Assuming the inractability of factoring, we show that the
output of the exponentiation modulo a composite function
$f_{N,g}(x)=g^x\bmod N$ (where $N=P\cdot Q$) is pseudorandom,
even when its input is restricted to be half the size.
This result is equivalent to the simultaneous hardness of
the upper half of the bits of $f_{N,g}$, proven by Hastad,
Schrift and Shamir.
Yet, we supply a different proof that is significantly simpler
than the original one. In addition, we suggest a pseudorandom
generator which is more efficient than all previously known
factoring based pseudorandom generators.
Our work provides also an evidence for the difficulty of
the Decisional Diffie-Hellman problem, when considered modulo
a composite.
