MAT 448 Cryptography

This is a sample syllabus only. Ask your instructor for the official syllabus for your course.

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Course Description

The objective of this course is to study the central and contemporary notions of cryptography, along with the necessary mathematical concepts. The topics will be studied both from theoretical perspectives and from a practical viewpoint. The core topics covered will be: Basic Number Theory, Basic Cryptography, DES and AES, Public-Key Cryptography. Related history of the subject will be outlined throughout. If time permits, additional topics from the following might be covered: True and Probabilistic Primality Testing, Different methods of factoring, Internet security, and Elliptic Curve Cryptography.

Prerequisites

Textbook

A. Stanoyevitch, Introduction to Cryptography, with Mathematical Foundations and Computer Implementations, Chapman & Hall (2011)

Learning Outcomes:

By the end of this course, students will be able to:

Course Outline

Week Topics
1 Overview of the subject with introductions to some key historical cryptographic systems and events
2 Solving Problems and Proving Theorems involving Divisibility and Primes. Unique Factorization
3 Working with Congruencies and Modular Arithmetic
4 The evolution of codemaking until the computer era
5 Vector and matrices of modular integers Exam #1
6 Working with vectors and strings on computing platforms
7 The evolution of codebreaking until the computer era (including the exciting cryptographic breakthroughs that help end World War II earlier than it would have otherwise ended)
8 Representation of integers in different bases
9 The data encryption standard (DES) cryptosystem
10 Computer Implementations of DES Exam #2
11 Topics in Number Theory
12 Public Key Cryptography Digital Signatures: A means for authentication and nonrepudiation
13 Finite Fields in General and GF(28) in particular
14 The advanced encryption standard (AES) cryptosystem
15 Review for final

Grading Policy

Students' grades are based on homework, in-class exams, final exam, special project etc. as deterermined by the instructor.

Attendance Requirements

Attendance policy is set by the instructor.

Policy on Due Dates and Make-Up Work

Due dates and policy regarding make-up work are set by the instructor.

Schedule of Examinations

The instructor sets all test dates except the date of the final exam. The final exam is given at the date and time announced in the Schedule of Classes.

Academic Integrity

The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

Accomodations for Students with Disabilities

Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the DSS in WH B250. For information call (310) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028.


Revision history:

Prepared by A. Stanoyevitch spring 2011. Revised for the web 3/4/2011 by G. Jennings.