This paper presents an efficient ZKIP for SAT by using the K-th reisude cryptosystem. The proposed ZKIP is generalized to a ZKIP for the following problem. Let F(i)(i = 1, 2, ..., m) be a rational function over mod K. Given {F(i)}, does there exist (x1, x2, ..., x(n)) such that F(i)(x1, x2, ..., x(n)) = 0 mod K for i = 1, 2, ..., m?