How can I detect if my router is backdoored, or being used as a residential proxy?
The most surefire way would be to put a device between your router and your ONT/modem to capture the packets and see what requests are being sent. It's not complicated but it IS a lot of information to sift through.
Your router may have the ability to log requests, but many don't, and even if yours does, if you're concerned the device may be compromised, how can you trust the logs?
BUT, with all that said, these attacks are typically not very sophisticated. Most of the time they're searching for routers at 192.168.1.1 with admin/admin as the login credentials. If you have anything else set, you're probably good from 97% of attackers (This number is entirely made up, but seriously that percentage is high). You can also check for security advisories on your model of router. If you find anything that allows remote access, assume you're compromised.
---
As a final note, it's more likely these days that the devices running these bots are IoT devices and web browsers with malicious javascript running.
> How can I detect if my router is backdoored, or being used as a residential proxy?
Aside from the obvious smoke tests (are settings changing without your knowledge? Does your router expose access logs you can check?), I'm not sure there's any general purpose way to check, but 2 things you can do are:
1. search for your router's model number to see if it's known to be vulnerable, and replace it with a brand-new reputable one if so (and don't buy it from Amazon).
2. There are vendors out there selling "residential proxy IP databases", (e.g., [1]) no idea how good they are, but if you have a stable public IP address you could check whether you're on that.
If it’s legit you can ask your ISP if they sell use of your hardware. Or just don’t use the provided hardware and instead BYO router or modem or media converter or whatever.
But I think what OP is implying is insecure hardware being infected by malware and access to that hardware sold as a service to disreputable actors. For that buy a good quality router and keep it up to date.
I'm dealing with such attack, so if you'd like, you can send me IPv4 addresses, and I'll grep my logs for them. Email address is on the website linked on my profile.
As for what you can do on your own, it really depends on your network. OpenWRT routers can run tcpdump, so you can check for suspicious connections or DNS requests, but it gets really hard to tell if you have lots of cloud-tethered devices at home. IoT, browser extensions, and smartphone applications are the usual suspects.