Paper 2018/1172

The impact of error dependencies on Ring/Mod-LWE/LWR based schemes

Jan-Pieter D'Anvers, Frederik Vercauteren, and Ingrid Verbauwhede


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.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Minor revision.PQCrypto 2019
Lattice cryptographyRing-LWEError Correcting CodesDecryption Failures
Contact author(s)
janpieter danvers @ esat kuleuven be
2019-02-20: last of 2 revisions
2018-12-03: received
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Creative Commons Attribution


      author = {Jan-Pieter D'Anvers and Frederik Vercauteren and Ingrid Verbauwhede},
      title = {The impact of error dependencies on Ring/Mod-LWE/LWR based schemes},
      howpublished = {Cryptology ePrint Archive, Paper 2018/1172},
      year = {2018},
      note = {\url{}},
      url = {}
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