This thesis studies the topic of the Paillier cryptosystem and its applications. Public key cryptosystems and homomorphic systems are described. Homomorphic systems can be grouped into partial and fully homomorphic schemes, and what characterizes them is the execution of various algebraic operations such as addition and multiplication over encrypted data without their prior decryption. It is therefore interesting in systems that must process information that is necessary to remain secure. Paillier’s cryptosystem is described through three main components: key generation, encryption, and decryption of information. In addition, its properties of additive and multiplicative homomorphism are described. It has been compared with other more well-known partial homomorphic schemes, and an overview of possible improvements is given. Finally, some possible applications are listed. As a part of the research, implementation in Python was made with an analysis of the efficiency of different parts of the cryptosystem.