@Kumasasa It could also be that their system time is off by a lot, thus meaning the computer renders the SSL certificate as invalid, I read that from MCL-346
Wait, nevermind. It is working now... Strange...
Sure seems that way. Shouldn't it say "Refreshing Auth" or something?
To prove my theory:
[04:16:25 INFO]: Finished downloading C:\Users\Owner\AppData\Roaming\.minecraft\versions\1.7.9\1.7.9.jar for job 'Version & Libraries': Couldn't connect to server (SSLException: 'Invalid TLS padding data') but have local file, assuming it's good
[04:16:25 INFO]: Job 'Version & Libraries' finished successfully (took 0:00:01.320)
Hmmm... It seems as though your internet is coming across an SSL error, and you have the local file, but it might be corrupted. That is what it looks like to me.
If the above doesn't work, please try opening whatever terminal your system uses and type the following:
Normally, OpenJDK 7 works better than Oracle/Sun's Java.
After the install finishes, remove Sun/Oracle's Java from your system.
Please post your results afterwards.