Code-based cryptography is currently the second most promising post-quantum mathematical tool for quantum-resistant algorithms. Since in 2022 the first post-quantum standard Key Encapsulation Mechanism, Kyber (a latticed-based algorithm), was selected to be established as standard, and after that the National Institute of Standards and Technology post-quantum standardization call focused in code-based cryptosystems. Three of the four candidates that remain in the fourth round are code-based algorithms. In fact, the only non-code-based algorithm (SIKE) is now considered vulnerable. Due to this landscape, it is crucial to update previous results about these algorithms and their functioning. The Fujisaki-Okamoto transformation is a key part of the study of post-quantum algorithms and in this work we focus our analysis on Classic McEliece, BIKE and HQC proposals, and how they apply this transformation to obtain IND-CCA semantic security. Since after security the most important parameter in the evaluation of the algorithms is performance, we have compared the performance of the code-based algorithms of the NIST call considering the same architecture for all of them.
Acknowledgements
This work was supported in part by project ORACLE, PCI2020-120691-2, funded by MCIN/AEI/10.13039/501100011033, in part by QURSA project TED2021-130369B-C33 funded by MCIN/AEI/10.13039/501100011033, both of them co-funded by the European Union ‘NextGenerationEU’/PRTR, in part by P2QProMeTe (PID2020-112586RB-I00), funded by MCIN/AEI/10.13039/501100011033, and in part by the EU Horizon 2020 research and innovation programme, project SPIRS (grant agreement no. 952622).