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Rate-Optimizing Compilers for Continuously Non-malleable Codes

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Applied Cryptography and Network Security (ACNS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11464))

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Abstract

We study the rate of so-called continuously non-malleable codes, which allow to encode a message in such a way that (possibly adaptive) continuous tampering attacks on the codeword yield a decoded value that is unrelated to the original message. Our results are as follows:

  • For the case of bit-wise independent tampering, we establish the existence of rate-one continuously non-malleable codes with information-theoretic security, in the plain model.

  • For the case of split-state tampering, we establish the existence of rate-one continuously non-malleable codes with computational security, in the (non-programmable) random oracle model. We further exhibit a rate-1/2 code and a rate-one code in the common reference string model, but the latter only withstands non-adaptive tampering. It is well known that computational security is inherent for achieving continuous non-malleability in the split-state model (even in the presence of non-adaptive tampering).

Continuously non-malleable codes are useful for protecting arbitrary cryptographic primitives against related-key attacks, as well as for constructing non-malleable public-key encryption schemes. Our results directly improve the efficiency of these applications.

S. Coretti—Supported by NSF grants 1314568 and 1619158. Work done while author was at New York University.

A. Faonio—Supported by the Spanish Ministry of Economy under the projects Dedetis (ref. TIN2015-70713-R) and Datamantium (ref. RTC-2016-4930-7), and by the Madrid Regional Government under project N-Greens (ref. S2013/ICE-2731).

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Notes

  1. 1.

    Strictly speaking, [6] only achieves continuous non-malleability for the weaker case of persistent tampering (where each tampering function is applied to the output of the previous tampering function).

  2. 2.

    Such codes are sometimes also called non-explicit. Explicit codes are obtained by enforcing algorithm \(\mathsf {Init}\) to output the empty string.

  3. 3.

    Importantly, each tampering function is applied to the original coding; this setting is sometimes known as non-persistent tampering.

  4. 4.

    While we describe the compiler in the CRS model, our instantiation in Sect. 5.2 does not require any trusted setup.

  5. 5.

    Note that the bits of \(\xi \) are indexed by the elements of \(\mathcal I\).

  6. 6.

    Recall that a non-adaptive attacker submits all tamper queries at once.

  7. 7.

    Such an encoding roughly guarantees that \(\ell \) bits of independent leakage from \(c_0'\) and \(c_1'\) do not reveal anything on the encoded message.

  8. 8.

    The leakage parameter can be improved to \(O(\lambda )\) by leaking a hash of the message.

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Authors and Affiliations

  1. IOHK, Hong Kong, China

    Sandro Coretti

  2. IMDEA Software Institute, Madrid, Spain

    Antonio Faonio

  3. Department of Computer Science, Sapienza University of Rome, Rome, Italy

    Daniele Venturi

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  1. Sandro Coretti
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  2. Antonio Faonio
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  3. Daniele Venturi
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Correspondence to Daniele Venturi .

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Editors and Affiliations

  1. Singapore Management University, Singapore, Singapore

    Robert H. Deng

  2. Universidad del Rosario, Bogota, Colombia

    Valérie Gauthier-Umaña

  3. Cyxtera Technologies, Bogota, Colombia

    Martín Ochoa

  4. Columbia University, New York, NY, USA

    Moti Yung

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Coretti, S., Faonio, A., Venturi, D. (2019). Rate-Optimizing Compilers for Continuously Non-malleable Codes. In: Deng, R., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds) Applied Cryptography and Network Security. ACNS 2019. Lecture Notes in Computer Science(), vol 11464. Springer, Cham. https://doi.org/10.1007/978-3-030-21568-2_1

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