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Published in:
Improved Security Proofs in Lattice-Based Cryptography: Using the Rényi Divergence Rather Than the Statistical Distance Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Multi-input Functional Encryption for Unbounded Arity Functions

Authors : Saikrishna Badrinarayanan, Divya Gupta, Abhishek Jain, Amit Sahai

Published in: Advances in Cryptology -- ASIACRYPT 2015

Publisher: Springer Berlin Heidelberg

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Abstract

The notion of multi-input functional encryption (MI-FE) was recently introduced by Goldwasser et al. [EUROCRYPT’14] as a means to non-interactively compute aggregate information on the joint private data of multiple users. A fundamental limitation of their work, however, is that the total number of users (which corresponds to the arity of the functions supported by the MI-FE scheme) must be a priori bounded and fixed at the system setup time.
In this work, we overcome this limitation by introducing the notion of unbounded input MI-FE that supports the computation of functions with unbounded arity. We construct such an MI-FE scheme with indistinguishability security in the selective model based on the existence of public-coin differing-inputs obfuscation for turing machines and collision-resistant hash functions.
Our result enables several new exciting applications, including a new paradigm of on-the-fly secure multiparty computation where new users can join the system dynamically.

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previous chapter Improved Security Proofs in Lattice-Based Cryptography: Using the Rényi Divergence Rather Than the Statistical Distance
next chapter Multi-party Key Exchange for Unbounded Parties from Indistinguishability Obfuscation
Footnotes
1
A recent work by [6] shows that SNARKs with privately generated auxiliary inputs are impossible assuming the existence of pc-diO for circuits. We stress, however, that [20] only assumes the existence of a much weaker notion of public-coin SNARKs for their positive result. Therefore, the impossibility result of [6] is not applicable to [20].
 
2
One should note, however, that due to its non-interactive nature, this solution only achieves a weaker indistinguishability-based notion of security for secure computation where the adversary also gets access to the residual function \(f(\mathbf {x}^b_H,\cdot )\). Here \((\mathbf {x}^0_H, \mathbf {x}^1_H)\) are vectors of inputs of the honest parties.
 
3
The same idea can be naturally extended to multiple databases.
 
4
It was shown in [10] that simulation-based security even for bounded arity MiFE implies the strong notion of black-box obfuscation. Hence, we do not consider that notion in this paper.
 
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Metadata
Title
Multi-input Functional Encryption for Unbounded Arity Functions
Authors
Saikrishna Badrinarayanan
Divya Gupta
Abhishek Jain
Amit Sahai
Copyright Year
2015
Publisher
Springer Berlin Heidelberg
Book
Advances in Cryptology -- ASIACRYPT 2015

Print ISBN: 978-3-662-48796-9

Electronic ISBN: 978-3-662-48797-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-662-48797-6_2

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