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Paper Title The Asymptotic Complexity of Coded-BKW with Sieving Using Increasing Reduction Factors
Paper IdentifierFR1.R7.1
Authors Erik Mårtensson, Lund University, Sweden
Session Post-Quantum Cryptography II
Location Bièvre, Level 5
Session Time Friday, 12 July, 09:50 - 11:10
Presentation Time Friday, 12 July, 09:50 - 10:10
Manuscript  Click here to download the manuscript
Abstract The Learning with Errors problem (LWE) is one of the main candidates for post-quantum cryptography. At Asiacrypt 2017, coded-BKW with sieving, an algorithm combining the Blum-Kalai-Wasserman algorithm (BKW) with lattice sieving techniques, was proposed. In this paper, we improve that algorithm by using different reduction factors in different steps of the sieving part of the algorithm. In the Regev setting, where $q = n^2$ and $\sigma = n^{1.5}/(\sqrt{2\pi}\log_2^2 n)$, the asymptotic complexity is $2^{0.8917n}$, improving the previously best complexity of $2^{{0.8927n}}$. When a quantum computer is assumed or the number of samples is limited, we get a similar level of improvement.