Course Catalog 2013-2014
Basic

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Course Catalog 2013-2014

MAT-63256 Mathematical Cryptology, 7 cr

Additional information

The course is lectured biennially.
Suitable for postgraduate studies

Person responsible

Keijo Ruohonen, Stephane Foldes

Lessons

Study type P1 P2 P3 P4 Summer Implementations Lecture times and places
Lectures
Excercises


 


 
 4 h/week
 2 h/week
+4 h/week
+2 h/week


 
MAT-63256 2013-01 Thursday 10 - 12, TB219
Friday 10 - 12, TB219

Requirements

Closed-book written exam.
Completion parts must belong to the same implementation

Learning Outcomes

After completing the course the student is familiar with the mostly used cryptosystems in modern cryptography, and their basic properties. The student also masters the required prerequisites in number theory and algebra. In particular, the student identifies the division of algorithms into intractable and tractable, so essential in cryptography. Completing the course the student is able to identify common cryptosystems, and evaluate their advantages and disadvantages, and the underlying mathematical paradigms, and for cryptographic protocols, too, to an extent (this is however mostly left to the relevant courses in information technology). Despite modern cryptology being the result of relatively recent research, it has progressed far and wide, and therefore it is simply not possible to include outcomes for it all within a single course. Completing the course the student nevertheless should be able the generalize and extend the skills.

Content

Content Core content Complementary knowledge Specialist knowledge
1. Elements and basic algorithms of number theory and algebra. Simple examples.  Applications to analysis of more complex cases. Alternative algorithms.   
2. The AES cryptosystem, its goals and algebraic background.  Further analysis of the AES cryptosystem.   
3. Computational complexity and its relation to cryptographic concerns, in particular to public-key systems.     
4. The RSA cryptosystem, its goals, analyses and number-theoretic background.  Further analysis of RSA, its variants and special uses.   
5. Cryptosystems based on group-theoretic concepts: ELGAMAL, DIFFIE-HELLMAN, ECC.  Further analyses of these systems, their variants and special uses.   
6. Overview of the NTRU cryptosystem.    Further analysis and structure of NTRU. 
7. Quantum encryption, its background and systems.     

Instructions for students on how to achieve the learning outcomes

Final grade is determined from tutorial activity and the final closed-book exam. Passing the course requires passing the final exam, and for this at most half of the maximum points are required. Bonus points obtained by tutorial activity may be used to add the exam points according to a given scheme. A thorough mastering of the core content should be sufficient for passing the course with grade 3. To get the degree 4 at least some complementary knowledge is usually required, getting the grade 5 then requires a more thorough mastering of this knowledge.

Assessment scale:

Numerical evaluation scale (1-5) will be used on the course

Partial passing:

Completion parts must belong to the same implementation

Study material

Type Name Author ISBN URL Edition, availability, ... Examination material Language
Book   An Introduction to Cryptography   Mollin, R.A.   1-58488-127-5       No    English  
Book   An Introduction to Mathematical Cryptography   Hoffstein, J., Pipher, J., Silverman, J.H.   978-0-387-77993-5       No    English  
Other online content   Homepage           No    English  
Summary of lectures   Mathematical Cryptology   Ruohonen, K.         Yes    English  

Prerequisites

Course Mandatory/Advisable Description
MAT-60050 Algebra Advisable   1
MAT-60056 Algebra Advisable   1
MAT-02650 Algoritmimatematiikka Advisable    

1 . The courses are interchangable.

Prerequisite relations (Requires logging in to POP)



Correspondence of content

Course Corresponds course  Description 
MAT-63256 Mathematical Cryptology, 7 cr MAT-52606 Mathematical Cryptology, 6 cr  

More precise information per implementation

Implementation Description Methods of instruction Implementation
MAT-63256 2013-01 Lectures and tutorials of Mathematical Cryptology.       Contact teaching: 0 %
Distance learning: 0 %
Self-directed learning: 0 %  

Last modified13.12.2013