A Multi-stage Secret Sharing Scheme Using All-or-Nothing Transform Approach

Abstract

Abstract.A multi-stage secret sharing (MSS) scheme is a method of sharing a number of secrets among a set of participants, such that any authorized subset of participants could recover one secret in every stage. The first MSS scheme was proposed by He and Dawson in 1994, based on Shamir's well-known secret sharing scheme and one-way functions. Several other schemes based on different methods have been proposed since then. In this paper, the authors propose an MSS scheme using AllOr-Nothing Transform (AONT) approach. An AONT is an invertible map with the property that having "almost all" bits of its output, one could not obtain any information about the input. This characteristic is employed in the proposed MSS scheme in order to reduce the total size of secret shadows, assigned to each participant. The resulted MSS scheme is computationally secure. Furthermore, it does not impose any constraint on the order of secret reconstructions. A comparison between the proposed MSS scheme and that of He and Dawson indicates that the new scheme provides more security features, while preserving the order of public values and the computational complexity.

Share secrets stage by stage with homogeneous linear feedback shift register in the standard model

“…From Table , it is easy to see that Fatemi scheme requires the most and our schemes requires the least public information. Li et al .…”

“…Two categories of MSS according to the secret reconstruction have been proposed, the multistage SSS (MSSS) and the general MSS (GMSS); and depending on any specific situation, each category may be preferable. In a GMSS, all of the secrets are reconstructed simultaneously in one stage , while, in an MSSS, the secrets have different levels of importance, and any authorized subset of the participants can recover only one secret in each stage . In the literature, there are two different types of MSSSs.…”

“…In the literature, there are two different types of MSSSs. In the first type (MSSST1), the secret reconstruction can be executed in any order, for example, the schemes . In the second type (MSSST2), the secret reconstruction must be executed in the dealer's predefined order, for example, .…”

“…Most of the earlier proposed MSSs (GMSSs and MSSSs) with threshold access structure are simple modification of the SSS of Shamir . In fact, in either of these threshold MSSs , the dealer employs polynomials in order to distribute the secrets, and the authorized participants should use the Lagrange interpolation formula to recover them. In 2008, for the first time, we employed linear feedback shift registers (LFSRs) instead of polynomials in GMSSs .…”

Scalable secret sharing of compressed multimedia

“…This all-or-nothing (Fatemi et al, 2009) property might not be suitable for certain applications, which require the secret data to be gradually reconstructed based on the number of shares available.…”