MATH 626: Cryptography, Spring Semester 2007

MATH 626: Cryptography,

Spring Semester 2009

“The urge to discover secrets is deeply ingrained in human nature; even the least curious mind is roused by the promise of sharing information withheld from others.” — John Chadwick

Professor: Dr. J. Carmelo Interlando

Office: GMCS (Geology, Math, and Computer Science) 581
E-mail: interlan@mail.sdsu.edu
Telephone: (619) 594-7237

Classes Days / Time: T–TH / 4:00 – 5:15 PM
Location: GMCS 328, San Diego State University

Class Website: https://blackboard.sdsu.edu

Office Hours: T: 2:00 – 3:00 PM, W: 1:00 – 2:00 PM, TH: 2:00 – 3:00 PM. In addition to that, I am in my office every weekday. I encourage you to visit me at any time. However, if you set up a time with me before hand, then you can be sure that I will be there. I strongly encourage you to see me if there is anything related to the course that you are unclear on or would like to know more about. I want to help you learn the material and do well in the class.

Textbook

D. R. Stinson, Cryptography: Theory and Practice. Third Edition, Chapman & Hall/CRC, 2006.

Course Description, Relevance, and Learning Outcomes

Basically, cryptography provides techniques for: 1) keeping information secret (i.e., confidentiality), 2) determining that information has not been tampered with (i.e., data integrity), 3) determining who authored pieces of information (i.e., non-repudiation), and 4) access control via passwords. The objective of the present course is to understand how these techniques work and also how to estimate their efficiency and security. As we go along, you will see matrices, functions and their inverses, prime numbers, and frequency analysis “brought to life.” Roughly, we will cover the first seven chapters of the textbook, which is core material, and time permitting, Chapters 8 and 9 as well. Since cryptography is such a broad area, you will also have the opportunity to study a topic of your own choice and write a report on it. The topic can be of theoretical or computational nature, or it can involve a subject of historical/educational importance.

Relevance: Cryptography has been used throughout history, probably since four thousand years ago in Egypt. Nowadays it is fundamental for personal communications, commerce, government, and military, as it provides the ability to securely store and transfer sensitive information. Such ability has proved to be a critical factor for success in war and business. The algorithms used in cryptography can be important for protecting the survival of our nation. Moreover, because of the recent boom of electronic communication and commerce, cryptography has expanded its significance way beyond its historical role in national security into our daily lives. Therefore, it is important that even those who do not intend on becoming specialists in the area have a basic understanding of the modern systems, their capabilities, and their limitations.

Learning Outcomes: The course will give you insight into a branch of applied mathematics that has tremendous practical significance. You will have an understanding of the fundamental mathematics that lies behind the standards adopted by the U.S. Department of Commerce and U.S. National Institute of Standards and Technology (NIST) that allow secure transactions within the business and private sectors. By the end of it, you will have learned how cryptographic techniques work and also how to estimate their efficiency and security. The course will prepare you to work as a professional in the area.

Prerequisite

It is important that you are comfortable with concepts and results from elementary number theory (such as modular arithmetic), taught for example in MATH-521A or MATH-522. Basic facts about finite fields (as taught in MATH-521B) will be used. Computer programming skills are required if you choose to work on a project that involves implementation of some protocol or algorithm.

Examinations, Homework, and Grading

There will be two exams worth 300 points each and a final project worth 250 points. The project will consist of a particular topic that you will choose from a list. You will be allowed to choose topics which are not on the list, but you will need to discuss your choice with me before proceeding. Besides a written report, the project will involve a presentation to the class.

Exam 1: Tuesday, March 3, in class.

Exam 2: Thursday, April 23, in class.

Homework will be assigned weekly, and some of it will be collected for evaluation purposes (150 points). Feel free to work with your colleagues on the homework assignments, but remember that copying is not permitted. Typically, you will be given between 7 and 10 days to return an assignment.

In summary:

Homework	150
Tests	600
Project	250
Total	1000

The numerical points for letter grades (A, A–, B+, … ,) will be based only on the test scores, the project, and homework. Roughly, an A is above 85%, A– is above 80%, B is above 70%, C is above 60%, etc.

References for Further Reading

1. Hankerson et al., Coding Theory and Cryptography: The Essentials. Second Edition, Marcel Dekker, 2000. (very good introductory text).

2. T. W. Hungerford, Abstract Algebra, an Introduction, Second Edition, Brooks Cole, 1997. (excellent and accessible algebra text, containing some of the background needed in this course).

3. D. Khan, The Codebreakers, Scribner, Revised Edition, 1996. (non-technical, but provides a complete historical account).

4. N. Koblitz, A Course in Number Theory and Cryptography, Second Edition. Springer-Verlag, Graduate Texts in Mathematics, Vol. 114, 1994. (intermediate level – the first two chapters are devoted to the necessary background from number theory).

5. A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography. CRC Press, 1997. (complete account, now freely available on the internet).

6. R. A. Mollin, An Introduction to Cryptography, Chapman & Hall/CRC, 2001 (very good introductory text).

7. K. H. Rosen, Elementary Number Theory and its Applications, Fifth Edition, Addison Wesley, 2005. (excellent number theory text, with some chapters on cryptography).

8. C. E. Shannon, “Communication theory of secrecy systems,” Bell System Technical Journal, 27, (1948), 656-715. (this paper marks the beginning of cryptography as a science).

9. S. Singh, The Code Book. Free download (non-technical).

10. http://www.iacr.org/ - Website of the International Association for Cryptologic Research. It contains conferences, workshops, and publications in the area.