  We study random number expansion protocols based on the $n \to 1$ quantum
random access codes (QRACs). We consider them in the semi-device independent
scenario where the inner workings of the devices are unknown to us but we can
certify the dimensions of the systems being communicated. This approach does
not require the use of the entanglement and makes the physical realization of
these protocols much easier than in the standard device independent scenario.
In our work, we propose a protocol for randomness expansion, compute
min-entropy for the semi-device independent protocol, and investigate $n\to 1$
QRACs with a view to their use in randomness expansion protocols. We also
calculate the dependence of the effectiveness of the randomness generation on
$n$ and find it optimal for $n=3$, and provide the explanation for this fact.
