On correctness of conditions for the CSIDH algorithm implementation on Edwards curves

Incorrect formulation and incorrect solution of the problem CSIDH algorithm implementation on Edwards curves was revealed in one famous works. The purpose this paper is to present a detailed critique such concept with proof its inconsistency. Specific properties three non-isomorphic classes super singular generalized form are considered: full, quadratic, twisted curves. Conditions for existence all 3 order over prime field determined. isogenies odd degrees based use quadratic twist pairs elliptic To end, can be built both complete within class, forming twist. In contrast this, authors well-known work trying prove theorems that state there class parameter which square. critical analysis theorems, lemmas, erroneous statements carried out. Theorem 2 proved. modification presented. illustrate correct problem, an example Alice Bob calculations secret sharing scheme according considered for.