Paper 2024/748

PERK: Compact Signature Scheme Based on a New Variant of the Permuted Kernel Problem

Slim Bettaieb, Technology Innovation Institute
Loïc Bidoux, Technology Innovation Institute
Victor Dyseryn, XLIM
Andre Esser, Technology Innovation Institute
Philippe Gaborit, XLIM
Mukul Kulkarni, Technology Innovation Institute
Marco Palumbi, Technology Innovation Institute
Abstract

In this work we introduce PERK a compact digital signature scheme based on the hardness of a new variant of the Permuted Kernel Problem (PKP). PERK achieves the smallest signature sizes for any PKP-based scheme for NIST category I security with 6 kB, while obtaining competitive signing and verification timings. PERK also compares well with the general state-of-the-art. To substantiate those claims we provide an optimized constant-time AVX2 implementation, a detailed performance analysis and different size-performance trade-offs. Technically our scheme is based on a Zero-Knowledge Proof of Knowledge following the MPC-in-the-Head paradigm and employing the Fiat-Shamir transform. We provide comprehensive security proofs, ensuring EUF-CMA security for PERK in the random oracle model. The efficiency of PERK greatly stems from our particular choice of PKP variant which allows for an application of the challenge-space amplification technique due to Bidoux-Gaborit (C2SI 2023). Our second main contribution is an in-depth study of the hardness of the introduced problem variant. First, we establish a link between the hardness of our problem variant and the hardness of standard PKP. Then, we initiate an in-depth study of the concrete complexity to solve our variant. We present a novel algorithm which outperforms previous approaches for certain parameter regimes. However, the proximity of our problem variant to the standard variant can be controlled via a specific parameter. This enables us to effectively safeguard against our new attack and potential future extensions by a choice of parameters that ensures only a slight variation from standard PKP.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. Designs, Codes & Cryptography (2024)
DOI
10.1007/s10623-024-01381-2
Keywords
Post-Quantum CryptographyCryptanalysisNew Hardness AssumptionDigital SignaturesPKPPoKMPC
Contact author(s)
slim bettaieb @ tii ae
loic bidoux @ tii ae
victor dyseryn_fostier @ unilim fr
andre r esser @ gmail com
gaborit @ unilim fr
mukul kulkarni @ tii ae
marco palumbi @ tii ae
History
2024-05-20: approved
2024-05-16: received
See all versions
Short URL
https://ia.cr/2024/748
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/748,
      author = {Slim Bettaieb and Loïc Bidoux and Victor Dyseryn and Andre Esser and Philippe Gaborit and Mukul Kulkarni and Marco Palumbi},
      title = {{PERK}: Compact Signature Scheme Based on a New Variant of the Permuted Kernel Problem},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/748},
      year = {2024},
      doi = {10.1007/s10623-024-01381-2},
      url = {https://eprint.iacr.org/2024/748}
}
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