I want to update the BIOS on my Gigabyte motherboard as this hopefully solves a problem. However, the archive containing the BIOS update and flashing tool can only be downloaded over http and there is no way to verify it's integrity as neither signed or non-signed checksums are available.
I'm extremely uncomfortable with just installing the update without being able to verify it's integrity, as I would forever think about if the BIOS has been modified in case the download server has been compromised or by MITM attack while I'm downloading.
What can I do?
But what you're saying points to a larger problem. How do you know that anything you download from any vendor (and that includes such hallowed things in the industry as Apple/Ubuntu/Red Hat/Microsoft/Google updates), is really secure?
The only way to get true security for anything is to build your own processor, build your own PC, write your own operating system, build your own network card, and then hope that there aren't any bugs...
Historically, things that were once thought to be secure -- have been proven over and over again not to be. Case in point: Windows NT -- it had labels all over the box, to the effect, "It's secure, it's secure". Well, fast forward 17 years or so. Numerous incidents and issues have historically proven those assertions to be in error... don't take my word for it... look at the history... Google "Windows NT security vulnerabilities" and you can also add the word "historical" in there, if you want.
That, and I'm pretty sure as a novice computer historian, that history repeats itself, although chances are that your BIOS might be perfectly safe even if you do download it with http (although, make no mistake about it, you are taking a chance, so "chance-taker beware", as the old saying goes...)
Computer security is a tough business, because on the one hand there's too little security, and on the other is outright paranoia... what's the correct balance between those two extremes? I sure as heck don't know...
Anyway... good luck with your BIOS update...