Fall 2004

MATH 478.01 (3 credits), M_W_F, 2:00PM-2:50PM, Wickersham 109

**Prerequisites:**A grade of C- or better in MATH 220 (

*Introduction to Mathematical Proof*)**Instructor:**Dr. Buchanan

Office: Wickersham 218, Phone: 872-3659, FAX: 871-2320

Office Hours: 10:00AM-10:50AM (MTuWThF) or by appointment

Email:`Robert.Buchanan@millersville.edu`

URL:`http://banach.millersville.edu/~bob`**Textbook:***An Introduction to Cryptography*, Richard A. Mollin, Chapman & Hall/CRC, Boca Raton (2001), ISBN 1-58488-127-5.**Objectives:**The objectives of this course include introducing students to the basic mathematical principles of cryptography. Upon successful completion of this course students should be able to

- understand modular arithmetic, congruences, and some topics from
elementary number theory,
^{1} - understand the design, structure, and operation of symmetric-key cryptosystems such as block ciphers and stream ciphers,
- understand the design, structure, and operation of public-key cryptosystems including RSA and authentication,
- compare and contrast symmetric-key and public-key cryptosystems,
- understand the role of prime numbers in cryptography and various algorithms for primality testing,
- understand the design, structure, and operation of cryptosystems based on elliptic curves,
- describe the state of research and development of quantum cryptosystems, quantum computers, and their implications for existing cryptosystems.

- understand modular arithmetic, congruences, and some topics from
elementary number theory,
**Course Contents:**- A list of topics to be covered in this course includes:
- Origin and history of cryptography
- The Integers
- Divisibility
- Greatest Common Divisor
- Euclidean Algorithm
- Extended Euclidean Algorithm
- Factoring
- Primality testing

- Symmetric-Key Cryptosystems
- Congruences
- Block ciphers
- Permutations
- Multiple encryption
- Data Encryption Standard (DES)
- Stream ciphers

- Public-Key Cryptosystems
- Exponentiation
- Discrete Logarithms
- RSA Cryptosystem
- Authentication
- Knapsack problem

- Digital signatures
- Primality Testing
- Elliptic curves
- Quantum cryptography

If time permits other topics may be covered as well.

**Attendance:**Students are expected to attend all class meetings. If you must be absent from class on the day an assignment is due, you must complete and hand in the assignment prior to the absence. If you know you will be absent on the day of a test, you must notify me before the time the test is scheduled in order to schedule a make-up test. Students who miss a test should provide a valid excuse, otherwise you will not be allowed to make up the test. Tests should be made up within one week of their scheduled date. No final examination exemptions.

**Homework:**Students are expected to do their homework and participate in class. Students should expect to spend a minimum of three hours outside of class on homework and review for every hour spent in class. Occasionally specific homework problems will be assigned for collection and grading. I anticipate approximately ten graded homework assignments during the semester. Students should submit all homeworks by their respective due dates. Late homework will not be accepted without valid excuse. Discussion between students on homework assignments is encouraged, but homework submitted for grading should be written up separately.

**Tests:**There will be two tests and a comprehensive final examination.

- Friday, October 1, 2004
- Friday, November 5, 2004

**Grades:**Course grade will be calculated as follows.

Tests 25% each Homework 25% Exam 25% Tests and the final examination will be graded individually on a 100-point scale. Homework sets will vary in the number of problems assigned, but generally each homework problem will be worth ten points. For example on a homework assignment of five problems, the maximum numerical grade would be 50 points. To ensure that all homework assignments are weighted equally, each student's score will be normalized by the maximum score for that assignment. Again for example, on a five problem homework assignment grades will be among the set of scores . I keep a record of students' test, homework, and exam scores. Students should also keep a record of graded assignments, tests, and other materials. As an example of the calculation of the numerical course grade, suppose a student's two test grades were 87 and 70 (out of a maximum of 100 points on each test), the student's final examination grade was 75 (again, out of a maximum of 100), and the student's ten homework grades were . This student's homework average is . The student's numerical course grade is then

The course letter grades will be calculated as follows. I will not ``curve'' course grades.

90-92 A 93-100 A 80-82 B 83-86 B 87-89 B 70-72 C 73-76 C 77-79 C 60-62 D 63-66 D 67-69 D 0-59 F **Inclement Weather Policy:**If we should miss a class day due to a school closing because of weather, any activities planned for that missed day will take place the next time the class meets. For example, if a test is scheduled for a day that class is canceled on account of snow, the test will be given the next time the class meets.

**Final Word:**Math is not a spectator sport. What you learn from this course and your final grade depend mainly on the amount of work you put forth. Daily contact with the material through homework assignments and review of notes taken during lectures is extremely important. Organizing and conducting regular study sessions with other students in this class will help you to understand the material better.

Robert.Buchanan@millersville.edu

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