On the condition number of the Vandermonde matrix of the nth 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( ) of the Vandermonde matrix associated to the th cyclotomic polyn...

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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
Subjects:
condition number
cyclotomic polynomial
Learning
Number theory
PLWE
Polynomials
Primary: 11C99
Prime numbers
Rings (mathematics)
RLWE
Secondary: 15A12, 15B05
Upper bounds
Vandermonde matrix
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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( ) of the Vandermonde matrix associated to the th cyclotomic polynomial. We prove some results on the singular values of and, in particular, we determine Cond( ) for = 2 , where , ≥ 0 are integers and is an odd prime number.
ISSN:1862-2976
1862-2984
DOI:10.1515/jmc-2020-0009