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I am reading "Elliptic curve cryptosystems" and the link is here(https://www.ams.org/journals/mcom/1987-48-177/S0025-5718-1987-0866109-5/S0025-5718-1987-0866109-5.pdf). I don't understand the meaning of "product of two cyclic groups" in it. Can anyone explain it to me? It's better to have a simple example.

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It means that the group of points of $E_K$ is isomorphic to $\mathbb{Z}_n \times \mathbb{Z}_m$ (2-dimensional vectors). Addition of points on $E_K$ corresponds to addition of vectors. In other words, the group is generated by (at most) two points: there exists points $P,Q$ (generators) such that any point $V$ can be written as $[a]P + [b]Q$ for some integers $a,b$. Here, $(a,b) \in \mathbb{Z}_n \times \mathbb{Z}_m $ is the vector representation.

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