### Leakage-resilient Identity-based Encryption in Bounded Retrieval Model with Nearly Optimal Leakage-Ratio

Ryo Nishimaki and Takashi Yamakawa

##### 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 $\ell/|\textsf{sk}|$ leakage-ratio where $|\textsf{sk}|$ 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.

Available format(s)
Publication info
Keywords
Leakage-resilienceBounded retrieval modelIdentity-based EncryptionIdentity-based hash proof system
Contact author(s)
takashi yamakawa ga @ hco ntt co jp
ryo nishimaki zk @ hco ntt co jp
History
2019-01-31: revised
See all versions
Short URL
https://ia.cr/2019/045

CC BY

BibTeX

@misc{cryptoeprint:2019/045,
author = {Ryo Nishimaki and Takashi Yamakawa},
title = {Leakage-resilient Identity-based Encryption in Bounded Retrieval Model with Nearly Optimal Leakage-Ratio},
howpublished = {Cryptology ePrint Archive, Paper 2019/045},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/045}},
url = {https://eprint.iacr.org/2019/045}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.