## Cryptology ePrint Archive: Report 2018/511

Return of GGH15: Provable Security Against Zeroizing Attacks

James Bartusek and Jiaxin Guan and Fermi Ma and Mark Zhandry

Abstract: The GGH15 multilinear maps have served as the foundation for a number of cutting-edge cryptographic proposals. Unfortunately, many schemes built on GGH15 have been explicitly broken by so-called zeroizing attacks,'' which exploit leakage from honest zero-test queries. The precise settings in which zeroizing attacks are possible have remained unclear. Most notably, none of the current indistinguishability obfuscation (iO) candidates from GGH15 have any formal security guarantees against zeroizing attacks.

In this work, we demonstrate that all known zeroizing attacks on GGH15 implicitly construct algebraic relations between the results of zero-testing and the encoded plaintext elements. We then propose a GGH15 zeroizing model" as a new general framework which greatly generalizes known attacks.

Our second contribution is to describe a new GGH15 variant, which we formally analyze in our GGH15 zeroizing model. We then construct a new iO candidate using our multilinear map, which we prove secure in the GGH15 zeroizing model. This implies resistance to all known zeroizing strategies. The proof relies on the Branching Program Un-Annihilatability (BPUA) Assumption of Garg et al. [TCC 16-B] (which is implied by PRFs in NC^1 secure against P/Poly) and the complexity-theoretic p-Bounded Speedup Hypothesis of Miles et al. [ePrint 14] (a strengthening of the Exponential Time Hypothesis).

Category / Keywords: cryptographic protocols / multilinear maps, obfuscation, GGH15

Original Publication (with major differences): IACR-TCC-2018

Date: received 25 May 2018, last revised 28 Oct 2018

Contact author: fermima1 at gmail com

Available format(s): PDF | BibTeX Citation

Note: improved exposition, added comparison to CLT13 weak model, new title.

Short URL: ia.cr/2018/511

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