A Performance Analysis and Evaluation of SIDH Applied Several Implementation-Friendly Quadratic Extension Fields

It is well-known that quadratic extension fields (QEFs) based on optimal extension fields (OEFs) are typically used for supersingular isogeny Diffie-Hellman (SIDH) key exchange protocol. On the other hand, there is a possibility of the performance improvement of SIDH by employing other attractive choices of QEFs with efficient performing arithmetics which are based on all-one polynomial extension fields (AOPFs) and extension fields with normal basis representation (EFNs). Thus, the authors confirm that the applicability of the new candidates of QEFs for SIDH and evaluate SIDH applied the possible choices of QEFs. As a result of the experiment, the authors found that the performances of SIDH applied the QEFs based on AOPF and EFN are comparable to that of the previous QEF. Moreover, one of the QEFs based on EFN result in a new efficient implementation of the SIDH with SIDH-friendly prime given as p= 2^{e_A}3^{e_B}f+1 where e_A, e_B and $f$ are positive integers.