The IETF P2PSIP Working Group is currently designing a standard overlay protocol, named RELOAD, that employs a centralized node identifier (node-id) assignment for security reasons. Given this scenario, we propose the utilization of a Low Discrepancy Sequence (LDS) for the assignment of node-ids in the P2PSIP architecture. We perform an analytical and simulation study considering a Chord DHT that demonstrates that using a LDS-based node-id assignment guarantees a fair distribution of the node's zone of responsibility, even in high churn scenarios. Previous studies have shown that a fairer distribution of the zones of responsibility sizes leads to a fairer distribution of the storage and routing load. Therefore we conclude that the proposed LDS node-id assignment provides these features without adding any extra overhead.