How to securly share files within a local network
My setup is simple. I have a router that is connected to the Internet via a phone socket (ADSL). In addition, I have two computers which connect wirelessly to the router. Both computers are running Linux Mint (no other operating systems are involved).
I would like to share files between my two computers. One use of this would be, for example, to view on computer B, a video file that is stored on computer A. Or at least to be able to copy the file over, without using a memory stick, and then watch it locally.
I'm not sure whether computer A and B can 'talk' directly with each other, or whether the router needs to be involved in the process.
Another important aspect is I do not want to compromise the security of my network. I want computer A and B to share files between them but not to any other computer.
Could someone please point me in the right direction?