  A remarkable aspect of quantum theory is that certain measurement outcomes
are entirely unpredictable to all possible observers. Such quantum events can
be harnessed to generate numbers whose randomness is asserted based upon the
underlying physical processes. We formally introduce, design and experimentally
demonstrate an ultrafast optical quantum random number generator that uses a
totally untrusted photonic source. While considering completely general quantum
attacks, we certify and generate in real-time random numbers at a rate of
$8.05\,$Gb/s with a rigorous security parameter of $10^{-10}$. Our security
proof is entirely composable, thereby allowing the generated randomness to be
utilised for arbitrary applications in cryptography and beyond. To our
knowledge, this represents the fastest composably secure source of quantum
random numbers ever reported.
