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Course Information
Course Unit Title : Elliptic Curves in Cryptography
Course Unit Code : 01MAT5188
Type of Course Unit : Optional
Level of Course Unit : Second Cycle
Year of Study : Preb
Semester : 255.Semester
Number of ECTS Credits Allocated : 6,00
Name of Lecturer(s) : ---
Course Assistants :
Learning Outcomes of The Course Unit : At the end of the course the student is expected to learn: the basic facts about the elliptic curves, the implementation of Elliptic Curves and Algorithms to compute group order and MOV algorithm. the elliptic curve cryptosystems and the related algorithms.
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : Elliptic curves over finite fields, group structure, Weil conjectures, Supersingular curves, efficient implementation of elliptic curves, determining the group order, Schoof algorithm, the elliptic curve discrete logarithm problem, the Weil pairing, MOV attack, Elliptic curve primality test, Elliptic curve factorization.
Languages of Instruction : Turkish-English
Course Goals : The aim of this course is to introduce the Elliptic Curves in Cryptography. After introducing the basic facts about the elliptic curves, we shall discuss the implementation of Elliptic Curves and Algorithms to compute group order. The emphasis will be given the elliptic curve cryptosystems and the related algorithms. The other applications of Elliptic Curves in Cryptography such as primality and factorization tests will also be discussed.
Course Aims : The aim of this course is to introduce the Elliptic Curves in Cryptography. After introducing the basic facts about the elliptic curves, we shall discuss the implementation of Elliptic Curves and Algorithms to compute group order. The emphasis will be given the elliptic curve cryptosystems and the related algorithms. The other applications of Elliptic Curves in
Cryptography such as primality and factorization tests will also be discussed.
WorkPlacement   Not used.
Recommended or Required Reading
Textbook : -
Additional Resources : 1) D. Hankerson, A. Menezes, S. Vanstone, Guide to Elliptic Curve Cryptography, Springer, 2004.
2) I. Blake, G. Seroussi and N. Smart, Elliptic Curves in Cryptography, London Math. Soc. Lec. Note Series. No.256, 1999.
3) L. C. Washington, Elliptic Curves: Number Theory and Cryptography, Second Edition, CRC Press, 2008.
4) N. Koblitz, A Course in Number Theory and Cryptography, Springer-Verlag, Second edition, 1994.
5) N. Koblitz, Algebraic Aspects of Cryptography, Vol. 3, Algorithms and Computation in Mathematics, Springer-Verlag, 1998.
6) A. J. Menezes, Elliptic Curve Public Key Cryptosystems, Kluwer Academic Publishers, 1993.
Material Sharing
Documents :
Assignments :
Exams :
Additional Material :
Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)
ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.
Activity :
Number Duration Total  
Course Duration (Excluding Exam Week) :
14 3 42  
Time Of Studying Out Of Class :
14 3 42  
Homeworks :
5 15 75  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 30 30  
Finals :
1 30 30  
Workload Hour (30) :
30  
Total Work Charge / Hour :
0  
Course's ECTS Credit :
0      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
1 25
Quiz :
0 0
Homework :
5 75
Attendance :
14 0
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
100
The ratio of the term to success :
70
The ratio of final to success :
30
TOTAL :
100
Weekly Detailed Course Content
Week Topics  
1 Introduction to elliptic curves
 
2 Group law
 
3 Group order and group structure
 
4 j-invariant
 
5 Isomorphism classes
 
6 Point representation and the group law
 
7 Supersingular curves
 
8 Torsion points
 
9 Division polynomials
 
10 Weil pairing
 
11 Elliptic curve discrete logarithm problem (ECDLP)
 
12 Attacks on ECDLP
 
13 Factoring using elliptic curves
 
14 Primality testing
 
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