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Registered ABE via Predicate Encodings

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Advances in Cryptology – ASIACRYPT 2023 (ASIACRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14442))

Abstract

This paper presents the first generic black-box construction of registered attribute-based encryption (Reg-ABE) via predicate encoding [TCC’14]. The generic scheme is based on k-Lin assumption in the prime-order bilinear group and implies the following concrete schemes that improve existing results:

  • the first Reg-ABE scheme for span program in the prime-order group; prior work uses composite-order group;

  • the first Reg-ABE scheme for zero inner-product predicate from k-Lin assumption; prior work relies on generic group model (GGM);

  • the first Reg-ABE scheme for arithmetic branching program (ABP) which has not been achieved previously.

Technically, we follow the blueprint of Hohenberger et al. [EUROCRYPT’23] but start from the prime-order dual-system ABE by Chen et al. [EUROCRYPT’15], which transforms a predicate encoding into an ABE. The proof follows the dual-system method in the context of Reg-ABE: we conceptually consider helper keys as secret keys; furthermore, malicious public keys are handled via pairing-based quasi-adaptive non-interactive zero-knowledge argument by Kiltz and Wee [EUROCRYPT’15].

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Notes

  1. 1.

    Let \(\textbf{w}=(w_1,\ldots ,w_n)\). With the same substitution \(w_i\in \mathbb {Z}_N\mapsto \textbf{W}_i\in \mathbb {Z}_p^{(k+1)\times (k+1)}\) and

    $$ [sw_i]_1 \mapsto [\textbf{s}\textbf{A}\textbf{W}_i]_1,\quad [rw_i]_2 \mapsto [\textbf{W}_i\textbf{B}\textbf{r}^\top ]_2, $$

    we have

    $$\begin{aligned} {} & {} {[s\textbf{w}]_1} = [sw_1\Vert \ldots \Vert sw_n]_1 = [\textbf{s}\textbf{A}\textbf{W}_1\Vert \cdots \Vert \textbf{s}\textbf{A}\textbf{W}_n]_1 = [\textbf{s}\textbf{A}(\textbf{W}_1\Vert \cdots \Vert \textbf{W}_n)]_1 \\ {} & {} {[r\textbf{w}]_2} = [rw_1\Vert \ldots \Vert rw_n]_2 = [\textbf{W}_1\textbf{B}\textbf{r}^\top \Vert \cdots \Vert \textbf{W}_n\textbf{B}\textbf{r}^\top ]_2 = [(\textbf{W}_1\Vert \cdots \Vert \textbf{W}_n)(\textbf{I}_n\otimes \textbf{B}\textbf{r}^\top )]_2 \end{aligned}$$

    where we obtain \(\textbf{W}=(\textbf{W}_1\Vert \cdots \Vert \textbf{W}_n)\in \mathbb {Z}_p^{(k+1)\times (k+1)n}\).

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Acknowledgement

We want to thank anonymous reviewers from Asiacrypt 2023 for their insightful comments and Hoeteck Wee for his encouragement! This work is partially supported by National Natural Science Foundation of China (62002120), Shanghai Rising-Star Program (22QA1403800), Innovation Program of Shanghai Municipal Education Commission (2021-01-07-00-08-E00101) and the “Digital Silk Road” Shanghai International Joint Lab of Trustworthy Intelligent Software (22510750100).

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Authors and Affiliations

  1. East China Normal University, Shanghai, China

    Ziqi Zhu, Junqing Gong & Haifeng Qian

  2. Shanghai University of Electric Power, Shanghai, China

    Kai Zhang

  3. Shanghai Qi Zhi Institute, Shanghai, China

    Junqing Gong

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  1. Ziqi Zhu
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Correspondence to Junqing Gong .

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Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Jian Guo

  2. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

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© 2023 International Association for Cryptologic Research

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Zhu, Z., Zhang, K., Gong, J., Qian, H. (2023). Registered ABE via Predicate Encodings. In: Guo, J., Steinfeld, R. (eds) Advances in Cryptology – ASIACRYPT 2023. ASIACRYPT 2023. Lecture Notes in Computer Science, vol 14442. Springer, Singapore. https://doi.org/10.1007/978-981-99-8733-7_3

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  • DOI: https://doi.org/10.1007/978-981-99-8733-7_3

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