My first approach would be to use a couple of bandpass filters that are reasonably spread out over the frequency.
If all of the filters get "sufficiently much" simultaneous signal energy out of them when you send in your data, you can assume that you have a wide energy spectrum (which is one of the characteristics of white noise).
If that wouldn't work, I would use a DFT like philfrei suggested. Note that you have to split up the data in smaller chunks where you smooth the edges. The bandpass filter approach is probably cheaper though but if you use many filters it may not.
You can probably use the filter part of a vocoder as well, if I am not mistaken