Cheapest way to securely connect to close networks

The location of this scenario is a two-floor appartment in a house with more appartments that all share the same cellar. In the cellar, there is a room with a box where all the LAN cables for all the appartments meet. That’s right, there is a central patch panel for all people. The two floors of the appartment are only connected through the patch panel, with a LAN outlet for each floor that both go down to the patch panel. The goal is to create a single network in which all devices in the appartment can talk to each other. However, there are stupid devices (ironically called “smart” devices by their sellers) that cannot encrypt their traffic, so a MitM attack from the cellar becomes trivial since the patch panel is accessible to anyone. On the other hand, once out of the outlet in the appartment, the network is safe from tampering. I therefore have two distinct, tempering-proof zones that are connected by an insecure link.

I visualized the situation in this ferocious piece of art:

Visualization of the described situation

So my question is: What is the cheapest way to link those floors securely at 1Gbps/s speed? This would be the magic “??” star in each zone. With enough budget, those would simply be two routers, one at each outlet, tunelling traffic between the two floors. However I know of no router model that is both cheap and able to deliver Gigabit through a secure VPN.

Are there special boxes out there to perform the job? Or is there a very affordable router (less than $ 100) that delivers enough throughput? Or am I doomed to tape an extra LAN cable to the stairs despite theoretically having an existing infrastructure?

What is the difference between nearest and cheapest insertion algorithms for a Traveling salesman problem?

I know that in the cheapest insertion algorithm we include the node which is not in the “base group” that has smaller cost given all possible combinations, and for the nearest we include the node with smaller cost. So, do they differ only in how combinations are made?

For example, I have the following weighted matrix graph:

     2  13  14  17  20 2  0.0 Inf Inf 1.9 1.7 13 Inf 0.0 7.3 7.4 7.2 14 Inf 7.3 0.0 7.7 7.8 17 1.9 7.4 7.7 0.0 9.2 20 1.7 7.2 7.8 9.2 0.0 

If I start from node 2 from each method:

Nearest

1) 2-20-2

2.1) 2-17-20-2 = 12,8

2.2) 2-17-20-2 = 12,8 *Choosen

3.1) 2-13-20-17-2 = Inf

3.2) 2-20-13-17-2 = 18,2 *Choosen

3.3) 2-20-17-13-2 = Inf

4.1) 2-14-20-13-17-2 = Inf

4.2) 2-20-14-13-17-2 = 26,1

4.3) 2-20-13-14-17-2 = 25,8 *Choosen one

4.4) 2-20-13-17-14-2 = Inf

Cheapest

1) 2-20-2 2.1.a) 2-13-20-2 = Inf

2.1.b) 2-20-13-2 = Inf

2.2.a) 2-14-20-2 = Inf

2.2.b) 2-20-14-2 = Inf

2.3.a) 2-17-20-2 = 12,8

2.3.b) 2-20-17-2 = 12,8

So, with the cheapest approach, do I explicitly make all combinations?

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