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Reza Rezaeian Farashahi

Publications and source records attributed to Reza Rezaeian Farashahi.

5 recordsLinked to original sources
arXiv2026

Differential Addition on Twisted Edwards Curves

This paper presents new differential addition (i.e., the addition of two points with the known difference) and doubling formulas, as the core step in Montgomery scaler multiplication, for twisted Edwards curves. The formulas are provided with cost of 5M+4S+1D, 3M+7S+1D when the given difference point is in affine form. Here, M,S,D denote the costs of a field multiplication, a field squaring and a field multiplication by a constant, respectively.

math.NT↗
arXiv2026

Differential addition on Jacobi quartic Curves

In this paper we present new differential addition and doubling formulas for Jacobi quartic curves. Several differential addition and doubling formulas are presented with cost of 5M+4S+1D,3M+7S+1D,3M+6S+3D when the given difference point is in affine form. Here M,S,D denote the costs of a field multiplication, a field squaring and a field multiplication by a constant, respectively.

math.NT↗
arXiv2010

On group structures realized by elliptic curves over a fixed finite field

We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all elliptic curves over a finite field. We use these formulas to derive some asymptotic estimates and tight upper and lower bounds for various counting functions related to classification of elliptic curves accordingly to their group structure. Finally, we present results of some numerical tests which exhibit several interesting phenomena in the distribution of group structures. We pose getting an explanation to these as an open problem.

math.NT↗