Course Details for A.Y. 2015/2016

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

• A.Y. 2012/2013
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• A.Y. 2019/2020