In the era of Big Data, releasing private data to the future is a challenging problem. Making private data accessible at a future point in time requires mechanisms to keep the encryption keys of encrypted private data secure and undiscovered so that protected data is not available prior to the legitimate release time and the data appears automatically at the expected release time. In this paper, we develop new mechanisms to support self-emerging data storage that securely hide keys of encrypted data in a Distributed Hash Table (DHT) network that makes the encryption keys automatically appear at the predetermined release time so that the protected encrypted private data can be decrypted at the release time. We show that a straight-forward approach of privately storing the keys in a DHT is prone to a number of attacks that could either make the hidden data appear before the prescribed release time (release-ahead attack) or destroy the hidden data altogether (drop attack). We develop a suite of self-emerging key routing schemes on DHTs for securely storing and routing the encryption key in the DHT. We show that the proposed scheme is resilient to both release-ahead attack and drop attack as well as to attacks that arise due to traditional churn issues in DHT networks. Our experimental evaluation demonstrates the performance of the proposed schemes in terms of attack resilience and churn resilience.