  The idea that compressed sensing may be used to encrypt information from
unauthorised receivers has already been envisioned, but never explored in depth
since its security may seem compromised by the linearity of its encoding
process. In this paper we apply this simple encoding to define a general
private-key encryption scheme in which a transmitter distributes the same
encoded measurements to receivers of different classes, which are provided
partially corrupted encoding matrices and are thus allowed to decode the
acquired signal at provably different levels of recovery quality.
  The security properties of this scheme are thoroughly analysed: firstly, the
properties of our multiclass encryption are theoretically investigated by
deriving performance bounds on the recovery quality attained by lower-class
receivers with respect to high-class ones. Then we perform a statistical
analysis of the measurements to show that, although not perfectly secure,
compressed sensing grants some level of security that comes at almost-zero cost
and thus may benefit resource-limited applications.
  In addition to this we report some exemplary applications of multiclass
encryption by compressed sensing of speech signals, electrocardiographic tracks
and images, in which quality degradation is quantified as the impossibility of
some feature extraction algorithms to obtain sensitive information from
suitably degraded signal recoveries.
