Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
8MATH406MATHEMATICS OF PUBLIC KEY CRYPTOGRAPHY3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course Introduction of mathematical foundations of public-key cryptography.
Course Content Fundamentals and services of cryptology, symmetric encryption, public key encryption, RSA encryption, Rabin ve Pallier encryption, primality testing, ElGamal Encryption, Diffie Hellman key exchange protocol, digital signatures, public key infrastructure and digital certificates, key management
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers BERKANT USTAO─×LU
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 30
Quizzes 0 % 0
Homeworks 8 % 30
Other activities 1 % 10
Laboratory works 0 % 0
Projects 1 % 10
Final examination 1 % 20
Total
13
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 42 1 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 10 12 120
Exams and Exam Preparations 3 6 18
Total Work Load   Number of ECTS Credits 6 180

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Recognize mathematical concepts behind cryptographic applications.
2 Compare different mathematical structures relative to the cryptosystem requirements.
3 Demonstrate the ability to abstract in security context.
4 To model and solve practical problems with the assistance of mathematical tools.
5 To analyze problems and devise appropriate modeling structures.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Time estimates for doing arithmetic. Divisibility and Eucledian algorithm D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
2 Congruences and finite fields. D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
3 Classical cryptographic algorithms D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
4 The idea of public-key cryptography, knapsack, LLL algorithm D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
5 RSA, Rabin, Primality testing. D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
6 Factorization algorithms D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
7 Other attacks on RSA. D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
8 Discrete logarithm problem (DLP). El Gamal encryption scheme. D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
9 DLP in finite fields. D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
10 Elliptic curves. DLP in elliptic curves D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
11 Elliptic curve primality tests and factorization D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
12 Signature schemes, hash functions and the random oracle model D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
13 El Gamal signature scheme. Full domain hash D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
14 Diffie-Hellman problem D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
15 Final 1st week D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002
16 Final 2nd week D. Stinson, Cryptography: Theory and Practice, CRC Press, 2002


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 1 4 3 1 3 4 2 2 1 2 2 4 4
C2 4 1 4 2 1 4 1 4 2
C3 4 4 2 1 3 1 4 3
C4 4 4 1 4 4 4 2
C5 4 4 1 4 3 4 4 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=163204&lang=en