OPERATIONS ON THE TWISTED EDWARS CURVE, AND ITS APPLICABILITY IN CRYPTOGRAPHY
DOI:
https://doi.org/10.32689/maup.it.2021.1.8Keywords:
finite field, algebraic curve, group of points of an elliptic curve, divisibility of a point of a curve in half, generator of cryptostable sequenceAbstract
Most cryptosystems in modern cryptography can naturally be «translated» into elliptical curves. We consider Edwards algebraic curves over a finite field, which are currently one of the most promising carriers of point sets used for fast group operations available in asymmetric cryptosystems, in particular, for constructing random cryptostable sequences. It is shown that the projective curve is not elliptical. The conditions for the existence of divisibility in half of an element from the group of points of a twisted Edwards curve, which is important in algorithms, are investigated. The genus of the twisted Edwards curve is found. The aim of this work is to find the criterion for dividing the point of the curve in half over the field and to analyze the properties of the twisted Edwards curve necessary to construct a generator of pseudo-random cryptostable sequences and construct a one-way function for it.
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