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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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  1. Inria Paris, Paris, France

    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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