  By testing the classical correlation violation between two systems, the
random number can be expanded and certified without applying classical
statistical method. In this work, we propose a new random number expansion
protocol without entanglement, and the randomness can be guaranteed only by the
2-dimension quantum witness violation. Furthermore, we only assume that the
dimensionality of the system used in the protocol has a tight bound, and the
whole protocol can be regarded as a semi-device independent black-box scenario.
Comparing with the device independent random number expansion protocol based on
entanglement, our protocol is much easier to implement and test.
