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Lockable Obfuscation from Circularly Insecure Fully Homomorphic Encryption

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Public-Key Cryptography – PKC 2022 (PKC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13178))

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Abstract

In a lockable obfuscation scheme, a party called the obfuscator takes as input a circuit \(C\), a lock value y, and a message m, and outputs an obfuscated circuit. Given the obfuscated circuit, an evaluator can run it on an input x and learn the message if \(C(x) = y\). For security, we require that the obfuscation reveals no information on the circuit as long as the lock y has high entropy even given the circuit \(C\).

The only known constructions of lockable obfuscation schemes require indistinguishability obfuscation (\(i\mathcal {O}\)) or the learning with errors (LWE) assumption. Furthermore, in terms of technique, all known constructions, excluding \(i\mathcal {O}\)-based, are build from provably secure variations of graph-induced multilinear maps.

We show a generic construction of a lockable obfuscation scheme built from a (leveled) fully homomorphic encryption scheme that is circularly insecure. Specifically, we need a fully homomorphic encryption scheme that is secure under chosen-plaintext attack (IND-CPA) but for which there is an efficient cycle tester that can detect encrypted key cycles. Our finding sheds new light on how to construct lockable obfuscation schemes and shows why cycle tester constructions were helpful in the design of lockable obfuscation schemes. One of the many use cases for lockable obfuscation schemes are constructions for IND-CPA secure but circularly insecure encryption schemes. Our work shows that there is a connection in both ways between circular insecure encryption and lockable obfuscation.

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Notes

  1. 1.

    The folklore counterexample for 1-cycles is an augmented construction of any \(\mathsf {IND}\text {-}\mathsf {CPA}\) secure encryption. In short, we append \(y \leftarrow F(\mathsf {sk})\) to the public key, where F is a one-way function. Encryption of a message m is as in the original encryption scheme, except we return m if \(F(m) = y\).

  2. 2.

    Specifically, Wichs and Zirdelis show a lockable obfuscator from null-\(i\mathcal {O}\), that is, \(i\mathcal {O}\) for evasive functions. However, the only known realization requires lockable obfuscation and witness encryption which we know how to build from \(i\mathcal {O}\) or multilinear maps that imply \(i\mathcal {O}\).

  3. 3.

    As pointed by Kluczniak [Klu20], the definition by Bishop, Hohenberger, and Waters [BHW15] does not make a distinction between a cycle tester and an encryption scheme with an efficient zero tester.

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Funding

This work has been partially funded/supported by the German Ministry for Education and Research through funding for the project CISPA-Stanford Center for Cybersecurity (Funding number 16KIS0927).

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  1. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Kamil Kluczniak

  2. Stanford University, Stanford, USA

    Kamil Kluczniak

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  1. National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

    Goichiro Hanaoka

  2. Yokohama National University, Yokohama, Japan

    Junji Shikata

  3. The University of Electro-Communications, Tokyo, Japan

    Yohei Watanabe

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Kluczniak, K. (2022). Lockable Obfuscation from Circularly Insecure Fully Homomorphic Encryption. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds) Public-Key Cryptography – PKC 2022. PKC 2022. Lecture Notes in Computer Science(), vol 13178. Springer, Cham. https://doi.org/10.1007/978-3-030-97131-1_3

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  • DOI: https://doi.org/10.1007/978-3-030-97131-1_3

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  • Online ISBN: 978-3-030-97131-1

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