Could the Intel vulnerability have compromised private keys?

[taera249]

As you may know, Intel has been exposed heavily in the past few hours with 2 different exploits that can deliver pretty scare results if used maliciously:

Quote
Meltdown and Spectre

Bugs in modern computers leak passwords and sensitive data.

Meltdown and Spectre exploit critical vulnerabilities in modern processors. These hardware bugs allow programs to steal data which is currently processed on the computer. While programs are typically not permitted to read data from other programs, a malicious program can exploit Meltdown and Spectre to get hold of secrets stored in the memory of other running programs. This might include your passwords stored in a password manager or browser, your personal photos, emails, instant messages and even business-critical documents.

Meltdown and Spectre work on personal computers, mobile devices, and in the cloud. Depending on the cloud provider's infrastructure, it might be possible to steal data from other customers.

https://meltdownattack.com/

On the site you can see them in action:

What do you think about this when it comes to bitcoin?

Even if I moved all of my private keys into an airgapped laptop which has never seen the internet after being formatted, when I wanted to sign an offline transaction into the online node... the node is still connected to the internet, could somehow a exploit happen in the process?