How does bitcoin network verify transaction is allowed by each user?

Hi, I’m interested in the cryptocurrency because I don’t know it well, and people talk it’s evolution of network.
Therefore, I’m reading bitcoin’s white paper first, and planing to read Ether.

So, here’s my question.
How can bitcoin public the transaction but knows it was permitted by each user?

For example,
Let’s set owner A wants to send 1 btc to owner B.

  1. A’s private key is sent to the transaction node, A and B’s public key is sent to transaction node.

  2. A and B’s public key is sent to the transaction node.

Which is right?

If 1 is right, then transaction node can hack the A’s wallet.
If 2 is right, then transaction node can make a fake transaction.

Each way have problem.
How did bitcoin solved it?

I think, transaction must made by each owner.
But it’s not…
I really need help…

Hi @user,

Thanks for being a part of the GitHub community! We’re glad you’re here.

I wanted to jump in and mention that if you’re looking for help for this specific topic, you might want to try asking for help somewhere that focuses on bitcoin. It’s definitely possible that another GitHub user might have run into this same issue and can help, but the GitHub Community Forum focuses primarily on topics related to GitHub itself or collaboration on project development and ideas. We want to make sure you’re getting the best support you can, but this forum may not be the right place for this particular topic.

Best of luck!