Efficient dynamic-resharing “verifiable secret sharing” against mobile adversary

Abstract

We present the notion of "Dynamic Re-sharing Verifiable Secret Sharing" (VSS) where the dealing of shares is dynamically and randomly refreshed (without changing or corrupting the secret). It works against the threat of the recently considered mobile adversary that may control all the trustees, but only a bounded number thereof at any time period. VSS enables a dealer to distribute its secret to a set of trustees, so that they are assured that the sharing is vMid and that they can open it later, and further no small group of trustees can open it prematurely. Recently, such sharing of cryptographic tools gained much attention, e.g., in the context of "key escrow cryptography;' where a user enables a group of trustees to potentially open its information (when authorized by the Court). Our dynamic-sharing VSS allows for mobile adversary attacking different sets of trustees at different time periods (modeling, e.g., network viruses that get spread as well as get elinlinated). Technically, we concentrate on simple direct methods that are conlbinatorim and number-theoretic in nature, and employ only simple public-key functions. (All previous schemes withstanding linear number of faults embedded secrets in polynomials which we do not do). In addition, our protocols are constant round. The work is a sequence of reductions. We reduce t(t