Attacks on RSA cryptosystem with small private exponent

U ovom radu predstavljeni su rizici RSA kriptosustava sa malim tajnim eksponentom. Rad se sastoji od tri cjeline. Prvi dio sadrži matematičku osnovu potrebnu za razumijevanje teme diplomskog rada. U sklopu drugog dijela dana je teorijska osnova za shvaćanje RSA kriptosustava, prvog kriptosustava s javnim ključem, kao i sama implementacija RSA kriptosustava. Također, u ovom dijelu opisana je sigurnost RSA kriptosustava te potencijalni rizici. Posljedni dio sadži neke od napada na RSA kriptosustav s malim tajnim eksponentom. Primjenom grube sile moguće je probiti svaki kriptosustav, no taj posao nije efikasan. Javljaju se algoritmi koji koriste neke slabosti kriptosustava, te u razumnom vremenu razbijaju kriptosustav. Obrađeni napadi probijaju RSA kriptosustav s malim tajnim eksponentom do N^{\delta } za \delta ≥ 1/4. Najpoznatiji od njih je Wienerov napad koji koristi verižne razlomke, a najjači je Boneh i Durfee napad koji koristi rešetke.This paper presents the risks of RSA with small private exponent. The paper consists of three parts. The first part provides the mathematical basis needed for the understanding of the thesis. Within the second part, the theoretical basis for the understanding of RSA, the first public key cryptosystem, is given, as well as its implementation. Further more, this part explains the security of RSA and the potential risks. The last part contains some of the attacks on the RSA cryptosystem with small private exponent. Every cryptosystem can be broken using brute-force search attack. However, this is not practical. Advanced algorithms use some of the weaknesses of cryptosystem, and are able to break cryptosystem in a reasonable time. All of the attacks can efficiently break RSA with private exponents up to N^{\delta } for some \delta ≥ 1/4.The best known of these algorithms is the Wiener’s attack that uses a continued fractions, but the strongest is Boneh and Durfee’s attack that uses the lattice