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I have an elliptic curve $E\left (\mathbb{F}_p \right )$, where $p=4ln-1$ is prime, for a small $l$

I am told there is a point $P \in E\left ( \mathbb{F}_p \right )$ of order $n$ which can be calculated as follows:

  • Choose a random $P'\in E \left ( \mathbb {F}_p\right )$
  • Set $P=\left [4l\right ]P'$

Could someone explain the $\left [ \cdot \right]$ notation to me please

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    Maybe it's the reduction modulo $4l$ of $P'$? – 2017-02-06
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    It's just multiplication by $4l$, which is to say it's $P'+P'+\cdots+P'$ with $4l$ summands. – 2017-02-06
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    @GerryMyerson can you explain what is assumed here (the order of the elements of $E(\mathbb{F}_p)$) ? – 2017-02-06
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    If you're told there's a point of order $n$, then you know there are points of all orders $d$ dividing $n$. I'm not sure if you can say much more than that. – 2017-02-06

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