4 citations · 5 across the 6 of their papers we have counts for
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Differential addition on Jacobi quartic Curves
Seyed Golamhossein Hosseini, Reza Rezaeian Farashahi
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 5…
Differential Addition on Twisted Edwards Curves
Seyed Gholamhossein Hosseini, Reza Rezaeian Farashahi
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 multiplicati…
On Pseudopoints of Algebraic Curves
Reza R. Farashahi, Igor E. Shparlinski
Following Kraitchik and Lehmer, we say that a positive integer is an -pseudosquare if it is a quadratic residue for each odd prime , yet is not a squar…
Pseudorandom Bits From Points on Elliptic Curves
Reza R. Farashahi, Igor E. Shparlinski
Let $\E$ be an elliptic curve over a finite field $\F_{q}$ of elements, with , given by an affine Weierstraß equation. We also use to denote the -compone…
On group structures realized by elliptic curves over a fixed finite field
Reza Rezaeian Farashahi, Igor E. Shparlinski
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 form…