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Spatial Encryption Revisited: From Delegatable Multiple Inner Product Encryption and More

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Computer Security – ESORICS 2022 (ESORICS 2022)

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Abstract

Spatial encryption (SE), which involves encryption and decryption with affine/vector objects, was introduced by Boneh and Hamburg at Asiacrypt 2008. Since its introduction, SE has been shown as a versatile and elegant tool for implementing many other important primitives such as (Hierarchical) Identity-based Encryption ((H)IBE), Broadcast (H)IBE, Attribute-based Encryption, and Forward-secure cryptosystems.

This paper revisits SE toward a more compact construction in the lattice setting. In doing that, we introduce a novel primitive called Delegatable Multiple Inner Product Encryption (DMIPE). It is a delegatable generalization of Inner Product Encryption (IPE) but different from the Hierarchical IPE (HIPE) (Okamoto and Takashima at Asiacrypt 2009). We point out that DMIPE and SE are equivalent in the sense that there are security-preserving conversions between them. As a proof of concept, we then successfully instantiate a concrete DMIPE construction relying on the hardness of the decisional learning with errors problem. In turn, the DMIPE design implies a more compact lattice-based SE in terms of sizes compared with SEs converted from HIPE (e.g., Xagawa’s HIPE at PKC 2013) using the framework by Chen et al. (Designs, Codes, and Cryptography, 2014). Furthermore, we demonstrate that one can also use SE to implement the Allow-/Deny-list encryption, which subsumes, e.g., puncturable encryption (Green and Miers at IEEE S &P 2015).

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Notes

  1. 1.

    For instance, see at https://www.nature.com/articles/d41586-019-03213-z.

  2. 2.

    Some papers (e.g., [8, 23, 33]) denote this max-absolute-value norm by \(\Vert \cdot \Vert _{\infty }\).

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Acknowledgement

The authors are grateful to anonymous reviewers for their insightful comments. This work is partially supported by the Australian Research Council Linkage Project LP190100984. Huy Quoc Le has been sponsored by a CSIRO Data61 PhD Scholarship and CSIRO Data61 Top-up Scholarship. Josef Pieprzyk has been supported by the Polish National Science Center (NCN) grant 2018/31/B/ST6/03003.

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Authors and Affiliations

  1. Institute of Cybersecurity and Cryptology, School of Computing and Information Technology, University of Wollongong, Northfields Avenue, Wollongong, NSW, 2522, Australia

    Huy Quoc Le, Dung Hoang Duong & Willy Susilo

  2. CSIRO Data61, Sydney, NSW, Australia

    Huy Quoc Le & Josef Pieprzyk

  3. Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland

    Josef Pieprzyk

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  1. Huy Quoc Le
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  2. Dung Hoang Duong
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Correspondence to Huy Quoc Le , Dung Hoang Duong , Willy Susilo or Josef Pieprzyk .

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Editors and Affiliations

  1. Rutgers University, Newark, NJ, USA

    Vijayalakshmi Atluri

  2. Hamad Bin Khalifa University, Doha, Qatar

    Roberto Di Pietro

  3. Technical University of Denmark, Kongens Lyngby, Denmark

    Christian D. Jensen

  4. Technical University of Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

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Le, H.Q., Duong, D.H., Susilo, W., Pieprzyk, J. (2022). Spatial Encryption Revisited: From Delegatable Multiple Inner Product Encryption and More. In: Atluri, V., Di Pietro, R., Jensen, C.D., Meng, W. (eds) Computer Security – ESORICS 2022. ESORICS 2022. Lecture Notes in Computer Science, vol 13554. Springer, Cham. https://doi.org/10.1007/978-3-031-17140-6_14

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