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Continuously Non-Malleable Codes in the Split-State Model from Minimal Assumptions

  • Rafail Ostrovsky
  • Giuseppe Persiano
  • Daniele Venturi
  • Ivan Visconti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10993)

Abstract

At ICS 2010, Dziembowski, Pietrzak and Wichs introduced the notion of non-malleable codes, a weaker form of error-correcting codes guaranteeing that the decoding of a tampered codeword either corresponds to the original message or to an unrelated value. The last few years established non-malleable codes as one of the recently invented cryptographic primitives with the highest impact and potential, with very challenging open problems and applications.

In this work, we focus on so-called continuously non-malleable codes in the split-state model, as proposed by Faust et al. (TCC 2014), where a codeword is made of two shares and an adaptive adversary makes a polynomial number of attempts in order to tamper the target codeword, where each attempt is allowed to modify the two shares independently (yet arbitrarily). Achieving continuous non-malleability in the split-state model has been so far very hard. Indeed, the only known constructions require strong setup assumptions (i.e., the existence of a common reference string) and strong complexity-theoretic assumptions (i.e., the existence of non-interactive zero-knowledge proofs and collision-resistant hash functions).

As our main result, we construct a continuously non-malleable code in the split-state model without setup assumptions, requiring only one-to-one one-way functions (i.e., essentially optimal computational assumptions). Our result introduces several new ideas that make progress towards understanding continuous non-malleability, and shows interesting connections with protocol-design and proof-approach techniques used in other contexts (e.g., look-ahead simulation in zero-knowledge proofs, non-malleable commitments, and leakage resilience).

Keywords

Continuously non-malleable codes Split-state model Minimal assumptions 

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Rafail Ostrovsky
    • 1
  • Giuseppe Persiano
    • 2
  • Daniele Venturi
    • 3
  • Ivan Visconti
    • 4
  1. 1.Computer Science DepartmentUniversity of California Los AngelesLos AngelesUSA
  2. 2.DISA-MISUniversity of SalernoFiscianoItaly
  3. 3.Computer Science DepartmentSapienza University of RomeRomeItaly
  4. 4.DIEMUniversity of SalernoFiscianoItaly

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