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İzmir Ekonomi Üniversitesi

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    GRADUATE SCHOOL

    M.SC. in Computer Engineering (With Thesis)

    MATH 662 | Course Introduction and Application Information

    Course Name
    Cryptography
    Code
    Semester
    Theory
    (hour/week)
    Application/Lab
    (hour/week)
    Local Credits
    ECTS
    MATH 662
    Fall/Spring
    3
    0
    3
    7.5

    Prerequisites
    None
    Course Language
    English
    Course Type
    Elective
    Course Level
    Third Cycle
    Mode of Delivery -
    Teaching Methods and Techniques of the Course -
    National Occupation Classification -
    Course Coordinator -
    Course Lecturer(s)
    Assistant(s) -
    Course Objectives To provide a review of number theory and discuss cryptography with theoretical aspects as well as practical applications.
    Learning Outcomes

    The students who succeeded in this course;

    • will be able to extend natural arithmetic to finite fields.
    • will be able to explain the principles of cryptography.
    • will be able to compare symmetric and public cryptosystems.
    • will be able to design new systems upon particular a need.
    • will be able to estimate the power of a cryptosystem.
    • will be able to apply a particular cryptosystem to:authentication,sharing,signature,identify weak cryptosystems and avoid using them.
    Course Description Cryptography is one of the popular topics with direct applications to daily life. Topics include: congruences, factoring, quadratic residues as preliminaries from number theory and continue with cryptography and algebraic geometry.

     



    Course Category

    		Core Courses
    Major Area Courses
    Supportive Courses
    Media and Management Skills Courses
    Transferable Skill Courses

     

    WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

    Week Subjects Related Preparation Learning Outcome
    1 Crpytograpy, Public key. “Algebraic Aspects of Cryptography” N. Koblitz
    2 Complexity. “Algebraic Aspects of Cryptography” N. Koblitz
    3 Fields, finite fields, algebra. “Algebraic Aspects of Cryptography” N. Koblitz
    4 The ImaiMatsumoto System. “Algebraic Aspects of Cryptography” N. Koblitz
    5 Patarin's Little Dragon. “Algebraic Aspects of Cryptography” N. Koblitz
    6 CombinatorialAlgebraic Cryptosystems. “Algebraic Aspects of Cryptography” N. Koblitz
    7 Cryptographic Version of Ideal Membership. “Algebraic Aspects of Cryptography” N. Koblitz
    8 Elliptic Curves. “Algebraic Aspects of Cryptography” N. Koblitz
    9 Elliptic Curve Cryptosystems. “Algebraic Aspects of Cryptography” N. Koblitz
    10 Hyperelliptic Curves. “Algebraic Aspects of Cryptography” N. Koblitz
    11 Polynomial and Rational Functions. “Algebraic Aspects of Cryptography” N. Koblitz
    12 Zeros and Poles. “Algebraic Aspects of Cryptography” N. Koblitz
    13 Divisors. “Algebraic Aspects of Cryptography” N. Koblitz
    14 Reduced Divisors. “Algebraic Aspects of Cryptography” N. Koblitz
    15 Review.
    16 Review of the Semester  

     

    Course Notes/Textbooks “Algebraic Aspects of Cryptography” N. Koblitz
    Suggested Readings/Materials None.

     

    EVALUATION SYSTEM

    Semester Activities Number Weigthing
    Participation
    Laboratory / Application
    Field Work
    Quizzes / Studio Critiques
    Portfolio
    Homework / Assignments
    5
    20
    Presentation / Jury
    Project
    Seminar / Workshop
    Oral Exams
    Midterm
    1
    30
    Final Exam
    1
    50
    Total

    Weighting of Semester Activities on the Final Grade
    50
    Weighting of End-of-Semester Activities on the Final Grade
    50
    Total

    ECTS / WORKLOAD TABLE

    Semester Activities Number Duration (Hours) Workload
    Theoretical Course Hours
    (Including exam week: 16 x total hours)
    16
    3
    48
    Laboratory / Application Hours
    (Including exam week: '.16.' x total hours)
    16
    0
    Study Hours Out of Class
    15
    6
    90
    Field Work
    0
    Quizzes / Studio Critiques
    0
    Portfolio
    0
    Homework / Assignments
    5
    5
    25
    Presentation / Jury
    0
    Project
    0
    Seminar / Workshop
    0
    Oral Exam
    0
    Midterms
    1
    31
    31
    Final Exam
    1
    31
    31
        Total
    225

     

    COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

    #
    		 PC Sub Program Competencies/Outcomes
    * Contribution Level
    1
    2
    3
    4
    5
    1 Accesses information in breadth and depth by conducting scientific research in Computer Engineering; evaluates, interprets and applies information.
    -
    -
    -
    -
    -
    2 Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations.
    -
    -
    -
    -
    -
    3 Uses scientific methods to complete and apply information from uncertain, limited or incomplete data; can combine and use information from different disciplines.
    -
    -
    -
    -
    -
    4 Is informed about new and upcoming applications in the field and learns them whenever necessary.
    -
    -
    -
    -
    -
    5 Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions.
    -
    -
    -
    -
    -
    6 Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs
    -
    -
    -
    -
    -
    7 Designs and implements studies based on theory, experiments and modelling; analyses and resolves the complex problems that arise in this process.
    -
    -
    -
    -
    -
    8 Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations; can work independently and takes responsibility.
    -
    -
    -
    -
    -
    9 Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale.
    -
    -
    -
    -
    -
    10 Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.
    -
    -
    -
    -
    -
    11 Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications.
    -
    -
    -
    -
    -
    12 Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity.
    -
    -
    -
    -
    -

    *1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

     

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