Can anyone explain to me why Paillier crypto system does not provide good performance?
I read here (pdf) that RSA and ElGamal provide better performance than Paillier algorithm.
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There is no way to know what the authors of that paper even did. They say they used Python, but mention no libraries. If it is their own implementation of those algorithms in Python, it may tell you next to nothing of the real world performance of optimized implementations those algorithms.
Further, they say they encrypted files of 68-235 KB, but do not explain how they did that when raw RSA/ElGamal/Paillier all encrypt much shorter messages. (Presumably some kind of blocking, but all details, including padding, are skipped in the explanation.)
This is all in addition to the suspicious key size choices @mikeazo mentioned already in the comments. So please do not take that paper as fact.
Now Paillier is actually slower, primarily because the computations are done modulo $n^2$, which is twice as many bits as the modulus in RSA for similar security. It is not actually that bad because there are various shortcuts/optimizations, but you would expect RSA to be faster because the computations are simpler.
ElGamal is somewhat different, being based on a different problem, but probably faster than RSA. It is also possible to use with elliptic curves, where it has significantly smaller keys etc. and good performance.
