Secret image sharing without keeping permutation key

A well-known Thien and Lin´s (k, n) secret image sharing (SIS) scheme is to share a secret image into n noise-like shadow images, and the secret image can be recovered from any k shadow images. In Thien and Lin´s (k, n)-SIS scheme, a key is required to generate a permutation sequence to permute the pixels of the secret image, so that we can assure shadow images of complete randomness and no secret revealed. In Thien and Lin´s (k, n)-SIS scheme, the authors claimed that the key can be kept by system owner or shared among the owners of shadow images. In this paper, by using an inherent property of digital image that a new image with a chaotic reallocation of pixels without effect on their intensity levels, we propose a (k, n)-SIS scheme without keeping this permutation key in advance.