  From dice to modern complex circuits, there have been many attempts to build
increasingly better devices to generate random numbers. Today, randomness is
fundamental to security and cryptographic systems, as well as safeguarding
privacy. A key challenge with random number generators is that it is hard to
ensure that their outputs are unpredictable. For a random number generator
based on a physical process, such as a noisy classical system or an elementary
quantum measurement, a detailed model describing the underlying physics is
required to assert unpredictability. Such a model must make a number of
assumptions that may not be valid, thereby compromising the integrity of the
device. However, it is possible to exploit the phenomenon of quantum
nonlocality with a loophole-free Bell test to build a random number generator
that can produce output that is unpredictable to any adversary limited only by
general physical principles. With recent technological developments, it is now
possible to carry out such a loophole-free Bell test. Here we present certified
randomness obtained from a photonic Bell experiment and extract 1024 random
bits uniform to within $10^{-12}$. These random bits could not have been
predicted within any physical theory that prohibits superluminal signaling and
allows one to make independent measurement choices. To certify and quantify the
randomness, we describe a new protocol that is optimized for apparatuses
characterized by a low per-trial violation of Bell inequalities. We thus
enlisted an experimental result that fundamentally challenges the notion of
determinism to build a system that can increase trust in random sources. In the
future, random number generators based on loophole-free Bell tests may play a
role in increasing the security and trust of our cryptographic systems and
infrastructure.
