What tax law is being violated? If the company releases and pays taxes on the income it is just income, no different than ad generated income or booby generated income.
If you're lending your PC to a company, which makes money by calculating something, you'd have to sign some sort of an agreement. And you'd have to be paid for your involvement. You can be paid 0, obviously, but it is still a formal operation (i.e. "being paid 0" <> "not being paid").
Keep in mind that the company that uses your PC has to fill their balance sheet properly and it has to report where their revenue came from.
And if you're neither an employee not a subcontractor (another company), this instantly becomes a grey market activity. You can't enroll an unrelated, natural person to work for you or lend you anything - with or without payment.
World is pretty complicated on its own and adding corporate legal issues doesn't help. Don't blame me.
There are other concerns as well. E.g.: if such website mining wrecks your PC, are you eligible for compensation? You haven't agreed for this. You don't even know it's running.
Are you into volunteer computing?
http://boinc.berkeley.edu/wiki/Usage_rules
"The BOINC project and the University of California assume no liability for damage to your computer, loss of data, or any other event or condition that may occur as a result of participating in BOINC-based projects."
It ain't to get me to look at the hamburger, and it isn't for me to give my mouth something to do, it is to fill my stomach and provide my body with nutrients. If they blended it up, and fed it to me through a tube inserted directly into my stomach instead of me eating it, it would still serve its purpose. Different delivery method, same purpose fulfilled.
That's not what you said about ads. You said their only purpose is making money for the company. So this would have to be true for products in general, including burgers.
Whether you like it or not, the purpose of an advertisement is to
inform you about a product. And if it was hidden from view (like the mining window is), it wouldn't serve this purpose.
I.e. a TV commercial becomes an advertisement when it's aired for the first time. Before that it's just a corporate video.
The good thing about it is that you can actually sue a company for false advertising.
In fact, usually the first term of service is the Acceptance of the Terms of Service that state something along the lines of if you access or use the website, you are agreeing to the terms of service. The websites that use these miners all have terms and services, and buried in those terms of service is you giving them permission to do this either directly or indirectly.
You're right about the terms of service in general, but again: what's the purpose of this website? If I'm opening a porn site, am I agreeing to anything? Can they come to my house and kidnap my children? Because, based on how porn business is often connected to criminal organisations, it's clearly not out of their scope.
It is revenue. As long as they pay taxes on that revenue, there is no legal issue there. Try again.
Wrong side of the problem. There is a legal issue, because they haven't sold you anything. They bought something! (borrowed your PC)
So for them it's not about a product. It's about means of production.
They should pay you and you should pay the income tax.