ON THE CONDITION NUMBER OF THE VANDERMONDE MATRIX OF THE nTH CYCLOTOMIC POLYNOMIAL

ON THE CONDITION NUMBER OF THE VANDERMONDE MATRIX OF THE nTH CYCLOTOMIC POLYNOMIAL

Edoardo Signorini is an undergraduate student who is currently working on various projects in Telsy, while writing his thesis about the “Post Quantum Cryptography”. Furthermore, he also published his work together with two professors of the Polytechnic of Turin, Carlo Sanna and Antonio Jose’ Di Scala, as a part of the amazing job that he is doing within the Company.

Following the abstract:

Recently, Blanco-Chac´on 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(Vn) of the Vandermonde matrix Vn associated to the nth cyclotomic polynomial. We prove some results on the singular values of Vn and, in particular, we determine Cond(Vn) for n = 2k p ℓ , where k, ℓ ≥ 0 are integers and p is an odd prime number.

Discover more: https://arxiv.org/pdf/2002.08120.pdf

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