Cryptology ePrint Archive: Report 2018/555

Limits on the Power of Garbling Techniques for Public-Key Encryption

Sanjam Garg and Mohammad Hajiabadi and Mohammad Mahmoody and Ameer Mohammed

Abstract: Understanding whether public-key encryption can be based on one-way functions is a fundamental open problem in cryptography. The seminal work of Impagliazzo and Rudich [STOC'89] shows that black-box constructions of public-key encryption from one-way functions are impossible. However, this impossibility result leaves open the possibility of using non-black-box techniques for achieving this goal.

One of the most powerful classes of non-black-box techniques, which can be based on one-way functions (OWFs) alone, is Yao's garbled circuit technique [FOCS'86]. As for the non-black-box power of this technique, the recent work of Dottling and Garg [CRYPTO'17] shows that the use of garbling allows us to circumvent known black-box barriers in the context of identity-based encryption.

We prove that garbling of circuits that have OWF (or even random oracle) gates in them are insufficient for obtaining public-key encryption. Additionally, we show that this model also captures (non-interactive) zero-knowledge proofs for relations with OWF gates. This indicates that currently known OWF-based non-black-box techniques are perhaps insufficient for realizing public-key encryption.

Category / Keywords: Public-key encryption, one-way function, black-box constructions, non-black-box separations, garbling schemes

Original Publication (in the same form): IACR-CRYPTO-2018

Date: received 3 Jun 2018, last revised 3 Jun 2018

Contact author: sanjamg at berkeley edu, mdhajiabadi at berkeley edu, mohammad at virginia edu, am8zv at virginia edu

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Version: 20180604:223739 (All versions of this report)

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