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Continuous Space-Bounded Non-malleable Codes from Stronger Proofs-of-Space

  • Binyi ChenEmail author
  • Yilei ChenEmail author
  • Kristina Hostáková
  • Pratyay Mukherjee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11692)

Abstract

Non-malleable codes are encoding schemes that provide protections against various classes of tampering attacks. Recently Faust et al. (CRYPTO 2017) initiated the study of space-bounded non-malleable codes that provide such protections against tampering within small-space devices. They put forward a construction based on any non-interactive proof-of-space (NIPoS). However, the scheme only protects against an a priori bounded number of tampering attacks.

We construct non-malleable codes that are resilient to an unbounded polynomial number of space-bounded tamperings. Towards that we introduce a stronger variant of \(\text {NIPoS}\) called proof-extractable \(\text {NIPoS}\) (\(\text {PExt-NIPoS}\)), and propose two approaches of constructing such a primitive. Using a new proof strategy we show that the generic encoding scheme of Faust et al. achieves unbounded tamper-resilience when instantiated with a \(\text {PExt-NIPoS}\). We show two methods to construct \(\text {PExt-NIPoS}\):
  1. 1.

    The first method uses a special family of “memory-hard” graphs, called challenge-hard graphs (CHG), a notion we introduce here. We instantiate such family of graphs based on an extension of stack of localized expanders (first used by Ren and Devadas in the context of proof-of-space). In addition, we show that the graph construction used as a building block for the proof-of-space by Dziembowski et al. (CRYPTO 2015) satisfies challenge-hardness as well. These two CHG-instantiations lead to continuous space-bounded NMC with different features in the random oracle model.

     
  2. 2.

    Our second instantiation relies on a new measurable property, called uniqueness of \(\text {NIPoS}\). We show that standard extractability can be upgraded to proof-extractability if the \(\text {NIPoS}\) also has uniqueness. We propose a simple heuristic construction of \(\text {NIPoS}\), that achieves (partial) uniqueness, based on a candidate memory-hard function in the standard model and a publicly verifiable computation with small-space verification. Instantiating the encoding scheme of Faust et al. with this \(\text {NIPoS}\), we obtain a continuous space-bounded NMC that supports the “most practical” parameters, complementing the provably secure but “relatively impractical” CHG-based constructions. Additionally, we revisit the construction of Faust et al. and observe that due to the lack of uniqueness of their \(\text {NIPoS}\), the resulting encoding schemes yield “highly impractical” parameters in the continuous setting.

     

We conclude the paper with a comparative study of all our non-malleable code constructions with an estimation of concrete parameters.

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.University of CaliforniaSanta BarbaraUSA
  2. 2.VISA ResearchPalo AltoUSA
  3. 3.Technische Universität DarmstadtDarmstadtGermany

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