Secret sharing schemes with cheating detection

A secret sharing scheme allows a secret to be shared among a set of participants, P, such that only authorized subsets of P can recover the secret, but any unauthorized subset can not recover the secret. It can be used to protect important secret data, such as cryptographic keys, from being lost or destroyed without accidental or malicious exposure. In this paper, we consider secret sharing schemes based on interpolating polynomials. We show that, by simply increasing the number of shares held by each participant, there is a multiple assignment scheme for any monotone access structure such that cheating can be detected with very high probability by any honest participant even the cheaters form a coalition in order to deceive him.