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A key-insulated mechanism can resolve the private key exposure problem. To ensure the security of cloud storage, we introduce the key-insulated mechanism into GSC and propose a concrete scheme without bilinear pairings in the certificateless cryptosystem setting. We provide a formal definition and a security model of certificateless key-insulated GSC. Then, we prove that our scheme is confidential under the computational Diffie-Hellman (CDH) assumption and unforgeable under the elliptic curve discrete logarithm (EC-DL) assumption. Our scheme also supports both random-access key update and secure key update. Finally, we evaluate the efficiency of our scheme and demonstrate that it is highly efficient. 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