Paper 2023/615

Multi-Client Inner Product Encryption: Function-Hiding Instantiations Without Random Oracles

Elaine Shi, Carnegie Mellon University
Nikhil Vanjani, Carnegie Mellon University

In a Multi-Client Functional Encryption (MCFE) scheme, $n$ clients each obtain a secret encryption key from a trusted authority. During each time step $t$, each client $i$ can encrypt its data using its secret key. The authority can use its master secret key to compute a functional key given a function $f$, and the functional key can be applied to a collection of $n$ clients’ ciphertexts encrypted to the same time step, resulting in the outcome of $f$ on the clients’ data. In this paper, we focus on MCFE for inner-product computations. If an MCFE scheme hides not only the clients’ data, but also the function $f$, we say it is function hiding. Although MCFE for inner-product computation has been extensively studied, how to achieve function privacy is still poorly understood. The very recent work of Agrawal et al. showed how to construct a function-hiding MCFE scheme for inner-product assuming standard bilinear group assumptions; however, they assume the existence of a random oracle and prove only a relaxed, selective security notion. An intriguing open question is whether we can achieve function-hiding MCFE for inner-product without random oracles. In this work, we are the first to show a function-hiding MCFE scheme for inner products, relying on standard bilinear group assumptions. Further, we prove adaptive security without the use of a random oracle. Our scheme also achieves succinct ciphertexts, that is, each coordinate in the plaintext vector encrypts to only $O(1$) group elements. Our main technical contribution is a new upgrade from single-input functional encryption for inner-products to a multi-client one. Our upgrade preserves function privacy, that is, if the original single-input scheme is function-hiding, so is the resulting multi-client construction. Further, this new upgrade allows us to obtain a conceptually simple construction.

Available format(s)
Public-key cryptography
Publication info
Published by the IACR in PKC 2023
multi-client functional encryptionadaptive securitybilinear groupinner product
Contact author(s)
runting @ gmail com
nvanjani @ cmu edu
2023-05-01: approved
2023-04-30: received
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      author = {Elaine Shi and Nikhil Vanjani},
      title = {Multi-Client Inner Product Encryption: Function-Hiding Instantiations Without Random Oracles},
      howpublished = {Cryptology ePrint Archive, Paper 2023/615},
      year = {2023},
      note = {\url{}},
      url = {}
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