Cryptography is traditionally considered as a main information security mechanism, providing several security services such as confidentiality, as well as data and entity authentication. This aspect is clearly relevant to the fundamental human right of privacy, in terms of securing data from eavesdropping and tampering, as well as from masquerading their origin. However, cryptography may also support several other (legal) requirements related to privacy. For example, in order to fulfil the data minimisation principle—i.e., to ensure that the personal data that are being processed are adequate and limited only to what is necessary in relation to the purposes for which they are processed—the use of advanced cryptographic techniques such as secure computations, zero-knowledge proofs or homomorphic encryption may be prerequisite. In practice though, it seems that the organisations performing personal data processing are not fully aware of such solutions, thus adopting techniques that pose risks for the rights of individuals. This paper aims to provide a generic overview of the possible cryptographic applications that suffice to address privacy challenges. In the process, we shall also state our view on the public “debate” on finding ways so as to allow law enforcement agencies to bypass the encryption of communication.