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.