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In our daily life, lots of secret texts and images are often widely used and transmitted over the internet. About the storage and transmission of these multimedia files, the security is a research focus. And a large number of researchers in the multimedia community are interested in secret information protection. In view of this problem, secret image sharing (SIS) is a technique for image protection using mechanism of secret sharing (Shamir, 1979; Thien & Lin, 2002; Wang & Su, 2006). It shares a secret image into several noise-like shadows images and distributes them to the corresponding participants. In the decryption phase, a certain number of participants can collaborate to reveal the secret image with their shadows in the prescribed way. In full text, shadow images are referred to as shadows.
A (k, n)-threshold secret image sharing was first proposed by Shamir in 1979. In his scheme, a secret data is embedded into the constant coefficients of a (k − 1)-degree polynomial. Follow his scheme, Thien and Lin (2002) extended Shamir’s work and first proposed a (k, n)-SIS scheme by hiding the secret pixels into all coefficients of a (k − 1)-degree polynomial, and the shadow sizes is 1/k times of the secret image. Afterwards, the shadow sizes were further reduced by using Huffman code in (Wang & Su, 2006). Since SIS schemes is a new kind of method for image protection, various SIS schemes with specific function are proposed. As we all know, noise-like shadows transmitted on the network are easily suspect to censorships, so designing a (k, n)-SIS scheme with the meaningful shadows, which look like a cover image, is necessary. In (Lin & Tsai, 2004; Yang, Chen, Yu, & Wang, 2007; Wu, Kao, & Hwang, 2011; Yang, Ouyang, & Harn, 2012), some (k, n)-SIS schemes with meaningful shadows were proposed by using Steganography. These (k, n)-SIS schemes not only have the steganography property, but also possess authentication ability. Previous (k, n)-SIS schemes have the threshold property that recovers either the entire image or nothing. A novel scalable SIS (SSIS) scheme with the scalable decryption capability (i.e., the scalability) was introduced recently. The scalability means that the information amount of recovered image is proportional to the number of shadows participated in reconstruction. In (Wang & Shyu, 2007), Wang et al. first combined the scalability and the threshold property to construct a (2, n)-SSIS scheme. Then, based on Wang et al.’s work, Yang et al. constructed a general (k, n)-SSIS scheme (Yang & Huang, 2010). However, there have no property of the smooth scalability in the schemes (Wang & Shyu, 2007; Yang & Huang, 2010). The so-called smooth scalability refers to the information amount of a revealed image is “smoothly” proportional to the number of shadows. Subsequently, the SSIS schemes (Lin & Wang, 2010; Yang & Chu, 2011) with the property of smooth scalability were proposed. Except for the schemes mentioned above, another kind of SIS schemes, which combine SIS scheme and visual cryptography scheme (VCS) (Naor & Shamir, 1995) were proposed in (Yang & Ciou, 2010; Li, Yang & Kong, 2016), it has two decoding options in revealing phase. For more details of the SIS schemes, one can refer to (Cimato & Yang, 2011).