Noise canceling cell phone case

I working on, just like it sounds, a cellphone case that when activated would render the microphone inside the cell phone unable to distinguish background audio. Im not sure yet if true audio canceling would be the best way but that's how I'm moving forward. Ive been reading up on noise canceling headphones but cant find any suitable Arduino software and I am prepared to make it myself. I have no previous Arduino experience other then setting up my 3d printer. Any points in the right direction?

You can do some research into how noise-canceling microphones work, but they are imperfect since all sounds are air-pressure waves. And the noise-frequencies are usually in the voice-band, although you can filter-out the very-high and very-low frequencies. Generally they work by getting your lips right up next to the microphone and they try to cancel sounds from other directions and sounds that are farther away.

A noise canceling headset is not what you want, but it's more effective because it cancels the acoustic soundwaves without canceling the electrical signal.

Neither of these require digital processing, and the Arduino makes a lousy digital audio processor anyway.

You just need to play loud pink or white noise directly at the microphone on the phone to
deafen it… Much more robust and simple.

Or make the case out of solid thick steel and line it with several layers of acoustic felt/padding?

So the ultimate plan was to be able to play mp3 such that if the phone was being monitored the mp3 would be what was heard and no suspicion would be aroused. Thats why I passed on white noise. I Looked at for a schematic and it seems doable, But with your suggestion and DVDdoug’s warning that it would not be effective enough, I may look back into white noise.

A rustling noise like its bashing around in a noisy bag might be more what you want? Amplitude modulated
noise perhaps.