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Adaptive-Secure Identity-Based Inner-Product Functional Encryption and Its Leakage-Resilience

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Progress in Cryptology – INDOCRYPT 2020 (INDOCRYPT 2020)

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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 \(\varvec{x}\) and a new parameter, identity \(\mathrm {ID}\). Each secret key is also related to a vector \(\varvec{y}\) and an identity \(\mathrm {ID}'\). The decryption algorithm will output the inner-product value \(\langle \varvec{x},\varvec{y} \rangle \) only if \(\mathrm {ID}=\mathrm {ID}'\).

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).

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Notes

  1. 1.

    Unlike traditional PKE, the simulation-based security is not always achievable for FE [42]. So Indistinguishability-based security (IND-security) is widely used in FE research. Generally speaking, IND-security states that the adversary who has the secret keys for functions \(\{f_i\}_{i \in [\eta ]}\) cannot distinguish which of the challenge messages \(x_0\) or \(x_1\) was encrypted under the condition that for all \(i \in [\eta ]\), \(f_i(x_0)=f_i(x_1)\).

  2. 2.

    Here, let \(\mathcal {ID}\) be the identity space, \(\mathcal {V}\) be the vector space, and \(\mathcal {IP}\) be the inner-product value space.

  3. 3.

    Here we keep function h secret and set function f to be a black box, which means that one can only get the function value of f by making a query to the oracle, instead of computing it directly.

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Authors and Affiliations

  1. Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong SAR, China

    Linru Zhang, Xiangning Wang, Yuechen Chen & Siu-Ming Yiu

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    Karthikeyan Bhargavan

  2. University of Klagenfurt, Klagenfurt, Austria

    Elisabeth Oswald

  3. Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

    Manoj Prabhakaran

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Zhang, L., Wang, X., Chen, Y., Yiu, SM. (2020). Adaptive-Secure Identity-Based Inner-Product Functional Encryption and Its Leakage-Resilience. In: Bhargavan, K., Oswald, E., Prabhakaran, M. (eds) Progress in Cryptology – INDOCRYPT 2020. INDOCRYPT 2020. Lecture Notes in Computer Science(), vol 12578. Springer, Cham. https://doi.org/10.1007/978-3-030-65277-7_30

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