After reading your link, I can't believe people think RSA keys are secure. Although, and this might sound naïve/dumb, but what is safer?

RSA *is* secure*, if you do it right. Crypto is hard to do right; a theoretically secure cryptosystem can very often be compromised by some tiny detail implemented incorrectly. The link describes an attack on RSA when key generation is not done right.
As far as I'm aware, the alternative to RSA is elliptic curve cryptography. I don't understand the mathematics behind it (yet), though.
* unless, of course, the NSA or somebody has an unpublished algorithm that breaks it, and until quantum computers are well-developed enough to make Shor's algorithm practical...

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