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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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Correspondence to Carlo Brunetta .

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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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