The Impact of Error Dependencies on Ring/Mod-LWE/LWR Based Schemes

  • Jan-Pieter D’AnversEmail author
  • Frederik Vercauteren
  • Ingrid Verbauwhede
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11505)


Current estimation techniques for the probability of decryption failures in Ring/Mod-LWE/LWR based schemes assume independence of the failures in individual bits of the transmitted message to calculate the full failure rate of the scheme. In this paper we disprove this assumption both theoretically and practically for schemes based on Ring/Mod-Learning with Errors/Rounding. We provide a method to estimate the decryption failure probability, taking into account the bit failure dependency. We show that the independence assumption is suitable for schemes without error correction, but that it might lead to underestimating the failure probability of algorithms using error correcting codes. In the worst case, for LAC-128, the failure rate is \(2^{48}\) times bigger than estimated under the assumption of independence. This higher-than-expected failure rate could lead to more efficient cryptanalysis of the scheme through decryption failure attacks.


Lattice cryptography Ring-LWE Error correcting codes Decryption failures 



This work was supported in part by the Research Council KU Leuven grants: C16/15/058, C14/18/067 and STG/17/019 and by the European Commission through the Horizon 2020 research and innovation programme Cathedral ERC Advanced Grant 695305.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jan-Pieter D’Anvers
    • 1
    Email author
  • Frederik Vercauteren
    • 1
  • Ingrid Verbauwhede
    • 1
  1. 1.IMEC-COSIC, KU LeuvenLeuven-HeverleeBelgium

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