Spectral distortion and the ring learning with errors problem

Certain attacks on the ring learning with errors (RLWE) problem rely on reduction to the polynomial variant (PLWE) of the problem. The spectral distortion is used to measure the RLWE-to-PLWE reduction. We investigate the spectral distortion and answer questions posed by Y. Elias et al. (2016) regarding spectral distortion used as a condition for a successful attack. We provide a closed form for the spectral distortion of certain classes of cyclotomic polynomials. Moreover, we present a bound on the spectral distortion of cyclotomic polynomials.