The prospect of quantum computing has long been a field of interest in cryptography, as many prevalent public-key algorithms relying on computationally difficult problems may be compromised by a quantum computer with sufficient resources. This threshold still seems distant, but the design and development of quantum-resistant algorithms is an interesting and important topic nonetheless.
Hamming Quasi-Cyclic (HQC) is a code-based public key encryption scheme and a submission to the NIST Post-Quantum Cryptography Standardization project. This scheme relies heavily on coding theory, utilizing syndrome decoding over systematic quasi-cylic codes to provide efficient and secure public key encryption (HQC.PKE) and key encapsulation (HQC.KEM). This paper is a review of the theoretical background and implementations of this scheme and the advantages it offers in a post-quantum landscape.