This appears to be a common problem in Ubuntu, and there look like there are several ways the install can go wrong. Based on the errors, it looks like it is a certificate problem. Most of the solutions involve reinstalling java certificates. What else have you tried?
Had this issue too, ultimately I completely removed OpenJDK (all versions) and just had Oracle Java Version 8. I tried updating the cert's, no change, but then I did the reinstallation of the certs and it started working for me. Also side note on linuxmint 19 Beta (based on Ubuntu 18.04). Perhaps try updating the cert again?
If that doesn't work you can install and run the Snap version, yes you can install minecraft via snap.
- Install snapd if it isn't already.
- Install Minecraft -- " sudo snap install minecraft "
Not sure about vanilla Ubuntu, but with Linuxmint 19 (Cinnamon) you may have to relog for a shortcut to it to show up in the menu.
Also if you want to install mods and are looking to install forge direct it to "/home/<you>/snap/minecraft/common/.minecraft " that's where the profiles and saves and etc are stored.