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Leakage-Resilient Identity-Based Encryption in Bounded Retrieval Model with Nearly Optimal Leakage-Ratio

  • Ryo Nishimaki
  • Takashi YamakawaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11442)

Abstract

We propose new constructions of leakage-resilient public-key encryption (PKE) and identity-based encryption (IBE) schemes in the bounded retrieval model (BRM). In the BRM, adversaries are allowed to obtain at most \(\ell \)-bit leakage from a secret key and we can increase \(\ell \) only by increasing the size of secret keys without losing efficiency in any other performance measure. We call \(\ell /|\mathsf {sk}|\) leakage-ratio where \(|\mathsf {sk}|\) denotes a bit-length of a secret key. Several PKE/IBE schemes in the BRM are known. However, none of these constructions achieve a constant leakage-ratio under a standard assumption in the standard model. Our PKE/IBE schemes are the first schemes in the BRM that achieve leakage-ratio \(1-\epsilon \) for any constant \(\epsilon >0\) under standard assumptions in the standard model.

As previous works, we use identity-based hash proof systems (IB-HPS) to construct IBE schemes in the BRM. It is known that a parameter for IB-HPS called the universality-ratio is translated into the leakage-ratio of the resulting IBE scheme in the BRM. We construct an IB-HPS with universality-ratio \(1-\epsilon \) for any constant \(\epsilon >0\) based on any inner-product predicate encryption (IPE) scheme with compact secret keys. Such IPE schemes exist under the d-linear, subgroup decision, learning with errors, or computational bilinear Diffie-Hellman assumptions. As a result, we obtain IBE schemes in the BRM with leakage-ratio \(1-\epsilon \) under any of these assumptions. Our PKE schemes are immediately obtained from our IBE schemes.

Notes

Acknowledgments

We thank Daniel Wichs for helpful comments on the presentation.

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.NTT Secure Platform LaboratoriesTokyoJapan

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