Abstract: Cheating detection is a very important issue for （ t,n ） threshold schemes. An efficient cheater detection scheme based on quadratic residues is proposed in this paper. The attack is as difficult as factoring the product of two large prime numbers. The scheme doesn’t need any one way hash function. The integrity guarantee is given to the public parameters, which can prevent a conspirator from falsely accusing any specific members. It can be easily expanded to the multi secret sharing scheme. The quantity of communication is smaller than that in Chang Hwang scheme.