  Random numbers are a fundamental ingredient for many applications including
simulation, modelling and cryptography. Sound random numbers should be
independent and uniformly distributed. Moreover, for cryptographic applications
they should also be unpredictable. We demonstrate a real-time self-testing
source independent quantum random number generator (QRNG) that uses squeezed
light as source. We generate secure random numbers by measuring the quadratures
of the electromagnetic field without making any assumptions on the source; only
the detection device is trusted. We use a homodyne detection to alternatively
measure the Q and P conjugate quadratures of our source. Using the entropic
uncertainty relation, measurements on P allow us to estimate a bound on the
min-entropy of Q conditioned on any classical or quantum side information that
a malicious eavesdropper may detain. This bound gives the minimum number of
secure bits we can extract from the Q measurement. We discuss the performance
of different estimators for this bound. We operate this QRNG with a squeezed
state and we compare its performance with a QRNG using thermal states. The
real-time bit rate was 8.2 kb/s when using the squeezed source and between
5.2-7.2 kb/s when the thermal state source was used.
