On the condition number of the Vandermonde matrix of the n th cyclotomic polynomial

Recently, Blanco-Chacón proved the equivalence between the Ring Learning With Errors and Polynomial Learning With Errors problems for some families of cyclotomic number fields by giving some upper bounds for the condition number Cond( V n ) of the Vandermonde matrix V n associated to the n th cyclot...

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Bibliographic Details
Published in:Journal of mathematical cryptology 2021-01, Vol.15 (1), p.174-178
Main Authors: Scala, Antonio J. Di, Sanna, Carlo, Signorini, Edoardo
Format: Article
Language:English
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Summary:Recently, Blanco-Chacón proved the equivalence between the Ring Learning With Errors and Polynomial Learning With Errors problems for some families of cyclotomic number fields by giving some upper bounds for the condition number Cond( V n ) of the Vandermonde matrix V n associated to the n th cyclotomic polynomial. We prove some results on the singular values of V n and, in particular, we determine Cond( V n ) for n = 2 k p ℓ , where k , ℓ ≥ 0 are integers and p is an odd prime number.
ISSN:1862-2984
1862-2984
DOI:10.1515/jmc-2020-0009