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Multi-Input Quadratic Functional Encryption: Stronger Security, Broader Functionality

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13747))

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Abstract

Multi-input functional encryption, MIFE, is a powerful generalization of functional encryption that allows computation on encrypted data coming from multiple different data sources. In a recent work, Agrawal, Goyal, and Tomida (CRYPTO 2021) constructed MIFE for the class of quadratic functions. This was the first MIFE construction from bilinear maps that went beyond inner product computation. We advance the state-of-the-art in MIFE, and propose new constructions with stronger security and broader functionality.

  • Stronger Security: In the typical formulation of MIFE security, an attacker is allowed to either corrupt all or none of the users who can encrypt the data. In this work, we study MIFE security in a stronger and more natural model where we allow an attacker to corrupt any subset of the users, instead of only permitting all-or-nothing corruption. We formalize the model by providing each user a unique encryption key, and letting the attacker corrupt all non-trivial subsets of the encryption keys, while still maintaining the MIFE security for ciphertexts generated using honest keys. We construct a secure MIFE system for quadratic functions in this fine-grained corruption model from bilinear maps. Our construction departs significantly from the existing MIFE schemes as we need to tackle a more general class of attackers.

  • Broader Functionality: The notion of multi-client functional encryption, MCFE, is a useful extension of MIFE. In MCFE, each encryptor can additionally tag each ciphertext with appropriate metadata such that ciphertexts with only matching metadata can be decrypted together. In more detail, each ciphertext is now annotated with a unique label such that ciphertexts encrypted for different slots can now only be combined together during decryption as long as the associated labels are an exact match for all individual ciphertexts. In this work, we upgrade our MIFE scheme to also support ciphertext labelling. While the functionality of our scheme matches that of MCFE for quadratic functions, our security guarantee falls short of the general corruption model studied for MCFE. In our model, all encryptors share a secret key, therefore this yields a secret-key version of quadratic MCFE, which we denote by SK-MCFE. We leave the problem of proving security in the general corruption model as an important open problem.

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Notes

  1. 1.

    An MIFE scheme where corruption of all encrypting users is allowed is more commonly regarded as public-key MIFE, while disallowing corruption of any encrypting user is regarded as secret-key MIFE.

  2. 2.

    Formally, the inner product functionalities defined need to involve group elements as it is necessary for the proof. However, for simplicity of the overview, we use directly define them over \(\mathbb {Z}_p\).

  3. 3.

    When \(n=1\), we call MIFE just functional encryption (FE).

  4. 4.

    “sel” stands for “selective” meaning that the adversary has to select the challenge elements at the beginning of the security game. The opposite notion is “adaptive”. “pos” stands for “positive”. In MCFE, a user can decrypt ciphertexts only when it has ciphertexts for all slots with the same label, and a portion of them is useless for decryption. “pos” prohibits the adversary from querying the oracle on such useless challenge elements. “mh” and “fh” stand for “message-hiding” and “function-hiding”, respectively.

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Author information

Authors and Affiliations

  1. IIT Madras, Chennai, India

    Shweta Agrawal

  2. UW-Madison, Madison, USA

    Rishab Goyal

  3. NTT Social Informatics Laboratories, Tokyo, Japan

    Junichi Tomida

Authors
  1. Shweta Agrawal
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  2. Rishab Goyal
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  3. Junichi Tomida
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Corresponding author

Correspondence to Junichi Tomida .

Editor information

Editors and Affiliations

  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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Agrawal, S., Goyal, R., Tomida, J. (2022). Multi-Input Quadratic Functional Encryption: Stronger Security, Broader Functionality. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13747. Springer, Cham. https://doi.org/10.1007/978-3-031-22318-1_25

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  • DOI: https://doi.org/10.1007/978-3-031-22318-1_25

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