Abstract
An analysis of existence conditions of supersingular twisted Edwards curves over a prime field is given. Theorems on the conditions of existence of supersingular curves with j-invariants equal to zero and 123 in different classes of curves are formulated and proved. Based on these results, concrete parameters for some supersingular curves are obtained. A generalization of the results obtained earlier using an isomorphism of curves in Weierstrass and Edwards forms is given.
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