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Non-Trivial Witness Encryption and Null-iO from Standard Assumptions

Abstract : A witness encryption (WE) scheme can take any NP statement as a public-key and use it to encrypt a message. If the statement is true then it is possible to decrypt the message given a corresponding witness, but if the statement is false then the message is computationally hidden. Ideally, the encryption procedure should run in polynomial time, but it is also meaningful to define a weaker notion, which we call non-trivially exponentially efficient WE (XWE), where the encryption run-time is only required to be much smaller than the trivial 2 m bound for NP relations with witness size m. We show how to construct such XWE schemes for all of NP with encryption run-time 2 m/2 under the sub-exponential learning with errors (LWE) assumption. For NP relations that can be verified in NC 1 (e.g., SAT) we can also construct such XWE schemes under the sub-exponential Decisional Bilinear Diffie-Hellman (DBDH) assumption. Although we find the result surprising, it follows via a very simple connection to attribute-based encryption. We also show how to upgrade the above results to get non-trivially exponentially efficient indistinguishability obfuscation for null circuits (niO), which guarantees that the obfuscations of any two circuits that always output 0 are indistinguishable. In particular, under the LWE assumptions we get a XniO scheme where the obfuscation time is 2 n/2 for all circuits with input size n. It is known that in the case of indistinguishability obfuscation (iO) for all circuits, non-trivially efficient XiO schemes imply fully efficient iO schemes (Lin et al., PKC '16) but it remains as a fascinating open problem whether any such connection exists for WE or niO. Lastly, we explore a potential approach toward constructing fully efficient WE and niO schemes via multi-input ABE.
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https://hal.inria.fr/hal-01929279
Contributor : Alain Passelègue <>
Submitted on : Wednesday, November 21, 2018 - 10:10:38 AM
Last modification on : Friday, June 25, 2021 - 3:40:05 PM

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Zvika Brakerski, Aayush Jain, Ilan Komargodski, Alain Passelègue, Daniel Wichs. Non-Trivial Witness Encryption and Null-iO from Standard Assumptions. SCN 2018 - International Conference on Security and Cryptography for Networks, Sep 2018, Amalfi, Italy. pp.425-441, ⟨10.1007/978-3-319-98113-0_23⟩. ⟨hal-01929279⟩

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