DAC's output voltage managment on Arduino Due

You would need to transform the 12-bit DUE ADC to a virtual 13-bit ADC. The answer to this is oversampling, inputing white noise (dithering) and averaging.

http://www.atmel.com/images/doc8003.pdf

Note that the DUE TRNG controller is able to produce a gaussian noise (white noise).

And be careful, the DUE is 3.3V compliant only.