Secret image sharing scheme with lossless recovery and high efficiency

As a well-known secret image sharing scheme, Thien-and-Lin's scheme generates shadow images of reduced size, which is beneficial for storage, transmission, and processing. However, it has some drawbacks, such as lossy recovery, needing extra secure transmission channels. For decades, many improved schemes have been proposed, but none can solve all the drawbacks simultaneously. Therefore, this paper proposes a (k,n)-threshold secret image sharing scheme, trying to solve the drawbacks comprehensively. In the sharing phase, two 8-bit pixels of the secret image are linked as a 16-bit secret value, and all the coefficients of the generating polynomial are used to embed secrets. Then, Shamir's secret sharing is implemented in Galois Field GF(65,537), and the only invalid share 65,536 will be set to 0. In the recovery phase, lossless recovery can be realized through neighborhood consistency calculation. To avoid key transmission, we develop a robust statistical invariance index of the secret image to generate permutation keys. Then Arnold permutation is performed to prevent information leakage. The proposed scheme can realize lossless recovery efficiently, without pixel expansion, complex preprocessing, and extra secure transmission channels. Theoretical analysis and experiments are given to validate the effectiveness of our scheme.