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Non-Malleable Codes Against Bounded Polynomial Time Tampering

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Advances in Cryptology – EUROCRYPT 2019 (EUROCRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11476))

Abstract

We construct efficient non-malleable codes (NMC) that are (computationally) secure against tampering by functions computable in any fixed polynomial time. Our construction is in the plain (no-CRS) model and requires the assumptions that (1) \(\mathbf {E}\) is hard for \(\mathbf {NP}\) circuits of some exponential \(2^{\beta n}\) (\(\beta >0\)) size (widely used in the derandomization literature), (2) sub-exponential trapdoor permutations exist, and (3) \(\mathbf {P}\)-certificates with sub-exponential soundness exist.

While it is impossible to construct NMC secure against arbitrary polynomial-time tampering (Dziembowski, Pietrzak, Wichs, ICS ’10), the existence of NMC secure against \(O(n^c)\)-time tampering functions (for any fixed c), was shown (Cheraghchi and Guruswami, ITCS ’14) via a probabilistic construction. An explicit construction was given (Faust, Mukherjee, Venturi, Wichs, Eurocrypt ’14) assuming an untamperable CRS with length longer than the runtime of the tampering function. In this work, we show that under computational assumptions, we can bypass these limitations. Specifically, under the assumptions listed above, we obtain non-malleable codes in the plain model against \(O(n^c)\)-time tampering functions (for any fixed c), with codeword length independent of the tampering time bound.

Our new construction of NMC draws a connection with non-interactive non-malleable commitments. In fact, we show that in the NMC setting, it suffices to have a much weaker notion called quasi non-malleable commitments—these are non-interactive, non-malleable commitments in the plain model, in which the adversary runs in \(O(n^c)\)-time, whereas the honest parties may run in longer (polynomial) time. We then construct a 4-tag quasi non-malleable commitment from any sub-exponential OWF and the assumption that \(\mathbf {E}\) is hard for some exponential size \(\mathbf {NP}\)-circuits, and use tag amplification techniques to support an exponential number of tags.

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Notes

  1. 1.

    As we will see, in our setting of non-malleable codes against polynomially-bounded adversaries, our construction requires such derandomization assumptions in any case and so only standard one-way function is required in addition. However, for simplicity we will assume injective one-way function in the remainder of the exposition in this section.

  2. 2.

    For this exposition, we assume for simplicity that \(\psi '\) can be computed in deterministic time \(2^{\text{ input } \text{ length }}\) and that the injective OWF has linear circuit size. Recall that we do not require injective OWF and that any statistically binding, non-interactive commitment scheme is sufficient, but that for simplicity we assuming injective OWF in this exposition.

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Acknowledgments

The first and fifth authors are supported in part by NSF grant #CCF1423306 and the Leona M. & Harry B. Helmsley Charitable Trust. The first author is additionally supported in part by an IBM Research PhD Fellowship.The second and third authors are supported in part by NSF grants #CNS-1840893, #CNS-1453045 (CAREER), by a research partnership award from Cisco and by financial assistance award 70NANB15H328 from the U.S. Department of Commerce, National Institute of Standards and Technology. The fourth author is supported by NSF grants #CNS-1528178, #CNS-1514526, #CNS-1652849 (CAREER), a Hellman Fellowship, the Defense Advanced Research Projects Agency (DARPA) and Army Research Office (ARO) under Contract No. W911NF-15-C-0236, and a subcontract No. 2017-002 through Galois. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense, the National Science Foundation, or the U.S. Government. This work was performed, in part, while the first author was visiting IDC Herzliya’s FACT center and supported in part by ISF grant no. 1790/13 and the Check Point Institute for Information Security.

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Authors and Affiliations

  1. Columbia University, New York, USA

    Marshall Ball & Tal Malkin

  2. University of Maryland, College Park, USA

    Dana Dachman-Soled & Mukul Kulkarni

  3. University of Washington, Seattle, USA

    Huijia Lin

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  1. Technion, Haifa, Israel

    Yuval Ishai

  2. COSIC Group, KU Leuven, Heverlee, Belgium

    Vincent Rijmen

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Ball, M., Dachman-Soled, D., Kulkarni, M., Lin, H., Malkin, T. (2019). Non-Malleable Codes Against Bounded Polynomial Time Tampering. In: Ishai, Y., Rijmen, V. (eds) Advances in Cryptology – EUROCRYPT 2019. EUROCRYPT 2019. Lecture Notes in Computer Science(), vol 11476. Springer, Cham. https://doi.org/10.1007/978-3-030-17653-2_17

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