  The improvements on quantum technology are threatening our daily
cybersecurity, as a capable quantum computer can break all currently employed
asymmetric cryptosystems. In preparation for the quantum-era the National
Institute of Standards and Technology (NIST) has initiated in 2016 a
standardization process for public-key encryption (PKE) schemes,
key-encapsulation mechanisms (KEM) and digital signature schemes. In 2023, NIST
made an additional call for post-quantum signatures. With this chapter we aim
at providing a survey on code-based cryptography, focusing on PKEs and
signature schemes. We cover the main frameworks introduced in code-based
cryptography and analyze their security assumptions. We provide the
mathematical background in a lecture notes style, with the intention of
reaching a wider audience.
