Paper 2019/596

Discretisation and Product Distributions in Ring-LWE

Sean Murphy and Rachel Player


A statistical framework applicable to Ring-LWE was outlined by Murphy and Player (IACR eprint 2019/452). Its applicability was demonstrated with an analysis of the decryption failure probability for degree-1 and degree-2 ciphertexts in the homomorphic encryption scheme of Lyubashevsky, Peikert and Regev (IACR eprint 2013/293). In this paper, we clarify and extend results presented by Murphy and Player. Firstly, we make precise the approximation of the discretisation of a Normal random variable as a Normal random variable, as used in the encryption process of Lyubashevsky, Peikert and Regev. Secondly, we show how to extend the analysis given by Murphy and Player to degree-k ciphertexts, by precisely characterising the distribution of the noise in these ciphertexts.

Note: Accepted for MathCrypt 2019

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Publication info
Preprint. MINOR revision.
Ring-LWEDiscretisationHomomorphic Encryption.
Contact author(s)
s murphy @ rhul ac uk
rachel player @ rhul ac uk
2019-07-26: last of 2 revisions
2019-06-02: received
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      author = {Sean Murphy and Rachel Player},
      title = {Discretisation and Product Distributions in Ring-LWE},
      howpublished = {Cryptology ePrint Archive, Paper 2019/596},
      year = {2019},
      note = {\url{}},
      url = {}
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