Nodes verification in P2P network?

Sorry if this is the wrong place to post, I’m new here (also r/programming doesn’t let me post text) Basically I’m learning programming and am doing really well so far and decided to create a p2p network using c#. Now I want to update a small application, on every node in this network – we are talking about 2000 nodes as an example. How would I do this? I thought of sending the new zip file to one node who would then proceed to sending this zip file to all the other nodes. The first node would verify if I have the rights to do so by simple AES encryption and then continue. But how could the other nodes verify that the node sending them the new zip file is an actual node and not some malicious user trying to infect my nodes? I don’t want to send the zip to each node separately – I want to push the zip file into the network, and then it should start to spread without any more input by me. My code works fine right now (sending file to one node who shares it with all other nodes), but I’m concerned about the security. Any ideas?

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