Counting points on twisted Edwards curves over finite fields
DOI:
https://doi.org/10.54654/isj.v1i16.912Keywords:
counting points, twisted Edwards curve, Montgomery curve, Weierstrass curve, elliptic curveTóm tắt
Abstract— In this paper, we are interested in counting points on a twisted Edwards curve defined over a finite field. In particular, we construct explicit formulae allowing to determine exactly the number of k-rational points on a twisted Edwards curve when the number of k-rational points on the birational equivalent curve of Weierstrass or Montgomery form respectively is known. Using these formulae, we introduce an algorithm to count points on the twisted Edwards curve define over a finite field.
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