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Information
| Code | MT0011 |
| Name | Introduction to Cryptography |
| Term | 2022-2023 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | |
| Course Instructor |
1 |
Course Goal / Objective
To see the mathematical background of the crpytography. To give an idea about the importance of the time complexity in cryptography. To understand the mathematical foundations of the recent cryptosystems.
Course Content
The aim of the cryptography and basic cryptosystems, symmetric and asymmetric encryption, Diffie-Hellman key exchange, time complexity and the big-O notation, polynomial-time algorithms and the "P vs NP" problem, AES and RSA cryptosystems, primality tests, probability theory and its applications to cryptography, factoring methods, group cryptography and the ElGamal cryptosystem, Discrete Logarithm Problem, elliptic curve cryptography
Course Precondition
None.
Resources
CryptoSchool, Joachim von zur Gathen, Springer Berlin, Heidelberg, 2015
Notes
A Course in Number Theory and Cryptography, Neal Koblitz, Springer New York, NY, 1994
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | (S)he learns the definition of the polynomial time algorithms. |
| LO02 | (S)he understands the mathematical foundations of the recent cryptosystems. |
| LO03 | (S)he understands the importance of the factoring problem in cryptography. |
| LO04 | (S)he understands the Diffie-Hellman key exchange. |
| LO05 | (S)he learns the group cryptography and the discrete logarithm problem. |
| LO06 | (S)he understands the theoretical background of the security systems that uses elliptic curves. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 5 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | 5 |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 3 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | 2 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | 4 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Fundamental concepts of cryptography and algorithms | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Time complexity and the polynomial time algorithms | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Basic cryptosystems and the difference between symmetric and asymmetric cryptosystems | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | AES cryptosystem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | The structure of the RSA cryptosystem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | The correctness and the efficiency of the RSA cryptosystem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | The security of the RSA cryptosystem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Reviewed of the topics discussed in the lecture notes and source again | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | The cryptanalysis of the RSA cryptosystem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Group cryptography and the Diffie-Hellman key exchange | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | The ElGamal cryptosystem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | The security of the ElGamal cryptosystem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | The Discrete Logarithm Problem | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Elliptic curves and their usage in cryptography | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Elliptic curve cryptography and its security | Study the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Reviewed of the topics discussed in the lecture notes and source again | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Reviewed of the topics discussed in the lecture notes and source again | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||