Designing secure voting protocols is a notoriously challenging task, yet it helps offering a more verifiable and more accessible electoral process. Among the difficulties faced when building such protocols, receipt-freeness, or the inability of voters to prove how they voted, is a particularly hard property to achieve. Cryptography, the science of secure communications, has become a key ingredient in this quest of building privacy-friendly and trustworthy voting protocols. In this thesis, we develop new cryptographic algorithms in this regard. Equipped with these new tools, we then proceed to build secure voting protocols, with a particular attention to receipt-freeness. The first part of this thesis introduces a new cryptographic primitive, Traceable Receipt-Free Encryption and a new security notion, traceable CCA security, which are particularly well-suited to generically build single-pass receipt-free protocols. We then propose efficient realizations of this primitive based on standard cryptographic assumptions. The limits of this primitive are also explored, and we expose that it is impossible to achieve another property, cast-as-intended verifiability, without any interactive process with the voting server when the voting client is not trusted. This interaction can either have the form of a prior trusted registration or a casting process in several rounds. On the positive side, we build new protocols and we show that it is possible to attain these two properties simultaneously in each of these interactive scenarios. The second part of the thesis focuses on more practical settings. First, we explore how a popular and well-established ballot preparation protocol can be optimized. Especially, this protocol needs to verifiably encrypt many bits representing the choices of voters, and we study how to efficiently compute these encryptions and a proof that they effectively contain bits. Finally, we investigate postal voting protocols, an alternative to online voting systems. While being extensively used in practice in many countries, postal voting received little attention from the academic community so far. Hence, we propose a new security model and a new paper-based protocol that achieves better verifiability properties.