MT0011 Introduction to Cryptography

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code MT0011
Name Introduction to Cryptography
Term 2022-2023 Academic Year
Semester . Semester
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 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

Update Time: 21.11.2022 12:46