The current reversible data hiding algorithms in encrypted domain have the problems that the ciphertext images carrying secret have poor fault tolerance and disaster resistance after embedding secret data， once attacked or damaged， the original image cannot be reconstructed and the secret data cannot be extracted. In order to solve the problems， a new reversible data hiding algorithm in encrypted domain based on secret image sharing was proposed， and its application scenarios in cloud environment were analyzed. Firstly， the encrypted image was divided into n different ciphertext images carrying secret with the same size. Secondly， in the process of segmentation， the random quantities in Lagrange interpolation polynomial were taken as redundant information， and the mapping relationship between secret data and each polynomial coefficient was established. Finally， the reversible embedding of the secret data was realized by modifying the built-in parameters of the encryption process. When k ciphertext images carrying secret were collected， the original image was able to be fully recovered and the secret data was able to be extracted. Experimental results show that， the proposed algorithm has the advantages of low computational complexity， large embedding capacity and complete reversibility. In the （3，4） threshold scheme， the maximum embedding rate of the proposed algorithm is 4 bit per pixel （bpp）， and in the （4，4） threshold scheme， the maximum embedding rate of the proposed algorithm is 6 bpp. The proposed algorithm gives full play to the disaster recovery characteristic of secret sharing scheme. Without reducing the security of secret sharing， the proposed algorithm enhances the fault tolerance and disaster resistance of ciphertext images carrying secret， improves the embedding capacity of algorithm and the disaster recovery ability in the application scenario of cloud environment， and ensures the security of carrier image and secret data.