On the condition number of the Vandermonde matrix of the n th cyclotomic polynomial
Antonio J. Di Scala, Carlo Sanna, Edoardo Signorini · Journal of Mathematical Cryptology · 2020
Abstract 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.