The work proposes a protocol for quantum key distribution using Laguerre-Gaussian beams with space structured polarization invariant to rotation of the radial coordinate in a plane normal to the beam propagation axis. It is shown that axial polarization symmetry makes such beams insensitive to rotations relative to the optical axis, which makes it possible to use them to transmit information in cryptographic protocols in space communication systems. Keywords: quantum key distribution; satellite-to-ground communications; vector beams with structured polarization; cube corner reflectors.