting any of the above. The Academic Misconduct Disciplinary Policy will be followed in the event that academic misconduct occurs. Students should refer to the Student Affairs Handbook which can be obtained from the Student Life Office in Ferguson Center. The Academic Misconduct Disciplinary Policy will be followed in the event of academic misconduct (see also Student Handbook. ) The Academic Misconduct Disciplinary Policy will be followed in the event of academic misconduct.

DISABILITY ACCOMMODATION STATEMENT

Students with disabilities are encouraged to register with the Office of Disability Services, 348-4285 (see also Office of Disability Services). Thereafter, you are invited to schedule appointments to see me during my office hours to discuss accommodations and other special needs.

Course notes | Exams | Grading | Homework | Old Tests