syllabus

1. Information regarding the programme
1.1 Higher education institution 	Babeş-Bolyai University	
1.2 Faculty	Faculty of Mathematics and Computer Science	
1.3 Department	Department of Computer Science	
1.4 Field of study	Computer Science	
1.5 Study cycle	Bachelor	
1.6 Study programme / Qualification 	Computer Science	

2. Information regarding the discipline 
2.1 Name of the discipline	Public-Key Cryptography	
2.2 Course coordinator 	Assoc.Prof.PhD. Septimiu Crivei	
2.3 Seminar coordinator	Assoc.Prof.PhD. Septimiu Crivei	
2.4. Year of study	3	2.5 Semester	5	2.6. Type of evaluation	C	2.7 Type of discipline	Optional	

3. Total estimated time (hours/semester of didactic activities) 
3.1 Hours per week 	3	Of which: 3.2 course	2	3.3 seminar/laboratory	1	
3.4 Total hours in the curriculum 	42	Of which: 3.5 course	28	3.6 seminar/laboratory	14	
Time allotment:	hours	
Learning using manual, course support, bibliography, course notes	28	
Additional documentation (in libraries, on electronic platforms, field documentation) 	28	
Preparation for seminars/labs, homework, papers, portfolios and essays	28	
Tutorship	10	
Evaluations	14	
Other activities: ..................	0	
3.7 Total individual study hours 	108	
3.8 Total hours per semester	150	
3.9 Number of ECTS credits	6	

4. Prerequisites (if necessary)
4.1. curriculum	•		
4.2. competencies	•		

5. Conditions (if necessary)
5.1. for the course	•		
5.2.  for the seminar /lab activities	•		

6. Specific competencies acquired 
Professional competencies	•	Understanding of basic concepts of mathematics and use them to problem-solving activities
•	Ability to understand and approach problems of modeling nature from other sciences	
Transversal competencies	•	Ability to work independently and/or in a team in order to solve problems in defined professional contexts	

7. Objectives of the discipline (outcome of the acquired competencies)
7.1 General objective of the discipline	•	To present mathematical algorithms used in public-key cryptography. 	
7.2 Specific objective of the discipline	•	Number-theoretic and algebra algorithms will be studied and implemented in projects.	

8. Content
8.1 Course	Teaching methods	Remarks	
1.	Classical cryptography. Examples	exposition, algorithmization		
2.	Public-key cryptography	exposition, algorithmization		
3.	Algorithm complexity	exposition, algorithmization		
4.	Congruences	exposition, algorithmization		
5.	Primes, quadratic residues	exposition, algorithmization		
6.	Algorithms for testing primality	exposition, algorithmization		
7.	Factorization algorithms for integers I	exposition, algorithmization		
8.	Factorization algorithms for integers II	exposition, algorithmization		
9.	Rabin public-key cryptosystem	exposition, algorithmization		
10.	ElGamal public-key cryptosystem, finite fields	exposition, algorithmization		
11.	Factorization of polynomials: Berlekamp’s algortihm	exposition, algorithmization		
12.	Discrete logarithm	exposition, algorithmization		
13.	Practical aspects of public-key cryptosystems I	exposition, algorithmization		
14.	Practical aspects of public-key cryptosystems II	exposition, algorithmization		
Bibliography
1. S. Crivei, A. Marcus, C. Sacarea, C. Szanto, Computational algebra with applications to cryptography and coding theory, Editura EFES, 2006.
2. C. Gherghe, D. Popescu, Criptografie. Coduri. Algoritmi, Editura Univ. Bucuresti, 2005.
3. N. Koblitz, A Course in Number Theory and Cryptography, Springer-Verlag, 1994.
4. A.J. Menezes, P.C. van Oorschot, S.A. Vanstone, Handbook of Applied Cryptography. CRC Press,
Boca Raton, 1997. (http://www.math.uwaterloo.ca/~ajmeneze)
5. B. Schneier, Applied Cryptography. John Wiley & Sons, 1996.	
8.2 Laboratory	Teaching methods	Remarks	
1.	Classical cryptography	explanation, testing 	The lab is scheduled as 2 hours every second week	
2.	Algorithm complexity	explanation, testing 		
3.	Modular arithmetics	explanation, testing 		
4.	Algorithms for testing primality	explanation, testing 		
5.	Factorization algorithms	explanation, testing 		
6.	Public-key cryptography	explanation, testing 		
7.	Practical aspects of public-key cryptosystems	explanation, testing 		
Bibliography
1. S. Crivei, A. Marcus, C. Sacarea, C. Szanto, Computational algebra with applications to cryptography and coding theory, Editura EFES, 2006.
2. A.J. Menezes, P.C. van Oorschot, S.A. Vanstone, Handbook of Applied Cryptography. CRC Press,
Boca Raton, 1997. (http://www.math.uwaterloo.ca/~ajmeneze)
3. B. Schneier, Applied Cryptography. John Wiley & Sons, 1996.	

9. Corroborating the content of the discipline with the expectations of the epistemic community, professional associations and representative employers within the field of the program

•	 The contents is directed towards practical applications of public-key cryptography. The topic is present in the computer science study programme of all major universities.	

10. Evaluation
Type of activity	10.1 Evaluation criteria	10.2 Evaluation methods	10.3 Share in the grade (%)	
10.4 Course	Use of basic concepts in examples	Assessments	50	
10.5 Lab	Implement course concepts and algorithms	Practical examination	50	
10.6 Minimum performance standards	
•	Grade 5	

Date		Signature of course coordinator 		Signature of seminar coordinator
25.09.2012	Assoc.Prof.PhD. Septimiu CRIVEI		Assoc.Prof.PhD. Septimiu CRIVEI

Date of approval						Signature of the head of department	
25.09.2012							Assoc.Prof.PhD. Octavian AGRATINI