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Ring-Based Identity Based Encryption – Asymptotically Shorter MPK and Tighter Security

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Theory of Cryptography (TCC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13044))

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Abstract

This work constructs an identity based encryption from the ring learning with errors assumption (RLWE), with shorter master public keys and tighter security analysis. To achieve this, we develop three new methods: (1) a new homomorphic equality test method using nice algebraic structures of the rings, (2) a new family of hash functions with natural homomorphic evaluation algorithms, and (3) a new insight for tighter reduction analyses. These methods can be used to improve other important cryptographic tasks, and thus are of general interests.

Particularly, our homomorphic equality test method can derive a new method for packing/unpacking GSW-style encodings, showing a new non-trivial advantage of RLWE over the plain LWE. Moreover, our new insight for tighter analyses can improve the analyses of all the currently known partition-based IBE designs, achieving the best of the both from prior analytical frameworks of Waters (Eurocrypt ’05) and Bellare and Ristenpart (Eurocrypt ’09).

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Notes

  1. 1.

    \(\lambda \) is the security parameter and \(\epsilon \) is the adversary’s advantage in attacking the IBE scheme.

  2. 2.

    There is an unpublished work [4] that achieves essentially the same parameters as scheme II of [39], except [4] has an explicit bound on \(q=O(n^{15.5})\).

  3. 3.

    The plain-LWE schemes usually count how many basic matrices in \(\mathsf {mpk} \), where each matrix is larger than the basic ring vectors of Ring-LWE designs by at least a multiplicative factor of \(O(\lambda )\).

  4. 4.

    We note that \(m^{-1}\) with respect to \(\mathbb {Z}_q\) exists if we choose m and q to be co-prime.

  5. 5.

    We can define the common reference string model, where \(\mathsf {crs} \) is selected according to some sampling algorithm. In this work, the common random string model suffices.

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Acknowledgement

We would like to thank the anonymous reviewers of TCC 2021 for their insightful advices. Feng-Hao Liu and Zhedong Wang are supported by an NSF Award CNS-1657040 and an NSF Career Award CNS-1942400. Part of this work was done while Zhedong Wang was a postdoc at Florida Atlantic University. Parhat Abla and Han Wang are supported by the National Natural Science Foundation of China under Grant Number NSFC61772516 and the National Key R&D Program of China under Grant Number 2020YFA0712303, and Shandong Provincial Key Research and Development Program under Grant Number 2019JZZY020127. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the sponsors.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Science, Beijing, China

    Parhat Abla & Han Wang

  2. School of Cyber Security, University of Chinese Academy of Science, Beijing, China

    Parhat Abla & Han Wang

  3. Florida Atlantic University, Boca Raton, FL, USA

    Feng-Hao Liu

  4. School of Cyber Science and Engineering, Shanghai Jiao Tong University, Shanghai, China

    Zhedong Wang

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  1. Parhat Abla
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Correspondence to Han Wang .

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Editors and Affiliations

  1. Georgetown University, Washington, WA, USA

    Kobbi Nissim

  2. The University of Texas at Austin, Austin, TX, USA

    Brent Waters

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Abla, P., Liu, FH., Wang, H., Wang, Z. (2021). Ring-Based Identity Based Encryption – Asymptotically Shorter MPK and Tighter Security. In: Nissim, K., Waters, B. (eds) Theory of Cryptography. TCC 2021. Lecture Notes in Computer Science(), vol 13044. Springer, Cham. https://doi.org/10.1007/978-3-030-90456-2_6

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