  In this paper we investigate properties of several randomness generation
protocols in the device independent framework. Using Bell-type inequalities it
is possible to certify that the numbers generated by an untrusted device are
indeed random. We present a selection of certificates which guarantee two bits
of randomness for each run of the experiment in the noiseless case and require
the parties to share a maximally entangled state. To compare them we study
their efficiency in the presence of white noise. We find that for different
amounts of noise different operators are optimal for certifying most
randomness. Therefore the vendor of the device should use different protocols
depending on the amount of noise expected to occur. Another of our results that
we find particularly interesting is that using a single Bell operator as a
figure of merit is rarely optimal.
