Invalid signature when trying to apt-get update on Kali

You're missing the key that Kali uses to sign their packages. You can use gpg to download the key and apt-key add to add it:

^{gpg --keyserver pgpkeys.mit.edu --recv-key ED444FF07D8D0BF6 gpg -a --export ED444FF07D8D0BF6 | sudo apt-key add}