The multi-secret visual cryptography scheme (MVCS) allows for the encryption of multiple secret images into a given image area. The previous works on MVCS with probabilistic contrast can not guarantee that every original pixel will be reconstructed correctly. However, MVCS with deterministic contrast can reconstruct every original pixel with simple computation for high-end applications, but they are all simple 2-out-of-2 cases. These drawbacks limit the applicability of MVCSs existed. Based on ringed shares, MVCS with deterministic contrast has been defined in this paper. Furthermore, an (k, n)-MVCS with deterministic contrast, which makes the number of secret images not restricted, is proposed on the basis of the share rotation algorithm and the basis matrices of single secret sharing visual cryptography. Experimental results show that our scheme is the first (k, n)-MVCS with deterministic contrast, which can be applied on any k and n.