An improvement on the Lin-Wu (t,n) threshold verifiable multi-secret sharing scheme

Lin and Wu [IEE Proc. Comput. Digit. Tech. 146 (1999) 264] have proposed an efficient (t,n) threshold verifiable multi-secret sharing (VMSS) scheme based on the factorization problem and the discrete logarithm modulo a large composite problem. In their scheme, the dealer can arbitrarily give any set of multiple secrets to be shared, and only one reusable secret shadow is to be kept by every participant. On the other hand, they have claimed that their scheme can provide an efficient solution to the cheating problems between the dealer and any participant. However, He and Wu [IEE Proc. Comput. Digit. Tech. 148 (2001) 139] have shown that Lin and Wu's scheme is in fact insecure against a cheating participant. In this paper, we shall try to improve the security of Lin and Wu's scheme while providing more efficient performance than other VMSS schemes in terms of computational complexity.