Breaking Mignotte's Sequence Based Secret Sharing Scheme Using SMT Solver

TL;DR

This paper demonstrates how to break the security of Mignotte's sequence-based secret sharing scheme by employing an SMT solver to reconstruct the secret with fewer shares than the threshold.

Contribution

The authors introduce a novel approach using an SMT solver to reconstruct secrets in Mignotte's sequence-based schemes with fewer shares than traditionally required.

Findings

SMT solver can reconstruct secrets with fewer shares

Mignotte's scheme is vulnerable to this attack

New method improves secret recovery efficiency

Abstract

The secret sharing schemes are the important tools in cryptography that are used as building blocks in many secured protocols. It is a method used for distributing a secret among the participants in a manner that only the threshold number of participants together can recover the secret and the remaining set of participants cannot get any information about the secret. Secret sharing schemes are absolute for storing highly sensitive and important information. In a secret sharing scheme, a secret is divided into several shares. These shares are then distributed to the participants one each and thus only the threshold (t) number of participants can recover the secret. In this paper we have used Mignotte's Sequence based Secret Sharing for distribution of shares to the participants. A (k, m) Mignotte's sequence is a sequence of pair wise co-prime positive integers. We have proposed a new method for reconstruction of secret even with t-1 shares using the SMT solver.