NUMBER THEORY AND CRYPTOGRAPHY
Academic year and teacher
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- Versione italiana
- Academic year
- 2016/2017
- Teacher
- PAOLO CODECA'
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- MAT/05
Training objectives
- The aim of this course is to give an introduction to modern public-key cryptography.We present also the necessary mathematical tools.
Prerequisites
- None
Course programme
- Natural numbers.Divisibiliy.Prime numbers.Greatest common divisor.Euclidean algorithm.Linear congruences.Complete and reduced system of residues.Abelian groups.Chinese remainder theorem.Euler-Fermat theorem.Quadratic congruences.The law of quadratic reciprocity.Legendre and Jacobi symbols.Primitive roots and indices.Running time of the euclidean algorithm and of powermod.Primality testing.Cryptographical appplications.R.S.A.,Rabin,and El Gamal cryptosystems.Key exchange schemes.The Diffie-Hellman problem.The Massey Omura protocol.Digital signatures.
Didactic methods
- Theoretical/practical lessons.
Learning assessment procedures
- We have a four-hour written examination,divided in two parts.
- In the first part ( two hours of time),the candidates must solve problems strictly linked with the cryptosystems they have studied (for example how to cipher and decipher messages,how to use digital signatures or key exchange systems,etc..)
- In the second part ( two hours of time) the candidates must prove mathematical results which are fundamental in the applications (for example the running time of euclidean algorythm and of modular power,how cryptosystems like R.S.A.,El Gamal and Rabin work and why they are considered difficult to crack,etc...).
Passing the final exam is the proof that knowledge and abilities outlined in the training objectives of the course have been achieved. Reference texts
- -Stinson,Douglas R."Cryptography-Theory and practice"
Chapman & Hall/CRC.2002
-Koblitz,Neal "A course in number theory and Cryptography" Second edition;Springer,1994.
-Languasco,A.,Zaccagnini,A. "Introduzione alla crittografia" Hoepli(Informatica).2004
