Redistribution of mechanical secret shares

Abstract

Vaults are used extensively in the financial world. Some of these vaults use a secret sharing scheme in which the shares are mechanical keys. Reorganization of a corporation sometimes requires to change the access structure of those authorized to open the vault. Although changing access structure is studied in the context of secret sharing schemes, the techniques are inadequate in the case that the shares are mechanical keys. For example, some schemes require that an existing secret sharing scheme (vault in our case) be fitted with new sets of shares (mechanical keys in our case). That is a number of share sets (key sets) be produced that open the same vault. Making such a modification to a mechanical vault is very expensive, if at all possible. We study how one can redistribute secret shares only by using copying of these shares, which is the only operation one can allow to deal with mechanical shares without changing the mechanical vault mechanism.