This bachelor's degree thesis deals with homomorphic public-key cryptography, or in other words cryptosystems with special addition properties. Such cryptosystems are widely used in real life situations, for instance to make electronic voting secure. In Chapter 1 a few basic algebra results and other key concepts are introduced. Chapters 2 and 3 contain the algorithms and properties of the two cryptosystems which are considered to be the best for e-voting: Paillier and Joye-Libert. The thesis is concluded in Chapter 4, by comparing running times of the two above-mentioned cryptosystems, in simulations of real-life e-voting systems, with up to tens of thousands of voters, and different levels of security. Through these simulations, we discern the situations where each of the two cryptosystems is preferable.