Analysis of the FO Transformation in the Lattice-Based Post-Quantum Algorithms

González de la Torre MÁ, Hernández Encinas L, Queiruga-Dios A
Mathematics 2022, 10, 2967.

Newer variants of the Fujisaki–Okamoto transformation are used in most candidates of the third round of the NIST Post-Quantum Cryptography standardization call in the category of public key encryption schemes. These transformations are applied to obtain a highly secure key encapsulation mechanism from a less secure public key encryption scheme. Furthermore, there are five candidates (three finalists and two alternatives) that passed to the third round of the process and whose security is based in lattice problems. This work analyzes the different ways in which the lattice-based candidates of the NIST call apply the Fujisaki–Okamoto transformation and the particularities of each application. The study of such differences and their repercussion in the design of the proposals will allow a better understanding of the algorithms. Moreover, we propose a modification of the Kyber algorithm—the only public key encryption candidate established as a PQC standard by NIST in its more recent publication—in order to avoid the re-encryption in the decapsulation algorithm and, in this way, to reduce the side channel attacks vulnerability.

Funding. This work was supported in part by ORACLE Project, with reference PCI2020-120691-2, funded by MCIN/AEI/10.13039/501100011033, and European Union “NextGenerationEU/PRTR” and in part by the Spanish State Research Agency (AEI) of the Ministry of Science and Innovation (MCIN), project P2P2QProMeTe (PID2020-112586RB-I00/AEI/10.13039/501100011033), and in part by the EU Horizon 2020 research and innovation programme, project SPIRS (Grant Agreement No. 952622).