Asymmetric cryptography uses two keys for encryption public key and for decryption private key. The asymmetric cryptosystems include RSA, ElGamal, Elliptic Curves and others. Generally, asymmetric cryptography is mainly used for secure short messages and transmission encryption key for symmetric cryptography. The thesis deals with these systems and implements selected systems (RSA, ElGamal, McEliece, elliptic curves and NTRU) into the application. The application can test the features of chosen cryptosystems. These systems and their performance are compared and evaluated with the measured values. These results can predict the future usage of these systems in modern informatics systems.

The security and integrity of TLS certificates are essential for ensuring secure transmission over the internet and protecting millions of people from man-in-the-middle attacks. Certificate Authorities (CA) play a crucial role in issuing and managing thesecertificates. This bachelor thesis presents a longitudinal analysis of certificate chains forpopular domains, examining their evolution over time and across different categories. Using publicly available certificate data from sources such as crt.sh and censys.io, we createda longitudinal dataset of certificate chains for domains from the Top 1-M list of Tranco.We categorized the certificates based on their type, and the particular service categories.We analyzed a selected set of domains over time and identified the patterns and trendsthat emerged in their certificate chains. Our analysis revealed several noteworthy trends,including an increase in the use of new CAs and a shift of which types of certificates areused, we also found a trend in shorter certificate chains and fewer paths from domain toroot certificate. This implies a more streamlined and simplified certificate process overtime until today. Our findings have implications for the broader cybersecurity communityand demonstrate the importance of ongoing monitoring and analysis of certificate chainsfor popular domains.