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2018 | OriginalPaper | Chapter

Non-malleable Randomness Encoders and Their Applications

Authors : Bhavana Kanukurthi, Sai Lakshmi Bhavana Obbattu, Sruthi Sekar

Published in: Advances in Cryptology – EUROCRYPT 2018

Publisher: Springer International Publishing

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Abstract

Non-malleable Codes (NMCs), introduced by Dziembowski, Peitrzak and Wichs (ITCS 2010), serve the purpose of preventing “related tampering” of encoded messages. The most popular tampering model considered is the 2-split-state model where a codeword consists of 2 states, each of which can be tampered independently. While NMCs in the 2-split state model provide the strongest security guarantee, despite much research in the area we only know how to build them with poor rate (\(\varOmega (\frac{1}{logn})\), where n is the codeword length). However, in many applications of NMCs one only needs to be able to encode randomness i.e., security is not required to hold for arbitrary, adversarially chosen messages. For example, in applications of NMCs to tamper-resilient security, the messages that are encoded are typically randomly generated secret keys. To exploit this, in this work, we introduce the notion of “Non-malleable Randomness Encoders” (NMREs) as a relaxation of NMCs in the following sense: NMREs output a random message along with its corresponding non-malleable encoding.

Our main result is the construction of a 2-split state, rate-\(\frac{1}{2}\) NMRE. While NMREs are interesting in their own right and can be directly used in applications such as in the construction of tamper-resilient cryptographic primitives, we also show how to use them, in a black-box manner, to build a 3-split-state (standard) NMCs with rate \(\frac{1}{3}\). This improves both the number of states, as well as the rate, of existing constant-rate NMCs.

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previous chapter A Concrete Treatment of Fiat-Shamir Signatures in the Quantum Random-Oracle Model

next chapter Non-malleable Codes from Average-Case Hardness: , Decision Trees, and Streaming Space-Bounded Tampering

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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.

We refer the reader to Appendix A.2 for an alternate proof of this claim.

Here, we abuse the notation: \(b_{same^{*}}\) and \(b_{\bot }\) represent the particular values taken by the corresponding random variables.

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Title: Non-malleable Randomness Encoders and Their Applications
Authors: Bhavana Kanukurthi
Sai Lakshmi Bhavana Obbattu
Sruthi Sekar
Publisher: Springer International Publishing
Book: Advances in Cryptology – EUROCRYPT 2018
Print ISBN: 978-3-319-78371-0

Electronic ISBN: 978-3-319-78372-7

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-78372-7_19

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