Score:0

what does "product of two cyclic groups" mean

dk flag

enter image description here

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.

Score:1
in flag

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.

mangohost

Post an answer

Most people don’t grasp that asking a lot of questions unlocks learning and improves interpersonal bonding. In Alison’s studies, for example, though people could accurately recall how many questions had been asked in their conversations, they didn’t intuit the link between questions and liking. Across four studies, in which participants were engaged in conversations themselves or read transcripts of others’ conversations, people tended not to realize that question asking would influence—or had influenced—the level of amity between the conversationalists.