Sharing several secrets based on Lagrange's interpolation formula and Cipher feedback mode

Abstract

In a multi-secret sharing scheme, several secret values are distributed among a set of n participants. In 2000 Chien et al.’s proposed a (t;n) multi-secret sharing scheme. Many storages and public values required in Chien’s scheme. Motivated by these concerns, some new (t;n) multi-secret sharing schemes are proposed in this paper based on the Lagrange interpolation formula for polynomials and cipher feedback mode (CFB), which are easier than Chien’s scheme in the secret reconstruction and require fewer number of public values and storages than Chien’s scheme. Also our schemes don’t need any one-way function and any simultaneous equations.