**Adaptive-secure identity-based inner-product functional encryption and its leakage-resilience**

*Linru Zhang and Xiangning Wang and Yuechen Chen and Siu-Ming Yiu*

**Abstract: **There are lots of applications of inner-product functional encryption (IPFE). In this paper, we consider two important extensions of it. One is to enhance IPFE with access control such that only users with a pre-defined identity are allowed to compute the inner product, referred as identity-based inner-product functional encryption (IBIPFE). We formalize the definition of IBIPFE, and propose the first adaptive-secure IBIPFE scheme from Decisional Bilinear Diffie-Hellman (DBDH)
assumption. In an IBIPFE scheme, the ciphertext is related to a vector $\vec{x}$ and a new parameter, identity ID. Each secret key is also related to a vector $\vec{y}$ and an identity ID'. The decryption algorithm will output the inner-product value $<\vec{x}, \vec{y}>$ only if ID $=$ ID'.
The other extension is to make IBIPFE leakage resilient. We consider the bounded-retrieval model (BRM) in which an adversary can learn at most $l$ bits information from each secret key. Here, $l$ is the leakage bound determined by some external parameters, and it can be set arbitrarily large. After giving the security definition of leakage-resilient IBIPFE, we extend our IBIPFE scheme into a leakage-resilient IBIPFE scheme in the BRM by hash proof system (HPS).

**Category / Keywords: **public-key cryptography / Identity-based access control · Inner-product functional en- cryption · Bounded-retrieval model · Hash proof system

**Original Publication**** (with minor differences): **Indocrypt 2020

**Date: **received 27 Oct 2020, last revised 27 Nov 2020

**Contact author: **lrzhang at cs hku hk,xnwang@cs hku hk,ycchen@cs hku hk,smyiu@cs hku hk

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

**Version: **20201127:070658 (All versions of this report)

**Short URL: **ia.cr/2020/1353

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