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Compact and Tightly Selective-Opening Secure Public-key Encryption Schemes

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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

We propose four public-key encryption schemes with tight simulation-based selective-opening security against chosen-ciphertext attacks (SIM-SO-CCA) in the random oracle model. Our schemes only consist of small constant amounts of group elements in the ciphertext, ignoring smaller contributions from symmetric-key encryption, namely, they have compact ciphertexts. Furthermore, three of our schemes have compact public keys as well.

Known (almost) tightly SIM-SO-CCA secure PKE schemes are due to the work of Lyu et al. (PKC 2018) and Libert et al. (Crypto 2017). They have either linear-size ciphertexts or linear-size public keys. Moreover, they only achieve almost tightness, namely, with security loss depending on the security parameters.

Different to them, our schemes are the first ones achieving both tight SIM-SO-CCA security and compactness. Our schemes can be divided into two families:

  • Direct Constructions. Our first three schemes are constructed directly based on the Strong Diffie-Hellman (StDH), Computational DH (CDH), and Decisional DH assumptions. Both their ciphertexts and public keys are compact. Their security loss is a small constant. Interestingly, our CDH-based construction is the first scheme achieving all these advantages based on a weak, search assumption.

  • A Generic Construction. Our last scheme is the well-known Fujisaki-Okamoto transformation. We show that it can turn a lossy encryption scheme into a tightly SIM-SO-CCA secure PKE. This transformation preserves both tightness and compactness of the underlying lossy encryption, which is in contrast to the non-tight proof of Heuer et al. (PKC 2015).

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Acknowledgments

This work is supported by the Research Council of Norway under Project No. 324235. We thank the anonymous reviewers from Asiacrypt 2022 for referring us to the work of Bellare et al. [2] and encouraging us to discuss its impacts on previous work in the random oracle model and ours. Moreover, we thank Benedikt Wagner (CISPA, Germany) and one of our reviewers for pointing out a mistake in Game 5 of our previous proof for Theorem 1. Wagner provided very constructive suggestions on it, during his visit at NTNU.

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  1. Department of Mathematical Sciences, NTNU – Norwegian University of Science and Technology, Trondheim, Norway

    Jiaxin Pan & Runzhi Zeng

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  1. Jiaxin Pan
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Correspondence to Jiaxin Pan .

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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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Pan, J., Zeng, R. (2022). Compact and Tightly Selective-Opening Secure Public-key Encryption Schemes. 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_13

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  • DOI: https://doi.org/10.1007/978-3-031-22969-5_13

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