  Despite the linearity of its encoding, compressed sensing may be used to
provide a limited form of data protection when random encoding matrices are
used to produce sets of low-dimensional measurements (ciphertexts). In this
paper we quantify by theoretical means the resistance of the least complex form
of this kind of encoding against known-plaintext attacks. For both standard
compressed sensing with antipodal random matrices and recent multiclass
encryption schemes based on it, we show how the number of candidate encoding
matrices that match a typical plaintext-ciphertext pair is so large that the
search for the true encoding matrix inconclusive. Such results on the practical
ineffectiveness of known-plaintext attacks underlie the fact that even
closely-related signal recovery under encoding matrix uncertainty is doomed to
fail.
  Practical attacks are then exemplified by applying compressed sensing with
antipodal random matrices as a multiclass encryption scheme to signals such as
images and electrocardiographic tracks, showing that the extracted information
on the true encoding matrix from a plaintext-ciphertext pair leads to no
significant signal recovery quality increase. This theoretical and empirical
evidence clarifies that, although not perfectly secure, both standard
compressed sensing and multiclass encryption schemes feature a noteworthy level
of security against known-plaintext attacks, therefore increasing its appeal as
a negligible-cost encryption method for resource-limited sensing applications.
