# Introduction to Crytopgraphy (MATH427) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Introduction to Crytopgraphy MATH427 3 0 0 3 6
Pre-requisite Course(s)
MATH 325 Elementary Number Theory
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Team/Group. This course is designed to introduce the fundamental concepts of cryptography and some classical private-key and public key cryptographic systems within a mathematical framework. The students who succeeded in this course; gain knowledge about mathematical basics of cryptography. understand and use some simple cryptosystems. know basics of private-key and public-key infrastructures. learn how basic cryptographic protocols work. Basics of cryptography, classical cryptosystems, substitution, review of number theory and algebra, public-key and private-key cryptosystems, RSA cryptosystem, Diffie-Hellman key exchange, El-Gamal cryptosystem, digital signatures, basic cryptographic protocols.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Basic Definitions and Theorems in Number Theory pp.12-30
2 Basic Definitions and Theorems in Number Theory (continued) pp.12-30
3 Basic Definitions of Cryptosystems
4 Shift Cipher pp. 54-65
5 Substitution Cipher pp. 54-65
6 Hill Cipher pp.65-82
7 Vigenere Cipher pp.65-82
8 Playfair Cipher
9 Finite Fields, Review of Quadratic Residues pp. 31-40, pp. 42-49
10 The Idea of Public Key Cryptography pp. 83-90
11 RSA Cryptosystem pp. 92-95
12 Discrete Logarithm Problem, Diffie-Hellman Key Exchange pp. 97-99
13 El Gamal Cryptosystem, The Massey-Omura Cryptosystem pp. 100-101
14 Some Basic Cryptographic Protocols
15 Review
16 Final Exam

### Sources

Course Book 1. A Course in Number Theory and Cryptography, Neal Koblitz , 2nd Edition, Springer, 1994 2. Algebraic Aspects of Cryptograhy, Neal Koblitz , Springer ,1998. 3. Cryptography: Theory and Practice, Douglas Stinson, CRC Press Inc, 1996. 4. Introduction to Cryptography, J. A. Buchmann, Springer-Verlag, 2000. 5. Handbook of Applied Cryptography, Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, CRC Press, 1996.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 10
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 40
Toplam 8 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Adequate knowledge in mathematics, science and subjects specific to the computer engineering discipline; the ability to apply theoretical and practical knowledge of these areas to complex engineering problems.
2 The ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose.
3 The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose.
4 The ability to develop, select and utilize modern techniques and tools essential for the analysis and determination of complex problems in computer engineering applications; the ability to utilize information technologies effectively.
5 The ability to design experiments, conduct experiments, gather data, analyze and interpret results for the investigation of complex engineering problems or research topics specific to the computer engineering discipline.
6 The ability to work effectively in inter/inner disciplinary teams; ability to work individually
7 Effective oral and writen communication skills in Turkish; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and to receive clear and understandable instructions.
8 The knowledge of at least one foreign language; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and to receive clear and understandable instructions.
9 Recognition of the need for lifelong learning; the ability to access information, to follow recent developments in science and technology.
10 The ability to behave according to ethical principles, awareness of professional and ethical responsibility;
11 Knowledge of the standards utilized in software engineering applications
12 Knowledge on business practices such as project management, risk management and change management;
14 Knowledge on sustainable development
15 Knowledge on the effects of computer engineering applications on the universal and social dimensions of health, environment and safety;
16 Awareness of the legal consequences of engineering solutions
17 An ability to describe, analyze and design digital computing and representation systems.
18 An ability to use appropriate computer engineering concepts and programming languages in solving computing problems.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 8 40
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 15 30
Prepration of Final Exams/Final Jury 1 20 20