Course Name | Introduction to Cryptography |
Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
---|---|---|---|---|---|
MATH 470 | Fall/Spring | 3 | 0 | 3 | 6 |
Prerequisites | None | |||||
Course Language | English | |||||
Course Type | Elective | |||||
Course Level | First Cycle | |||||
Mode of Delivery | - | |||||
Teaching Methods and Techniques of the Course | ||||||
Course Coordinator | - | |||||
Course Lecturer(s) | ||||||
Assistant(s) |
Course Objectives | To provide an introduction to number theory and cryptography for math major students with theoretical aspects as well as practical applications. |
Learning Outcomes | The students who succeeded in this course;
|
Course Description | Cryptography is one of the popular topics with direct applications to daily life. Topics include: congruences, factoring, quadratic residues as preliminaries from number theory and continue with cryptography; simple cryptosystems, publickey cryptosystems, practical applications such as authentication, key exchange and sharing. |
Related Sustainable Development Goals | |
| Core Courses | |
Major Area Courses | X | |
Supportive Courses | ||
Media and Managment Skills Courses | ||
Transferable Skill Courses |
Week | Subjects | Required Materials |
1 | Some topics in elementary number theory | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
2 | Time estimates for doing arithmetic | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
3 | Divisibility and Euclidean algortihm | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
4 | Congruences | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
5 | Applications of factoring | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
6 | Finite fields and quadratic residues | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
7 | Quadratic reciprocity | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
8 | Some simple cryptosystems | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
9 | Enciphering matrices | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
10 | Public key cryptography | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
11 | RSA | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
12 | Discrete log | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
13 | Elliptic curves | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
14 | Elliptic curve cryptosystems | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
15 | Semester Review | |
16 | Final Exam |
Course Notes/Textbooks | “A Course in Number Theory and Cryptography” by Neal Koblitz, Springer, 2nd Edition, 1994. ISBN-13: 978-0387942933 |
Suggested Readings/Materials | “Cryptography: An Introduction” by Nigel Smart, McGrawHill, 2004. ISBN-13: 978-0077099879 |
Semester Activities | Number | Weigthing |
Participation | ||
Laboratory / Application | ||
Field Work | ||
Quizzes / Studio Critiques | ||
Portfolio | ||
Homework / Assignments | 10 | 20 |
Presentation / Jury | ||
Project | ||
Seminar / Workshop | ||
Oral Exam | ||
Midterm | 2 | 40 |
Final Exam | 1 | 40 |
Total |
Weighting of Semester Activities on the Final Grade | 12 | 60 |
Weighting of End-of-Semester Activities on the Final Grade | 1 | 40 |
Total |
Semester Activities | Number | Duration (Hours) | Workload |
---|---|---|---|
Course Hours (Including exam week: 16 x total hours) | 16 | 3 | 48 |
Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | ||
Study Hours Out of Class | 14 | 3 | 42 |
Field Work | |||
Quizzes / Studio Critiques | |||
Portfolio | |||
Homework / Assignments | 10 | 3 | |
Presentation / Jury | |||
Project | |||
Seminar / Workshop | |||
Oral Exam | |||
Midterms | 2 | 20 | |
Final Exams | 1 | 20 | |
Total | 180 |
# | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. | X | ||||
2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. | |||||
3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. | X | ||||
4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. | X | ||||
5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. | X | ||||
6 | To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project. | |||||
7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. | |||||
8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. | |||||
9 | To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security. | |||||
10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. | |||||
11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. | |||||
12 | To be able to speak a second foreign language at a medium level of fluency efficiently. | |||||
13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. |
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest