  The extraction of randomness from weakly random seeds is a topic of central
importance in cryptography. Weak sources of randomness can be considered to be
either private or public, where public sources such as the NIST randomness
beacon broadcast the random bits once they are generated. The problem of
device-independent randomness extraction from weak public sources against
no-signalling adversaries has remained open. In this paper, we show protocols
for device-independent and one-sided device-independent amplification of
randomness from weak public Santha Vazirani (SV) sources that use a finite
number of devices and are secure against no-signaling adversaries.
Specifically, under the assumption that the device behavior is as prescribed by
quantum mechanics the protocols allow for amplification of public $\epsilon$-SV
sources for arbitrary initial $\epsilon \in [0,0.5)$. On the other hand, when
only the assumption of no-signaling between the components of the device is
made, the protocols allow for amplification of a limited set of weak public SV
sources.
