SUPERSINGULAR TWISTED EDWARDS CURVES OVER PRIME FIELDS. I. SUPERSINGULAR TWISTED EDWARDS CURVES WITH j-INVARIANTS EQUAL TO ZERO AND [12.sup.3]

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 [12.sup.3] in different classes of curves are formulated and proved. Based on these results, co...

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Bibliographic Details
Published inCybernetics and systems analysis Vol. 55; no. 3; pp. 347 - 353
Main Authors Bessalov, A.V, Kovalchuk, L.V
Format Journal Article
LanguageEnglish
Published Springer 01.05.2019
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Summary: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 [12.sup.3] 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.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-019-00140-9