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LR-FEAD: leakage-tolerating and attribute-hiding functional encryption mechanism with delegation in affine subspaces

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Abstract

In large-scale networks, such as cloud computing and Internet of Things, functional encryption mechanism provides a flexible and powerful cryptographic primitive in constructing the secure transmission and communication protocols. However, as the side-channel attacks in open environments, the attacker can gain partial sensitive information from the pre-defined system by virtue of the time, power analysis, cold-boot attacks, etc. In this work, we design a leakage-resilient functional encryption scheme, which tolerates amount of bounded master-key leakage and user private-key leakage. In our scheme, encryption policies are specified as point vectors and decryption roles are defined as affine subspaces. Role delegation is implemented by specifying the affine transformation over subspaces. Our scheme achieves payload hiding and attribute hiding in the sense that the attacker is able to specify any efficiently computable leakage functions and learns the function outputs taking the master/private keys as inputs. Also, our scheme can tolerate the continual leakage for master key and private key, since we can periodically update the master key and the private key to generate a new and re-randomized key with the same distribution to the previous keys. We construct the scheme in composite-order bilinear groups and prove the security with dual system encryption methodology. We also analyze and discuss the performance of allowable leakage bound, leakage ratio and possible leakage probability. Our scheme has flexible applications in secure data communication and authorization delegation in open cloud computing systems.

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Notes

  1. In this stage, \({\fancyscript{A}}\) cannot issue \({\mathcal O}_{\textit{Leak}}\) on master key or an affine space containing \({\varvec{x}}^*\) because \({\fancyscript{A}}\) can encode the entire decryption algorithm of \(\mathtt{CT}_{{\varvec{x}}^*}\) as a function on private key, and then wins the game.

  2. Given \(n\), it is intractable to find the factors \(p,q,r\) or \(s\).

  3. Note that the random elements in \({\mathcal G}_4\) can be obtained by raising \(U_4\) to random exponents from \({\mathbb F}_n\).

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Author information

Authors and Affiliations

  1. School of Computer Sciences, Hubei University of Technology, Wuhan, 430068, P. R. China

    Mingwu Zhang & Chunzhi Wang

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, P. R. China

    Mingwu Zhang

  3. Institute of Mathematics for Industry, Kyushu University, Fukuoka, 819-0395, Japan

    Kirill Morozov

Authors
  1. Mingwu Zhang
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  2. Chunzhi Wang
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  3. Kirill Morozov
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Corresponding author

Correspondence to Mingwu Zhang.

Additional information

This work is supported by the National Natural Science Foundation of China under Grants 61370224 and 61170135, the Key Program of Natural Science Foundation of Hubei Province under Grant 2013CFA046.

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Zhang, M., Wang, C. & Morozov, K. LR-FEAD: leakage-tolerating and attribute-hiding functional encryption mechanism with delegation in affine subspaces. J Supercomput 70, 1405–1432 (2014). https://doi.org/10.1007/s11227-014-1234-6

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  • DOI: https://doi.org/10.1007/s11227-014-1234-6

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