Those two recent discoveries of a system vulnerability is due to hardware design and kernel development. One of the two has been partially addressed and fixed if you have updated your linux kernel to a patched one. The remaining seem pretty hard to be dealt with. In summary there is a way for memory handling to be leaked to the network revealing any sensitive information that may be temporarily retained as RAM or graphical memory. It is best not to read on rumors and interpretations but read the originals and monitor the status of fixing. At least temporarily you may change some habits and constantly wipe your memory to minimize the risk. Below find a set of links that official information originates and judge for yourself.https://meltdownattack.com/
https://spectreattack.com/
https://meltdownattack.com/meltdown.pdf
https://spectreattack.com/spectre.pdf
https://security-tracker.debian.org/tra … -2017-5715
https://security-tracker.debian.org/tra … -2017-5753
https://security-tracker.debian.org/tra … -2017-5754
https://xenbits.xen.org/xsa/advisory-254.html
https://googleprojectzero.blogspot.co.u … -side.html
http://blog.cyberus-technology.de/posts … tdown.html
https://01.org/security/advisories/intel-oss-10003