Our main motivation is to design more user-friendly security protocols. Indeed, if the use of the protocol is tedious, most users will not behave correctly and, consequently, security issues occur. An example is the actual behavior of a user in front of an SSH certificate validation: while this task is of utmost importance, about 99% of SSH users accept the received certificate without checking it. Designing more user-friendly protocols may be difficult since the security should not decrease at the same time. Interestingly, insecure channels coexist with channels ensuring authentication. In practice, these latters may be used for a string comparison or a string copy, e.g., by voice over IP spelling. The shorter the authenticated string is, the less human interaction the protocol requires, and the more user-friendly the protocol is. This leads to the notion of SAS-based cryptography, where SAS stands for Short Authenticated String. In the first part of this thesis, we analyze and propose optimal SAS-based message authentication protocols. By using these protocols, we show how to construct optimal SAS-based authenticated key agreements. Such a protocol enables any group of users to agree on a shared secret key. SAS-based cryptography requires no pre-shared key, no trusted third party, and no public-key infrastructure. However, it requires the user to exchange a short SAS, e.g., five decimal digits. By using the just agreed secret key, the group can now achieve a secure communication based on symmetric cryptography. SAS-based authentication protocols are often used to authenticate the protocol messages of a key agreement. Hence, each new secure communication requires the interaction of the users to agree on the SAS. A solution to reduce the user interaction is to use digital signature schemes. Indeed, in a setup phase, the users can use a SAS-based authentication protocol to exchange long-term verification keys. Then, using digital signatures, users are able to run several key agreements and the authentication of protocol messages is done by digital signatures. In the case where no authenticated channel is available, but a public-key infrastructure is in place, the SAS-based setup phase is avoided since verification keys are already authenticated by the infrastructure. In the second part of this thesis, we also study two problems related to digital signatures: (1) the insecurity of digital signature schemes which use weak hash functions and (2) the privacy issues from signed documents. Digital signatures are often proven to be secure in the random oracle model. The role of random oracles is to model ideal hash functions. However, real hash functions deviate more and more from this idealization. Indeed, weaknesses on hash functions have already been discovered and we are expecting new ones. A question is how to fix the existing signature constructions based on these weak hash functions. In this thesis, we first try to find a better way to model weak hash function. Then, we propose a (randomized) pre-processing to the input message which transforms any weak signature implementation into a strong signature scheme. There remains one drawback due to the randomization. Indeed, the random coins must be sent and thus the signature enlarges. We also propose a method to avoid the increase in signature length by reusing signing coins. Digital signatures may also lead to privacy issues. Indeed, given a message and its signature, anyone can publish the pair which will confirm the authenticity of the message. In certain applications, like in electronic passports (e-passports), publishing the authenticated data leads to serious privacy issues. In this thesis, we define the required security properties in order to protect the data privacy, especially in the case of e-passport verification. The main idea consists for the e-passport to keep the signature secret. The e-passport should only prove that it knows a valid signature instead of revealing it. We propose a new primitive, called Offline Non-Transferable Authentication Protocol (ONTAP), as well as efficient implementations that are compatible with the e-passport standard signature schemes.