I mentioned your first link, the factoring of a 768-bit RSA key, in my first comment. RSA isn't a "broken encryption scheme": it's a perfectly fine one. It's just that you need to use key lengths long enough to defend against the computing power available to current and expected adversaries. That paper is just a demonstration of modern computing power, which just shows that you should use longer keys.
Your second link has garbage sensationalized headline. It actually describes a side channel attack that has nothing to do with cryptography algorithms. It's basically equivalent to a clever way of looking over someone's shoulder.
No, he did:
>>> 1024 bit keys are endangered? .... You can't even break 256 bits
1024 bit key = most likely something like RSA
256 bit key = some symmetric algorithm or ECC
He's implying a 1024 bit RSA key should be safe because a 256 bit key from some other algorithm is.