A Survey on Code-Based Cryptography
It addresses the need for post-quantum cryptographic standards for cybersecurity, but is incremental as a survey.
The paper surveys code-based cryptography as a solution to quantum computing threats to current asymmetric cryptosystems, covering frameworks and security assumptions for public-key encryption and signature schemes.
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.