Performance of Radical Isogenies Using the Hybrid Strategy Sample Clauses

Performance of Radical Isogenies Using the Hybrid Strategy i ∈ In this subsection, we benchmark the performance of radical isogenies when the hybrid strategy of Sect. 5 is used to integrate radical isogenies into CSIDH. Concretely, in comparison to the previous benchmark, we allow a strategy using both V´elu and radical isogenies for degree 3/9. We denote this by CRAD-H, and used our code to estimate the expected running time. We compared this against the results from Table 3. As a corollary of Lemma 3, CRAD-H may effectively become a ‘traditional’ CSIDH implementation, when mr = 0 turns out to be most optimal for all i R (i.e. we get the trivial ‘hybrid’ paramaters of ordinary CSIDH). We see this happening for primes larger than 1024 bits due to the scaling issues with radical isogenies. Table 4 shows the results4. Interestingly, an implementation using non-trivial hybrid parameters out- performs any of the other implementations for a prime of 512 bits. This shows that radical isogenies can improve performance in constant-time when using the hybrid strategy. We conclude that replacing V´elu 3-isogenies with radical 9-isogenies is too costly, but adding radical 9-isogenies after V´elu 3-isogenies can be cost effective. However, due to the scaling issues of radical isogenies, the value mr quickly drops to 0 and we get trivial parameters for primes larger than 1024 bits, implying that traditional CSIDH performs better for large primes than any