The use of communication protocols has become pervasive at all levels of our society. Yet, their uses come with risks, either about the security of the system or the privacy of the user. To mitigate those risks, we must provide the protocols with strong security guarantees: we need formal, extensive, modular and machine-checked proofs. However, such proofs are very difficult to obtain in practice. In this Thesis, we strive to ease this process in the case of cryptographic protocols and powerful attackers. The four main contributions of this Thesis, all based on symbolic methods, are 1) a methodology for extensive analyses via a case study of multi-factor authentication; 2) composition results to allow modular proofs of complex protocols in the computational model; 3) symbolic methods for deciding basic proof steps in computational proofs, formulated as problems on probabilistic programs; 4) a prototype of a mechanized prover in the Computationally Complete Symbolic Attacker model.