Paper 2019/452

A Central Limit Framework for Ring-LWE Decryption

Sean Murphy and Rachel Player


The main contribution of this paper is to develop a statistical framework, based on a Central Limit argument, for analysing the noise in ciphertexts in homomorphic encryption schemes that are based on Ring-LWE. Such an approach is very general: apart from finite variance, no assumption on the distribution of the noise is required (in particular, the noise need not be subgaussian). We demonstrate that such a Central Limit approach can be used to obtain a high-quality approximation of the distribution of the noise in an appropriate decoding basis, even in dimension as small as n = 100. We apply our framework and results to a homomorphic Ring-LWE cryptosystem of Lyubashevsky, Peikert and Regev (Eurocrypt 2013, full version) in order to illustrate the benefit of this approach. We show that a Central Limit approach leads to tighter bounds for the probability of decryption failure than have been obtained in prior work.

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Preprint. MINOR revision.
Ring-LWECentral Limit Theorem&#948-subgaussiandecryption failure probabilityhomomorphic encryption
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s murphy @ rhul ac uk
2020-07-21: last of 4 revisions
2019-05-08: received
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      author = {Sean Murphy and Rachel Player},
      title = {A Central Limit Framework for Ring-LWE Decryption},
      howpublished = {Cryptology ePrint Archive, Paper 2019/452},
      year = {2019},
      note = {\url{}},
      url = {}
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