# 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 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

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