**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.

**Category / Keywords: **Leakage-resilience, Bounded retrieval model, Identity-based Encryption, Identity-based hash proof system

**Original Publication**** (in the same form): **IACR-PKC-2019

**Date: **received 17 Jan 2019, last revised 30 Jan 2019

**Contact author: **takashi yamakawa ga at hco ntt co jp,ryo nishimaki zk@hco ntt co jp

**Available format(s): **PDF | BibTeX Citation

**Version: **20190131:051251 (All versions of this report)

**Short URL: **ia.cr/2019/045

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