We present the cryptographic primitives needed in the construction of electronic voting systems based on homomorphic encryptions and on verifiable secret sharing. Then "The theory and implementation of an electronic voting system" by Ivan Damgård, Jens Groth and Gorm Salomonsen is presented as an example of electronic voting systems based on homomorphic encryptions, while "Multi-authority secret-ballot election with linear work" by Ronald Cramer, Matthew Franklin, Berry Schoenmakers and Moti Yung is presented as an example of electronic voting systems based on verifiable secret sharing. Moreover, the mathematical background for these systems are studied with particular emphasis on the security issues of the relevant sub-protocols. Comparing these two examples we find that the presented voting system based on verifiable secret sharing is more secure then the one based on homomorphic encryptions, both in regard to privacy and robustness. On the other hand, we find that the presented voting system based on homomorphic encryptions is more efficient then the one based on verifiable secret sharing
