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.

翻译：量子技术的进步正威胁着我们的日常网络安全，因为一台具备量子计算能力的计算机可以破解当前所有已使用非对称密码系统。为迎接量子时代，美国国家标准与技术研究院（NIST）于2016年启动了一项标准化进程，涵盖公钥加密（PKE）方案、密钥封装机制（KEM）和数字签名方案。2023年，NIST又针对后量子签名提出了额外征集。本章旨在对基于编码的密码学进行综述，重点关注PKE和签名方案。我们涵盖了基于编码密码学中的主要框架，并分析了其安全性假设。我们以讲义风格提供数学背景知识，旨在面向更广泛的读者群体。