  Randomness in Bell test data can be device-independently certified by Bell's
theorem without placing assumptions about the experimental devices. The
device-independent randomness has very demanding requirement about the
experimental devices and relatively lower output randomness. With the same Bell
test data we can extract substantially more randomness without using Bell's
theorem. To achieve this goal, we introduce a remote state preparation
dimension witness and a semi-device-independent randomness certification model
which is based on it. This is one important step towards practical use of Bell
test in randomness generation.
