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Compact (Targeted Homomorphic) Inner Product Encryption from LWE

  • Jie Li
  • Daode Zhang
  • Xianhui Lu
  • Kunpeng Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10631)

Abstract

Inner product encryption (IPE) is a public-key encryption mechanism that supports fine-grained access control. Agrawal et al. (ASIACRYPT 2011) proposed the first IPE scheme from the Learning With Errors (LWE) problem. In their scheme, the public parameter size and ciphertext size are \(O(un^2\log ^3n)\) and \(O(un\log ^3n)\), respectively. Then, Xagawa (PKC 2013) proposed the improved scheme with public parameter of size \(O(un^2\log ^2n)\) and ciphertext of size \(O(un\log ^2n)\).

In this paper, we construct a more compact IPE scheme under the LWE assumption, which has public parameter of size \(O(un^2\log n)\) and ciphertext of size \(O(un\log n)\). Thus our scheme improves the size of Xagawa’s IPE scheme by a factor of \(\log n\).

Inspired by the idea of Brakerski et al. (TCC 2016), we propose a targeted homomorphic IPE (THIPE) scheme based on our IPE scheme. Compared with Brakerski et al.’s scheme, our THIPE scheme has more compact public parameters and ciphertexts. However, our scheme can only apply to the inner product case, while in their scheme the predicate f can be any efficiently computable polynomial.

Keywords

Inner product encryption Homomorphic encryption Learning with errors 

Notes

Acknowledgments

We thank the anonymous ICICS’2017 reviewers for their helpful comments. This work is supported by the National Basic Research Program of China (973 project, No. 2014CB340603) and the National Nature Science Foundation of China (No. 61672030).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Jie Li
    • 1
    • 2
    • 3
  • Daode Zhang
    • 1
    • 2
    • 3
  • Xianhui Lu
    • 1
    • 2
    • 3
  • Kunpeng Wang
    • 1
    • 2
    • 3
  1. 1.School of Cyber SecurityUniversity of Chinese Academy of SciencesBeijingChina
  2. 2.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  3. 3.Science and Technology on Communication Security LaboratoryBeijingChina

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