

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 
: 
FaceToFace

Prerequisities and Corequisities 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 
: 
TurkishEnglish

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, SpringerVerlag, Second edition, 1994. 5) N. Koblitz, Algebraic Aspects of Cryptography, Vol. 3, Algorithms and Computation in Mathematics, SpringerVerlag, 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

:


Course Duration (Excluding Exam Week)

:


Time Of Studying Out Of Class

:


Homeworks

:


Presentation

:


Project

:


Lab Study

:


Field Study

:


Visas

:


Finals

:


Workload Hour (30)

:


Total Work Charge / Hour

:


Course's ECTS Credit

:



Assessment Methods and Criteria
Studies During Halfterm

: 

Visa

: 

Quiz

: 

Homework

: 

Attendance

: 

Application

: 

Lab

: 

Project

: 

Workshop

: 

Seminary

: 

Field study

: 




TOTAL

: 

The ratio of the term to success

: 

The ratio of final to success

: 

TOTAL

: 


Weekly Detailed Course Content
Week

Topics

1

Introduction to elliptic curves



2

Group law



3

Group order and group structure



4

jinvariant



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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