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In single-cloud storage, ciphertext-policy attribute-based encryption (CP-ABE) allows one to encrypt any data under an access structure to a cloud server, specifying what attributes are required to decrypt. In multi-cloud storage, a secret sharing scheme (SSS) allows one to split any data into multiple shares, one to a single server, and specify which subset of the servers are able to recover the data. It is an interesting problem to remove some attributes/servers but still enable the remaining attributes/servers in every authorized set to recover the data. The problem is related to the contraction problem of access structures for SSSs. In this paper, we propose a method that can efficiently transform a given SSS for an access structure to SSSs for contractions of the access structure. We show its applications in solving the attribute removal problem in the CP-ABE based single-cloud storage and the data relocating problem in multi-cloud storage. Our method results in solutions that require either less server storage or even no additional server storage.
Feng et al. (Thu,) studied this question.