  We study the renormalization of the matrix elements of the twist-two
non-singlet bilinear quark operators, contributing to the $n=2$ and $n=3$
moments of the structure functions, at next-to-next-to-next-to-leading order in
QCD perturbation theory at the symmetric subtraction point. This allows us to
obtain conversion factors between the $\overline{\rm MS}$ scheme and the
regularization-invariant symmetric momentum subtraction (RI/SMOM, RI${}'$/SMOM)
schemes. The obtained results can be used to reduce errors in determinations of
moments of structure functions from lattice QCD simulations. The results are
given in Landau gauge.
