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Let \(Ep\) be an elliptic curve over a finite field \(\mathbb{F}p\), where \(p\) is a prime. We denote this by \(Ep / \mathbb{F}p\). and we denote the group of points of \(Ep\) over \(\mathbb{F}p\), with order \(q=# E\left(\mathbb{F}p\right)\). For this curve, we call \(\mathbb{F}p\) the “base field” and \(\mathbb{F}_q\) the “scalar field”.