Abstract

In our paper paper we propose a new binary elliptic curve of the form $a[x^2+y^2+xy+1]+(a+b)[x^2y+y^2x]=0$. If $m\geq 5$ we prove that each ordinary elliptic curve $y^{2}+xy=x^{3}+\alpha x^2+\beta,  \beta\neq 0$ over $\mathbb{F}_{2^m}$, is birationally equivalent over $\mathbb{F}_{2^m}$ to our curve. This paper also presents the formulas for the group law.

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