ABSTRACTIn Shamir's (t,n) secret sharing (SS) scheme, the secretsis divided intonshares by a dealer and is shared amongnshareholders in such a way that anytor more thantshares can reconstruct this secret; but fewer thantshares cannot obtain any information about the secrets. In this paper, we will introduce the security problem that an adversary can obtain the secret when there are more thantparticipants in Shamir's secret reconstruction. Asecure secret reconstruction scheme, which prevents the adversary from obtaining the secret is proposed. In our scheme,Lagrange components, which are linear combination of shares, are used to reconstruct the secret. Lagrange component can protect shares unconditionally. We show that this scheme can be extended to design a multi‐secret sharing scheme. All existing multi‐secret sharing schemes are based on some cryptographic assumptions, such as a secure one‐way function or solving the discrete logarithm problem; but, our proposed multi‐secret sharing scheme is unconditionally secure. Copyright © 2013 John Wiley & Sons, Ltd.