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Media type:
E-Article
Title:
RLWE and PLWE over cyclotomic fields are not equivalent
Contributor:
Di Scala, Antonio J.;
Sanna, Carlo;
Signorini, Edoardo
Published:
Springer Science and Business Media LLC, 2024
Published in:
Applicable Algebra in Engineering, Communication and Computing, 35 (2024) 3, Seite 351-358
Language:
English
DOI:
10.1007/s00200-022-00552-9
ISSN:
0938-1279;
1432-0622
Origination:
Footnote:
Description:
AbstractWe prove that the Ring Learning With Errors (RLWE) and the Polynomial Learning With Errors (PLWE) problems over the cyclotomic field $${\mathbb {Q}}(\zeta _n)$$ Q ( ζ n ) are not equivalent. Precisely, we show that reducing one problem to the other increases the noise by a factor that is more than polynomial in n. We do so by providing a lower bound, holding for infinitely many positive integers n, for the condition number of the Vandermonde matrix of the nth cyclotomic polynomial.