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Upper and Lower Bounds for Continuous Non-Malleable Codes

  • Dana Dachman-Soled
  • Mukul KulkarniEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11442)

Abstract

Recently, Faust et al. (TCC’14) introduced the notion of continuous non-malleable codes (CNMC), which provides stronger security guarantees than standard non-malleable codes, by allowing an adversary to tamper with the codeword in a continuous way instead of one-time tampering. They also showed that CNMC with information theoretic security cannot be constructed in the 2-split-state tampering model, and presented a construction in the common reference string (CRS) model from collision-resistant hash functions and non-interactive zero-knowledge proofs.

In this work, we ask if it is possible to construct CNMC from weaker assumptions. We answer this question by presenting lower as well as upper bounds. We show that it is impossible to construct 2-split-state CNMC, with no CRS, for one-bit messages from any falsifiable assumption, thus establishing the lower bound. We additionally provide an upper bound by constructing 2-split-state CNMC for one-bit messages, assuming only the existence of a family of injective one way functions. We note that in a recent work, Ostrovsky et al. (CRYPTO’18) considered the construction of a relaxed notion of 2-split-state CNMC from minimal assumptions.

We also present a construction of 4-split-state CNMC for multi-bit messages in CRS model from the same assumptions. Additionally, we present definitions of the following new primitives: (1) One-to-one commitments, and (2) Continuous Non-Malleable Randomness Encoders, which may be of independent interest.

Keywords

Continuous non-malleable codes Black-box impossibility Split-state 

Notes

Acknowledgments

We thank the anonymous PKC 2019 reviewers for pointing out an error and fix to our lower bound proof. We also thank them for extensive comments that helped to significantly improve our presentation.

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© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.University of MarylandCollege ParkUSA

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