Post Quantum cryptography is of great interest among the cryptographic research community. It is motivated by the need to find new schemes to keep cryptographic applications secure, even after large-scale quantum computers become available. For this reason, the National Institute of Standards and Technology (NIST) is currently running the PQC competition to standardize new PQC schemes. Even though not part of the competition, one promising candidate is the isogeny-based Commutative Supersingular Isogeny Diffie Hellman (CSIDH) [https://eprint.iacr.org/2018/383] key exchange scheme. CSIDH offers small keys and can be used as drop-in replacement in Diffie-Hellman-based protocol, such as Signals end-to-end encryption protocol for mobile messenger. The downside of CSIDH is its rather expensive performance. To this end Castryck and Decru published CSIDH on the surface (CSURF) in 2020 [https://eprint.iacr.org/2019/1404], which gives an 5.68% improvement. The same authors later revisited CSURF with some small tweaks to the arithmetic of the scheme [https://homes.esat.kuleuven.be/~wcastryc/summer_school_csurf.pdf]. In this work, we present the first implementation of the updated CSURF using optimized Fp arithmetic. While the results can not confirm the improvements of 5.68% by Castryck and Decru, we propose new parameters for a 511-bit prime that can tie the performance of a state-of-the-art CSIDH implementation.

based on [https://ctidh.isogeny.org/software.html]

Average cost in Mcyc for 1.300.000 runs.

Average Fp-arithmetic cost for 1.300.000 runs.