Cryptosystems are based on various computationally hard problems, such as the factorization problem and the discrete logarithm problem. Pascal Paillier studied the Composite Residuosity Class Problem, which represents a new computationally hard problem. In 1999, he proposed a new cryptosystem whose security is based on this problem. The homomorphic property of the Paillier cryptosystem enables new applications, such as the use in electronic elections. In this thesis, we study the Paillier cryptosystem and its homomorphic properties, which allow us to perform operations on encrypted data without decrypting it in the process. We prove its correctness and security. We use the cryptosystem as the basis for electronic voting in the semi-honest model. We conclude by describing three voting protocols, which differ from each other in terms of the number of candidates for which we can vote.
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