A trapdoor one-way function for verifiable secret sharing

Abstract

This paper proposes a ( t , n ) –threshold verifiable secret sharing scheme with changeable parameters based on a trapdoor one-way function. This scheme consists of a generation phase, a distribution phase, an encoding phase and a reconstruction phase. The generation and distribution phases are, respectively, based on Shamir’s and Feldman’s approaches, while the encoding phase is based on a novel trapdoor one-way function. In the reconstruction phase, the shares and reconstructed secret are validated using a cryptographic hash function. In comparison with existing schemes, the proposed scheme leaks no direct information about the secret from public information. Furthermore, unlike some existing schemes, the generation and distribution phases of the proposed scheme are both independent of the secret. This feature leads to a number of advantages over existing approaches such as the dealer’s ability to perform the following modifications without updating the shares (i) modify the secret and (ii) adjust the threshold parameters of the scheme. Furthermore, each participant receives a single share, and designated participants can be given the privilege of choosing their own shares for reconstructing a secret S . Moreover, the proposed scheme possesses a high level of security which is inherited from the schemes of Shamir and Feldman, in addition to the trapdoor one-way function and the employed cryptographic hash function.