Encryption is only as strong as the secrecy of its key. Once a key leaks, an attacker can read any data protected by it. A new arXiv paper (1901.08083) puts a fresh light on secure data storage in distributed systems by revisiting computational secret sharing as a mitigation for exactly this scenario.
Computational secret sharing distributes data across multiple shares, so that no single share reveals the original information. The paper examines what happens when an attacker possesses the encryption key but only a subset of the shares. In that situation, the protection relies on the difficulty of reconstructing the secret from incomplete shares, rather than on key secrecy alone.
The abstract indicates the paper comes with several contributions, though the available snippet cuts off before listing them. As a single source, this digest cannot compare it with other work, but the paper is available in full on arXiv for those who want the details.