Abstract
Proxy re-encryption (PRE) allows a proxy with a re-encryption key to translate a ciphertext intended for Alice (delegator) to another ciphertext intended for Bob (delegatee) without revealing the underlying message. However, with PRE, Bob can obtain the whole message from the re-encrypted ciphertext, and Alice cannot take flexible control of the extent of the message transmitted to Bob.
In this paper, we propose a new variant of PRE, called Fine-Grained PRE (FPRE), to support fine-grained re-encryptions. An FPRE is associated with a function family \(\mathcal {F}\), and each re-encryption key \(rk_{A\rightarrow B}^f\) is associated with a function \(f\in \mathcal {F}\). With FPRE, Alice now can authorize re-encryption power to proxy by issuing \(rk_{A\rightarrow B}^f\) to it, with f chosen by herself. Then the proxy can translate ciphertext encrypting m to Bob’s ciphertext encrypting f(m) with such a fine-grained re-encryption key, and Bob only obtains a function of message m. In this way, Alice can take flexible control of the message spread by specifying functions.
For FPRE, we formally define its syntax and formalize security notions including CPA security, ciphertext pseudo-randomness, unidirectionality, non-transitivity, collusion-safety under adaptive corruptions in the multi-user setting. Moreover, we propose a new security notion named ciphertext unlinkability, which blurs the link between a ciphertext and its re-encrypted ciphertext to hide the proxy connections between users. We establish the relations between those security notions.
As for constructions, we propose two FPRE schemes, one for bounded linear functions and the other for deletion functions, based on the learning-with-errors (LWE) assumption. Our FPRE schemes achieve all the aforementioned desirable securities under adaptive corruptions in the standard model. As far as we know, our schemes provide the first solution to PRE with security under adaptive corruptions in the standard model.
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Notes
- 1.
In fact, to the best of our knowledge, there is no PRE with security under adaptive corruptions in the standard model, no matter single-hop or multi-hop, unidirectional or bidirectional, interactive or non-interactive PREs.
- 2.
We explain the security notions in Table 1: “weak-CPA/CCA1” does not allow the adversary to issue any re-encryption key query from an honest user to a corrupted user, while “CPA/CCA” allows such queries (except for trivial attacks). “tbCCA” refers to tag-based CCA and was first introduced in [10], with a security level between weak-CCA1 and CCA. “HRA” refers to security against honest re-encryption attacks), proposed in [9], and its does not allow such re-encryption key query, but provides re-encryption oracle to answer re-encryptions of honestly generated ciphertexts for corrupted users. On the one hand, HRA does not allow the adversary to obtain any re-encryption key from the honest user to the corrupted user, which is weaker than our CPA; on the other hand, the adversary in the HRA model can obtain re-encryptions of the honestly-generated ciphertexts from the challenge user to the corrupted user, which is not allowed in our CPA model.
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Acknowledgments
We would like to thank the reviewers for their valuable comments. Yunxiao Zhou, Shengli Liu and Shuai Han were partially supported by the National Key R &D Program of China under Grant 2022YFB2701500, National Natural Science Foundation of China (Grant Nos. 61925207, 62372292, 62002223), Guangdong Major Project of Basic and Applied Basic Research (2019B030302008), and Young Elite Scientists Sponsorship Program by China Association for Science and Technology (YESS20200185). Haibin Zhang was partially supported by the National Key R &D Program of China under Grant 2022YFB2701500, the National Natural Science Foundation of China under 62272043, Major Program of Shandong Provincial Natural Science Foundation for the Fundamental Research under ZR2022ZD03.
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Zhou, Y., Liu, S., Han, S., Zhang, H. (2023). Fine-Grained Proxy Re-encryption: Definitions and Constructions from LWE. In: Guo, J., Steinfeld, R. (eds) Advances in Cryptology – ASIACRYPT 2023. ASIACRYPT 2023. Lecture Notes in Computer Science, vol 14443. Springer, Singapore. https://doi.org/10.1007/978-981-99-8736-8_7
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