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Towards Tightly Secure Deterministic Public Key Encryption

  • Daode Zhang
  • Bao Li
  • Yamin Liu
  • Haiyang Xue
  • Xianhui Lu
  • Dingding Jia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10631)

Abstract

In this paper, we formally consider the construction of tightly secure deterministic public key encryption (D-PKE). Initially, we compare the security loss amongst the D-PKE schemes under the concrete assumptions and also analyze the tightness of generic D-PKE constructions. Furthermore, we prove that the CPA secure D-PKE scheme of Boldyreva et al. (Crypto’08) is tightly PRIV-IND-CPA secure for block-sources. Our security reduction improves the security loss of their scheme from \(\mathcal {O}(n_{c^*})\) to \(\mathcal {O}(1)\). Additionally, by upgrading the all-but-one trapdoor function (TDF) in the construction of Boldyreva et al. to all-but-n TDF defined by Hemenway et al. (Asiacrypt’11), we give general construction of PRIV-IND-\(\frac{n}{2}\)-CCA secure (i.e., the number of challenge ciphertexts \(n_{c^*}\) is bounded by \(\frac{n}{2}\)) D-PKE scheme for block-sources. And we observe that if the security reduction of the all-but-n TDF is tight, the D-PKE scheme can be tightly PRIV-IND-\(\frac{n}{2}\)-CCA secure. Finally, we prove that the all-but-n TDF given by Hemenway et al. is tightly secure, which results in the first tightly PRIV-IND-\(\frac{n}{2}\)-CCA secure D-PKE scheme for block-sources, based on the s-DCR assumption.

Keywords

Deterministic public key encryption Tight security reduction Lossy trapdoor functions Standard model 

Notes

Acknowledgments

We thank the anonymous ICICS’2017 reviewers for their helpful comments. This work is supported by the National Cryptography Development Fund MMJJ20170116 and the National Nature Science Foundation of China (Nos. 61602473, 61502480, 61672019, 61772522, 61379137, 61572495).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Daode Zhang
    • 1
    • 2
    • 3
  • Bao Li
    • 1
    • 2
    • 3
  • Yamin Liu
    • 1
  • Haiyang Xue
    • 1
  • Xianhui Lu
    • 1
  • Dingding Jia
    • 1
  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 LaboratoryChengduChina

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