Francesca Guarnieri: Number theory and data security.
Diplom thesis, Ferrara 1998.
Original title: Teoria dei numeri e sicurezza dei dati.
INTRODUCTION

Data security
Public key cryptography

CONTINUOUS FRACTIONS

Formal continuous fractions and fundamental formulae
Continuous fraction representation of a real number
Equivalent numbers
Periodic continuous fractions
A theorem of Lenstra and Shallit
The free monoid SL(2,N)
Powers in SL(2,N)
The continuous fraction of \sqrt(n)
The algorithm of Walters and Davison for e^x
Conjugated words

FACTORIZATION METHODS AND PRIMALITY TESTS

The continuous fraction method for factorization
Factorization with random numbers
The Rabin-Miller test
The Pocklington-Lehmer test

GENERAL REMARKS

Authentication, digital signatures and trust centers
Electronic payment
Security of rooms and devices
Security problems of networks
Data security in medicine

REFERENCES