Course Details for A.Y. 2015/2016
Name:
Combinatorics and Cryptography / Combinatorics and Cryptography
Basic information
Credits:
: Master Degree in Mathematics 6 CFU (c)
: Master Degree in Mathematical Engineering 6 CFU (b)
Degree(s):
Master Degree in Mathematics 2nd anno curriculum Generale Elective
Master Degree in Mathematical Engineering 1st anno curriculum Comune Elective
Language:
English
Course Objectives
The student will be requested to have a good preparation on the presented topics, and to be able to implement some of the algorithms in a programming language
Course Content
- Abstract:
Basic cryptograpy and coding theory will be developed. Some protocols and algorithms will be discussed focusing an security and data integrity.
- Programme:
Elementary arithmetics:
Integers, divisibility, prime numbers, Euclidean division and g.c.d., Congruence classes, Chinese remainder theorem, cyclic and abelian groups, Lagrange theorem, Euler theorem, the structure of invertible classes mod p^n, Fields with p elements, polynomials, Euclidean division and g.c.d., Congruence classes of polynomials, Finite fields, primitive elements and polynomials, Legendre/Jacoby symbols and quadratic reciprocity.
Cryptography:
Classical cryptosystems: Shift cyphers, Vigenère Chipher, Substitution Chiper, One time pads, LFSR
Data Encryption Standard: Simplified DES and differential cryptanalysis, Attacks, password encryption
RSA: the algorithm, Attacks, Primality testing, the public key concept.
Discrete logarithms: Bit commitment, Diffie-Helman Key exchange, ELGAMAL
Hash function: SHA, birthday attacks
Digital signatures: RSA signatures, Hashing and signing, DSA
Error correcting codes:
Binary block codes, distance and correction of errors, classical bounds, linear codes, cyclic codes, Hamming codes, BCH and Reed-Solomon codes.
Assessment Methods and Criteria
oral examination
Textbooks
- Wade Trappe, Lawrence C. Washington, ntroduction to cryptography: with coding theory 2nd ed. , Pearson Prentice Hall. 2006.
Notes
- Si veda anche la pagina sul vecchio sito di ingegneria: http://www.ing.univaq.it/cdl/scheda_corso.php?codice=I0323_I4I
Course page updates
This course page is available (with possible updates) also for the following academic years:
To read the current information on this course, if it is still available, go to the university course catalogue .
Course information last updated on: 11 maggio 2016, 12:35