You might want to read this, Enhancing ADC resolution by oversampling:
http://www.atmel.com/images/doc8003.pdf
http://www.analog.com/en/analog-dialogue/articles/adc-input-noise.html
Adding 1 LSB of white noise to the analog input enhances the AD conversion. The DUE has a True Random Number Generator (TRNG) which passes the American NIST Special Publication 800-22 and Diehard Random Tests Suites.
The TRNG is able to provide a white noise (with a Gaussian characteristic) thru a DAC.
And there is a Library for the Arduino DUE SSC in I2S mode, ArduinoDueHifi: