Hybrid Approach to Public-Key Algorithms in the Near-Quantum Era

Application of post-quantum algorithms in newly deployed cryptosystems is necessary nowadays. In the NIST Post-Quantum Competition several algorithms that seem to be resistant against attacks mounted using quantum computers have been chosen as finalists. However, it is worth noting that one of finalists—SIKE—was catastrophically broken by a classical attack of Castryck and Decru only a month after qualifying for the final round. This shows that absolute trust cannot yet be placed in the algorithms being standardized. And so a proposition was made to use the novel, post-quantum schemes alongside the well-studied classical ones with parameters chosen appropriately to remain secure against quantum attacks at least temporarily, i.e., until a large enough quantum computer is built. This paper analyzes which classical public-key algorithms should be used in tandem with the post-quantum instances, and studies how to ensure appropriate levels of both classical and quantum security. Projections about the development of quantum computers are reviewed in the context of selecting the parameters of the classical schemes such as to provide quantum resistance for a specified amount of time.