RLWE/PLWE equivalence for the maximal totally real subextension of the $ 2^rpq $-th cyclotomic field
Iván Blanco Chacón, Lorena López‐Hernanz · Advances in Mathematics of Communications · 2024
We generalise our previous work [5] by giving a polynomial upper bound on the condition number of certain quasi-Vandermonde matrices to establish the equivalence between the RLWE and PLWE problems for the totally real subfield of the cyclotomic fields of conductor $ 2^r $, $ 2^rp $ and $ 2^rpq $ with $ r\geq 1 $ and $ p $, $ q $ arbitrary primes. Moreover, we give some cryptographic motivations for the study of these subfields.