title: Aritmetica finita e crittografia a chiave pubblica.
Un percorso didattico per studenti delle Scuole Medie Superiori
[Finite arithmetic and public-key cryptography: a didactic
approach for high school students]
author: Giovanni Alberti
published in "Ricordando Franco Conti [Remembering Franco Conti]",
pp. 21-29. Edited by A. Abbondandolo, M. Giaquinta, F. Ricci.
Pubblicazioni del Centro di Ricerca Matematica Ennio De Giorgi,
Scuola Normale Superiore, Pisa 2004.
ISBN: 8876421378
version: published (October 15, 2004) plus minor corrections
abstract: This paper contains an edited version of the notes
from a series of lectures held first in 2001 and then again in
2004 within a program "Seminari sulla matematica [Seminars on
Mathematics]" organized every year by the Mathematics Department
of the University of Pisa and aimed to senior high school
students.
The purpose of my lectures was to to explain some elementary
results in modular arithmetic, and show a few applications to
cryptography.
After a first lecture on cryptography and public-key cryptography
I introduced the basic notions of arithmetic modulo n, a suitably
simplified notion of computational cost of an algorithm, the
Euclidean algorithm for computing the greatest common divisor of
two integers, and Fermat's little theorem. Finally, in the fourth
(and last) lecture explaining the RSA algorithm for public-key
cryptography.
A preliminary version of these notes appeared in 2001 with title
"Aritmetica e crittografia [Arithmetic and cryptography]"