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]"