# MAT 448 Cryptography

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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

• Required: MAT 271 with a grade of C or better.
• Recommended: CSC 115 or 121 with a grade of C or better.

### 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:

• Write proofs of theorems about basic properties of numbers including even numbers, odd numbers, divisibility, and prime numbers.
• Write proofs of theorems in modular arithmetic and arithmetic in other bases.
• Compute and write encryptions in various cryptosystems.
• Demonstrate through explanation and solving problems how one might go about attacking cryptosystems.
• Analyze the security and any vulnerabilities of an assortment of cryptosystems.
• Write and run computer programs for encryption and decryption in complex contemporary cryptosystems.

### 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

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.