Common randomness (CR) is an important resource for future communication paradigms. Identification is one such future communication paradigm, and it has been proven that CR-assisted identification can improve identification capacity by a double exponential factor. To achieve this, the common source of observation must be perfectly correlated and contain sufficient entropy. Channel reciprocity-based CR generation (alternatively termed Physical Layer Secret Key (PLSK) generation) is one such CR generation scheme. Existing high-rate CR generation is based on the Carrier Frequency Offset (CFO); for practical implementation, CFO-based CR generation would require a re-design of the existing protocol stacks to pass the CFO from the physical layer to the higher protocol layers. In contrast, we develop high-rate CR generation based on the Received Signal Strength Indicator (RSSI), which is highly practical as the RSSI is passed to and widely used by the higher protocol layers in existing communication protocol stacks. For RSSI-based CR generation, we demonstrate that the memory resources dedicated to storing channel information play an important role in achieving a high CR generation rate. Specifically, we demonstrate, through an experimental testbed with Ettus N210 USRPs Software Defined Radios (SDRs) (from which we make datasets publicly available), how allocating higher memory resources for storing accurate RSSI channel information at the terminals (transceivers) increases the achievable CR generation rate.