Space-Efficient Verifiable Secret Sharing Using Polynomial Interpolation

Preserving data confidentiality in clouds is a key issue. Secret Sharing, a cryptographic primitive for the distribution of a secret among a group of n participants designed so that only subsets of shareholders of cardinality 0 < t <= n are allowed to reconstruct the secret by pooling their shares, can helpmitigating andminimizing the problem. A desirable feature of Secret Sharing schemes is cheater detection, i.e., the ability to detect one ormoremalicious shareholders trying to reconstruct the secret by obtaining legal shares from the other shareholders while providing themwith fake shares. Verifiable Secret Sharing schemes solve this problemby allowing shareholders verifying the others' shares. We present new verification algorithms providing arbitrary secret sharing schemeswith cheater detection capabilities, and prove their space efficiency with regard to other schemes appeared in the literature. We also introduce, in one of our schemes, the Exponentiating Polynomial Root Problem (EPRP), which is believed to beNP-Intermediate and therefore difficult.