Security Limitations of Using Secret Sharing for Data Outsourcing

Three recently proposed schemes use secret sharing to support privacy-preserving data outsourcing. Each secret in the database is split into n shares, which are distributed to independent data servers. A trusted client can use any k shares to reconstruct the secret. These schemes claim to offer security even when k or more servers collude, as long as certain information such as the finite field prime is known only to the client. We present a concrete attack that refutes this claim by demonstrating that security is lost in all three schemes when k or more servers collude. Our attack runs on commodity hardware and recovers a 8192-bit prime and all secret values in less than an hour for k = 8.