Enhancing secret sharing security : A verifiable hierarchical threshold model and cheating detection based on integer factorization

Secret sharing is the sharing of a secret between n shareholders so that only predefined subsets can retrieve the secret and other subsets called unauthorized subsets can not access the secret. In secret sharing, dishonest shareholders can always get exclusive access to the secret by offering a fake share, and other honest shareholders are deceived by getting a fake secret. Cheating detection is a well-known term in secret sharing that helps prevent cheating by dishonest participants in the secret reconstruction phase. In this paper, we propose a verifiable hierarchical threshold secret sharing model and a cheating detection scheme based on the difficulty of integer factorization. In this scheme, it is possible to verify the combiner by the shareholders so that they can recognize fake combiners, and the combiner in this scheme can never find out the contents of the secret. Also, in this paper, the security of secret restoration has significantly increased.