Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Licenţă
Domeniul: Calculatoare şi tehnologia informaţiei
Programul de studii: Ingineria informatiei - in limba engleza
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MML0007	Computational Algebra	

Semester	Hours: C+S+L+P	Category	Status	
4	2+0+1+1	complementary	optional	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
CRIVEI Septimiu	Ph.D.	Assoc.Prof.	Algebra, Mathematical Analysis and Geometry	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
An introduction to Computational Algebra by a survey of applications of algebraic algorithms in Cryptography, Coding Theory and Conceptual Knowledge Processing and Representation.	

IV. Course contents
1. Notions of algorithms complexity. The O notation, classes of complexity.
2. Congruences and residue classes. Euclid@s algorithm, Euler@s function, Chinese remainder theorem, quadratic residues, Legendre@s symbol.  Public key encryption algorithms: RSA, ElGamal. Electronic signatures. Hash functions.
3. Primality tests. Fermat, Solovay-Strassen and Miller-Rabin primality tests, deterministic tests.
4. Factorization methods. Elementary methods, Rho method, factor bases method, continued fractions method, quadratic sieve method. Applications to Cryptography and Coding Theory. Linear codes, cyclic codes, Reed-Muller codes.
5. Polynomials over finite fields. Finite fields, discret logarithm, irreducible polynomials, Berlekamp@s algorithm of polynomial factorization. Applications to Cryptography.
6. Other algorithms. Fast addition, fast Fourier transform.	

V. Bibliography
1. W. Bosma, A. van der Porten, Computational Algebra and Number Theory, Kluwer 1995. 
2. D. Bressoud, S. Wagon, A Course in Computational Number Theory, Springer-Verlag 2000. 
3. H. Cohen, A Course in Computational Algebraic Number Theory, Springer-Verlag, 2000.
3. H. Cohen, A.M. Cuypers, H. Sterk, Some Tapas of Computer Algebra, Springer-Verlag,  1999. 
4. R. Crandall, C. Pomerance, Prime Numbers. A Computational Perspective, Springer-Verlag, 2001.
5. K. Ireland, M. Rosen, A Classical Introduction to Number Theory, Springer-Verlag, 1990.
6. N. Koblitz, A Course in Number Theory and Cryptography, Springer-Verlag, 1994.
7. R. Lidl, G. Pilz, Applied Abstract Algebra, Springer-Verlag, 1998.
8. A.J. Menezes, P.C. van Oorschot, S.A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, 1997.
9. B. Schneier, Applied Cryptography, John Wiley & Sons, New York, 1996.
10. H.S. Wilf, Algorithmes et complexite, Masson, Paris, 1989.	

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Exam.	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Assoc.Prof. CRIVEI Septimiu, Ph.D.