White noise generator for audio jamming ( from 250 Hz to 4.5 KHz )
Seems like the optimum spectrum for masking speech yet not sounding too unpleasant is a 'haystack' spectrum that mimics speech. White noise is more unpleasant than pink noise but neither apparently work all that well. Cambridge Sound Management makes their opinion fairly clear: 


  Both white noise and pink noise are anything but unobtrusive, and neither is very
  effective at blocking speech. Should a vendor attempt to convince you that his system is better
  than another because it uses “pink” noise rather than “white” noise, run the other way, don’t walk.
  Such a vendor is at best naïve, and more likely a borderline charlatan.




Keep in mind that the document I lifted this from is intended to promote their products, but I think the principle is sound (no pun intended).

If you want to make white noise (which can be shaped into pink noise with a filter), the usual method is with a pseudo-random number generator. This can be a few CMOS chips or a small microcontroller. You might be able to do even better if you have a better processor by playing with speech samples. Of course if the samples or "white noise" are predictable it might be possible for someone to remove the noise.