Discretisation and Product Distributions in Ring-LWE

Journal of mathematical cryptology

article

Sean Murphy¹  Rachel Player¹ 

[1] Royal Holloway, University of London, United Kingdom

关键词: Ring-LWE;    Discretisation;    Homomorphic Encryption;   

DOI  :  10.1515/jmc-2020-0073

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY|CC BY-NC-ND