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International Conference on Information Security

ISC 2019: Information Security pp 171–189Cite as

Code-Based Zero Knowledge PRF Arguments

Part of the Lecture Notes in Computer Science book series (LNSC,volume 11723)

Abstract

Pseudo-random functions are a useful cryptographic primitive that, can be combined with zero-knowledge proof systems in order to achieve privacy-preserving identification. Libert et al. (ASIACRYPT 2017) has investigated the problem of proving the correct evaluation of lattice-based PRFs based on the Learning-With-Rounding (LWR) problem. In this paper, we go beyond lattice-based assumptions and investigate, whether we can solve the question of proving the correct evaluation of PRFs based on code-based assumptions such as the Syndrome Decoding problem. The answer is affirmative and we achieve it by firstly introducing a very efficient code-based PRG based on the Regular Syndrome Decoding problem and subsequently, we give a direct construction of a code-based PRF. Thirdly, we provide a zero-knowledge protocol for the correct evaluation of a code-based PRF, which allows a prover to convince a verifier that a given output y is indeed computed from the code-based PRF with a secret key k on an input x, i.e., \(y=f(k,x)\). Finally, we analytically evaluate the protocol’s communication costs.

Keywords

  • Coding theory
  • Zero knowledge
  • Pseudorandom function
  • PRF argument
  • Syndrome decoding

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Acknowledgement

We are grateful to the anonymous reviewers for their insightful comments. This work was partially supported by the Swedish Research Council (Vetenskapsrådet) through the grant PRECIS (621-2014-4845).

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Authors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Carlo Brunetta, Bei Liang & Aikaterini Mitrokotsa

Authors
  1. Carlo Brunetta
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  2. Bei Liang
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  3. Aikaterini Mitrokotsa
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Corresponding author

Correspondence to Carlo Brunetta .

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Editors and Affiliations

  1. The Ohio State University, Columbus, OH, USA

    Zhiqiang Lin

  2. University of Maryland, College Park, MD, USA

    Charalampos Papamanthou

  3. Stony Brook University, Stony Brook, NY, USA

    Michalis Polychronakis

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Brunetta, C., Liang, B., Mitrokotsa, A. (2019). Code-Based Zero Knowledge PRF Arguments. In: Lin, Z., Papamanthou, C., Polychronakis, M. (eds) Information Security. ISC 2019. Lecture Notes in Computer Science(), vol 11723. Springer, Cham. https://doi.org/10.1007/978-3-030-30215-3_9

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  • DOI: https://doi.org/10.1007/978-3-030-30215-3_9

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