Abstract: Group oriented (t,n) threshold digital signature schemes have a problem in that the underlying signature schemes will be broken if any t or more shadowholders conspire together with each other,thus the group secret key will be revealed.The new scheme proposed by us can avoid the conspiracy attack.It is based on the difficulty of computing the discrete logarithm modulo for a composite number and the factorization problem of large integer.The size of the group signature and verification time of the group signature are equivalent to that of an individual signature.