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Privacy Amplification from Non-malleable Codes

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Progress in Cryptology – INDOCRYPT 2019 (INDOCRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11898))

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Abstract

Non-malleable Codes give us the following property: their codewords cannot be tampered into codewords of related messages. Privacy Amplification allows parties to convert their weak shared secret into a fully hidden, uniformly distributed secret key, while communicating on a fully tamperable public channel. In this work, we show how to construct a constant round privacy amplification protocol from any augmented split-state non-malleable code. Existentially, this gives us another primitive (in addition to optimal non-malleable extractors) whose optimal construction would solve the long-standing open problem of building constant round privacy amplification with optimal entropy loss and min-entropy requirement. Instantiating our code with the current best known NMC gives us an 8-round privacy amplification protocol with entropy loss \(\mathcal {O}(\log (n)+ \kappa \log (\kappa ))\) and min-entropy requirement \(\varOmega (\log (n) +\kappa \log (\kappa ))\), where \(\kappa \) is the security parameter and n is the length of the shared weak secret. In fact, for our result, even the weaker primitive of Non-malleable Randomness Encoders suffice.

We view our result as an exciting connection between two of the most fascinating and well-studied information theoretic primitives, non-malleable codes and privacy amplification.

E. Chattopadhyay—Research supported by NSF grant CCF-1412958 and the Simons foundation.

B. Kanukurthi—Research supported in part by Department of Science and Technology Inspire Faculty Award.

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Notes

  1. 1.

    We can instantiate our construction with recent NMC constructions like [4, 31]. We wish to point out that while using [31] slightly improves the entropy loss here (not optimal though), using the constant rate NMC of [4] or [31] results in more entropy loss. This is because the error of their NMC is worse than [30].

  2. 2.

    Note that the non-malleable secret sharing schemes using split-state NMCs achieve non-malleability in the independent tampering model, not an arbitrary tampering.

  3. 3.

    Here \((f,g)(\mathsf {NMREnc}_2(\mathcal {R}))\) just denotes the tampering by the split-state tampering functions f and g on the corresponding states.

  4. 4.

    For simplicity in the proof, we may assume here that the decoder \(\mathsf {Dec}\) never outputs \(\bot \). This can be done by replacing \(\bot \) with some fixed string, like 00..0.

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Author information

Authors and Affiliations

  1. Cornell University and IAS, Ithaca, USA

    Eshan Chattopadhyay

  2. Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India

    Bhavana Kanukurthi & Sai Lakshmi Bhavana Obbattu

  3. Department of Mathematics, Indian Institute of Science, Bangalore, India

    Sruthi Sekar

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  1. Eshan Chattopadhyay
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  3. Sai Lakshmi Bhavana Obbattu
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Correspondence to Sruthi Sekar .

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Editors and Affiliations

  1. University of Warwick, Warwick, UK

    Feng Hao

  2. CSIRO Data61, Marsfield, NSW, Australia

    Sushmita Ruj

  3. Nanyang Technological University, Singapore, Singapore

    Sourav Sen Gupta

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Chattopadhyay, E., Kanukurthi, B., Obbattu, S.L.B., Sekar, S. (2019). Privacy Amplification from Non-malleable Codes. In: Hao, F., Ruj, S., Sen Gupta, S. (eds) Progress in Cryptology – INDOCRYPT 2019. INDOCRYPT 2019. Lecture Notes in Computer Science(), vol 11898. Springer, Cham. https://doi.org/10.1007/978-3-030-35423-7_16

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