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