Efficient Dynamic-Resharing "Verifiable Secret Sharing" Against Mobile Adversary

We present a novel efficient variant of Verifiable Secret Sharing (VSS) where the dealing of shares is dynamically refreshed (without changing or corrupting the secret) 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 valid 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 “escrowed 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 killed). Technically, we concentrate on simple direct methods that are combinatorial and numbertheoretic in nature, and employ only simple public-key functions (and no other cryptographic tools as did previous methods). We also present constant round protocols (e.g., a single round VSS) and do not use general (polynomial time, but inefficient) tools. We essentially reduce n out of t < n/2 VSS to n out-of n one (assuming ex-or homomorphic encryption), then we reduce dynamic resharing VSS to static VSS, finally we reduce proactive VSS (dynamic VSS with no dealer presence after sharing) to our dynamic resharing VSS.