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Anonymous Public Key Encryption Under Corruptions

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Advances in Cryptology – ASIACRYPT 2022 (ASIACRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13793))

Abstract

Anonymity of public key encryption (PKE) requires that, in a multi-user scenario, the PKE ciphertexts do not leak information about which public keys are used to generate them. Corruptions are common threats in the multi-user scenario but anonymity of PKE under corruptions is less studied in the literature. In TCC 2020, Benhamouda et al. first provide a formal characterization for anonymity of PKE under a specific type of corruption. However, no known PKE scheme is proved to meet their characterization.

To the best of our knowledge, all the PKE application scenarios which require anonymity also require confidentiality. However, in the work by Benhamouda et al., different types of corruptions for anonymity and confidentiality are considered, which can cause security pitfalls. What’s worse, we are not aware of any PKE scheme which can provide both anonymity and confidentiality under the same types of corruptions.

In this work, we introduce a new security notion for PKE called ANON-RSO\(_{ {k} }\) &C security, capturing anonymity under corruptions. We also introduce SIM-RSO\(_{ {k} }\) &C security which captures confidentiality under the same types of corruptions. We provide a generic framework of constructing PKE scheme which can achieve the above two security goals simultaneously based on a new primitive called key and message non-committing encryption (KM-NCE). Then we give a general construction of KM-NCE utilizing a variant of hash proof system (HPS) called Key-Openable HPS. We also provide Key-Openable HPS instantiations based on the matrix decisional Diffie-Hellman assumption. Therefore, we can obtain various concrete PKE instantiations achieving the two security goals in the standard model with compact ciphertexts. Furthermore, for some PKE instantiation, its security reduction is tight.

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Notes

  1. 1.

    In the Committee-Selection phase of the evolving-committee proactive secret sharing scheme considered in [5], some users are selected as committee members. Each committee member will encrypt one fresh secret key using its long term public key (\(\textsf{ct}\leftarrow \mathcal {E}_1.\textsf{Enc}_{\textsf{pk}}(\textsf{esk})\)). Since the same user may be selected as a committee member multiple times, the user’s public key may be used multiple times to encrypt multiple messages.

  2. 2.

    Actually, it does not make sense to only consider the anonymity of some PKE without considering its confidentiality. If confidentiality can be sacrificed, one can trivially achieve anonymity by assigning the identity map as the encryption and decryption algorithm, so that the ciphertext equals the message and is independent of any public key.

  3. 3.

    Ciphertext overhead means the ciphertext bitlength minus plaintext bitlength [15].

  4. 4.

    Tight reduction means that the security loss of the reduction is independent of the number of users, the number of challenges and the number of queries raised by the adversary.

  5. 5.

    For \({\textsf{PKE}}=({\textsf{Setup}},{\textsf{Gen}},{\textsf{Enc}},{\textsf{Dec}})\), we require that (i) the public parameter \(\textsf{pp}\) generated by Setup can be used for multiple users, and (ii) Gen does not output tk (i.e., the key generation algorithm of PKE firstly invokes the key generation algorithm of KM-NCE to generate (pk, sk, tk), and then outputs (pk, sk), ignoring tk).

  6. 6.

    Actually, \(\pi \) is only statistical close to uniform. According to the leftover hash lemma together with the union bound, the statistically distance between \(\pi \) and uniform distribution over \(\varPi \) is bounded by \(\frac{l}{2}\sqrt{\frac{2}{q}}\), which is exponentially small for polynomially bounded \(l\). Therefore, we omit this statistical distance here.

  7. 7.

    To get an instantiation \(\widetilde{\textsf{HPS}}\) which satisfies the conditions of Theorem 2, \(\widetilde{\textsf{HPS}}\) needs to share the same universe set \(\mathcal {X}\) with \(\textsf{HPS}\). In that way, we can set \((\mathcal {G},d, {k} ,\mathcal {D}_{d+ {k} ,d})\) in \({\widetilde{{\textsf{mpar}}}}\) to be exactly the same with the ones in \({\textsf{mpar}}\).

  8. 8.

    Similarly, we set \({\widetilde{{\textsf{par}}}}:={\textsf{par}}\) and \({\widetilde{\textsf{td}}}:={\textsf{td}}\) to make sure \(\widetilde{\textsf{HPS}}\) shares the same language \(\mathcal {L}\) with \(\textsf{HPS}\).

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Acknowledgment

We appreciate the anonymous reviewers for their valuable comments. This work was supported by National Natural Science Foundation of China (Grant Nos. 61922036, U2001205, 62002223, 61825203), Major Program of Guangdong Basic and Applied Research Project (Grant No. 2019B030302008), National Joint Engineering Research Center of Network Security Detection and Protection Technology, Guangdong Key Laboratory of Data Security and Privacy Preserving, Guangdong Provincial Science and Technology Project (Grant No. 2021A0505030033), Shanghai Sailing Program (20YF1421100), Young Elite Scientists Sponsorship Program by China Association for Science and Technology (YESS20200185), and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement 802823).

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Authors and Affiliations

  1. Peng Cheng Laboratory, Shenzhen, China

    Zhengan Huang

  2. College of Information Science and Technology, Jinan University, Guangzhou, China

    Junzuo Lai & Jian Weng

  3. School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China

    Shuai Han

  4. Bergische Universität Wuppertal, Wuppertal, Germany

    Lin Lyu

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  1. Zhengan Huang
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  2. Junzuo Lai
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Correspondence to Shuai Han or Lin Lyu .

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  1. Indian Institute of Technology Madras, Chennai, India

    Shweta Agrawal

  2. Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

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Huang, Z., Lai, J., Han, S., Lyu, L., Weng, J. (2022). Anonymous Public Key Encryption Under Corruptions. In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13793. Springer, Cham. https://doi.org/10.1007/978-3-031-22969-5_15

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  • DOI: https://doi.org/10.1007/978-3-031-22969-5_15

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