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

Authors:
Ryo Nishimaki
Takashi Yamakawa
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DOI: 10.1007/978-3-030-17253-4_16
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Conference: PKC 2019
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.
BibTeX
@inproceedings{pkc-2019-29290,
  title={Leakage-Resilient Identity-Based Encryption in Bounded Retrieval Model with Nearly Optimal Leakage-Ratio},
  booktitle={Public-Key Cryptography – PKC 2019},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={11442},
  pages={466-495},
  doi={10.1007/978-3-030-17253-4_16},
  author={Ryo Nishimaki and Takashi Yamakawa},
  year=2019
}