Abstract
Recently in IEEE Access (DOI: 10.1109/ACCESS.2018.2890565), Li <i>et al.</i> proposed a secure outsourcing algorithm for modular exponentiation in one single untrusted server model and a new method of generating transformation keys. They claimed that their solution can securely outsource encryption and decryption to untrusted ESP (encryption service providers) and DSP (decryption service providers), leaving only a constant number of simple operations for the DO (data owner) and eligible users to perform locally. In addition, both DO and qualified users can check the correctness of the results returned from ESP and DSP, respectively. Although the authors provide security proofs for their scheme, unfortunately, after carefully observing their scheme, we find that the scheme has security vulnerabilities. These vulnerabilities allow the adversary to generate the sub-key for any attribute and replace ciphertext sub-item, which result in the adversary to be able to break their scheme. In response to this problem, we propose an improved solution and proved its security.
Highlights
In 2019, Li et al.[1] proposed an ABE scheme with verifiable encryption and decryption outsourcing which can securely outsource encryption and decryption to untrusted ESP and DSP, respectively
Qualified users only need to perform a constant number of simple operations locally to complete the encryption and decryption work
DO and qualified users in this scheme can verify the correctness of the results returned from ESP and DSP
Summary
In 2019, Li et al.[1] proposed an ABE scheme with verifiable encryption and decryption outsourcing which can securely outsource encryption and decryption to untrusted ESP and DSP, respectively. Using gt or g H (x)t of the private key, the adversary can obtain the sub-key g H ( y)t of any attribute y S by the following way: (g t )H(y) = g H ( y)t or (g ) = g. The adversary sets up a S , which satisfies the challenger’s access structure (M * , * ) , and with the above way, the private key corresponding to the attribute y is generated as: SK = (K = g g at ,L = gt , x S ,Kx g H (x)t ). The adversary can decrypt the challenger’s ciphertext to obtain the plaintext mv by making the queried user’s private key matching the challenger’s access structure with the above two methods, and correctly give a guess v′ of v, i.e., v′ = v with probability 1
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