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Author/Affiliation: Abdelalim SeddikOpen AccessArticle
5 Pages, 287 KB 
Group law and the Security of elliptic curves on \(F_p[e_1,...,e_n]\)
Abstract:
In this paper, we study the elliptic curve \(E_{a,b}(A_P)\), with \(A_P\) the localization of the ring \(A=F _p[e_1,...,e_n]\) where \(e_ie_i=e_i\) and \(e_ie_j=0\) if \(i\neq j\), in the maximal ideal \(P=(e_1,...,e_n)\). Finally we show that \( \text{Card}(E_{a,b}(A_P)) \geq (\text{Card}(E_{a,b}(F_p)) - 3)^n + \text{Card}(E_{a,b}(F_p)) \) and the execution time to solve the problem of discrete logarithm in \(E_{a,b}(A_P)\)…
Read More(This article belongs to Section Applied Mathematics (MAP))