An improved multi-stage secret sharing scheme based on the factorization problem

Lee and Hwang proposed a multi-stage (t, n) secret sharing scheme which has fewer public values than pervious schemes. In their scheme, a group of participants share multiple secrets stage-by-stage, and only one secret share should been kept by each participant. However, in this article, we will show that multiple secrets cannot, in fact, be reconstructed stage-by-stage by the secret holder's determination and that the secret holder cannot determine the values of the secrets in Lee and Hwang's scheme. Moreover, their scheme belongs to the family of one-time-use schemes. At the same time, we shall also modify their scheme to improve the above weaknesses and show the improved scheme can be applied. The security of the proposed scheme is based on the factorization problem which provides higher security confidenc than using the hash function in Harn's and Chang et al.'s multi-stage secret sharing schemes.