Abstract of the diploma thesis: RSA cryptosystem is a public-key cryptosystem. It provides privacy and ensures authenticity of digital data. Security of RSA cryptosystem is based on intractability of RSA problem and integer factorization problem. Diploma consists of description, analysis and implementation of RSA cryptosystem. First two chapters present cryptography and mathematical tools for understanding RSA cryptosystem. Third chapter describes RSA cryptosystem and it's use in RSA encryption scheme and RSA signature scheme. Chapter 4 focuses on attacks on RSA cryptosystem and related security. As a student of applied mathematics I emphasized the implementation of RSA cryptosystem. The chapter about implementation includes descriptions of a algorithms, which were used to develop the enclosed software "RSA Encrypter&Signe r v1.0". It supports generation of RSA keys, encryption with RSA encryption scheme and digital signature with IFSSA scheme, included in the IEEE P1363 standard. My main goal was to introduce the reader to public-key cryptography, in particular to RSA cryptosystem, and with my implementation aid eventual developers of this or any similar cryptosystem.
Keywords: RSA cryptosystem, attacks on RSA, implementation of RSA,
cryptography, encryption, digital signatures, Euclidean algorithm,
congruences, primitive roots, primes, factorization, primality.
Math. subj. class (2000): 94A60, 68P25, 11A05, 11A07, 11A41, 11A51
Povzetek diplomskega dela: RSA kriptosistem spada med kriptositeme z javnimi ključi. Uporablja se za zagotavljanje zasebnosti in pristnosti podatkov. Varnost RSA kriptosistema temelji na težavnosti problema RSA in problema faktorizacije velikih števil. Diplomsko delo obsega opis, analizo in implementacijo RSA kriptosistema. Uvodni poglavji predstavita kriptografijo in matematična orodja, potrebna za razumevanje RSA kriptosistema. Tretje poglavje opiše RSA kriptosistem in njegovo uporabo v RSA šifrirni shemi in shemi RSA elektronskega podpisa. Sledi obravnava napadov na RSA kriptosistem in s tem povezane varnosti. Kot študent uporabne matematike sem poudarek posvetil implementaciji RSA kriptosistema. Poglavje o implementaciji vsebuje pregled algoritmov, ki sem jih uporabil pri programu "RSA Encrypter&Signer v1.0". Program je priložen diplomskemu delu na CD-ROM-u. Omogoča generiranje RSA ključev, šifriranje po RSA šifrirni shemi in elektronski podpis po shemi IFSSA, ki je del standarda IEEE P1363. Namen diplome je predstaviti bralcu pomembnost javne kriptografije, konkretno RSA kriptosistema, in mu z zgledom olajšati morebitno implementacijo tega ali kakega podobnega kriptosistema.
Ključne besede: RSA kriptosistem, napadi na RSA, implementacija RSA, kriptografi ja, šifriranje, elektronski podpis, Evklidov algoritem, kongruence, primitivni elementi, praštevila, faktorizacija, praštevilskost