PQC CSIKE algorithm on noncyclic Edwards curves with simultaneous formation of two independent keys encapsulation
DOI:
https://doi.org/10.30837/rt.2026.1.224.04Keywords:
the curve in generalized Edwards form, complete Edwards curve, twisted Edwards curve, quadratic Edwards curve, curve order, point order, isomorphism, isogeny, group action function, public key, secret key, encapsulation key, w-coordinatesAbstract
Using a 2-processor computer, parallel calculation of two different encapsulation keys in the original CSIKE algorithm with one public key instead of two in CSIDH is proposed. The conditions for its implementation on two classes of noncyclic Edwards curves are substantiated. The properties of quadratic and twisted supersingular Edwards curves that form quadratic ttwist pairs with order p+1≡0mod8 over the prime field Fp are considered. For every curve in these classes with parameter d, there exists an isomorphic curve with parameter d^-1. On a set of isomorphic curves, the second encapsulation key can be computed simultaneously with the first. For all isogenies of degrees 3, 5, 7, the parameters d of chains of isogenies of noncyclic supersingular Edwards curves on period T of chains of isogenies for p=839 is calculated. The simulation of the CSIKE scheme with Alice encrypting two independent keys encapsulation with Bob's public key, as well as the stage of decapsulation by Bob of these keys, is considered. The implementation of parallel computations provides almost perfect protection against side-channel attacks, because it is impossible to set the task of measuring the computation time of fragments of two different isogeny chains.
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