  Cloud-based and distributed computations are of growing interest in modern
control systems. However, these technologies require performing computations on
not necessarily trustworthy platforms and, thus, put the confidentiality of
sensitive control-related data at risk. Encrypted control has dealt with this
issue by utilizing modern cryptosystems with homomorphic properties, which
allow a secure evaluation at the cost of an increased computation or
communication effort (among others). Recently, a cipher based on a random
affine transformation gained attention in the encrypted control community. Its
appeal stems from the possibility to construct security providing homomorphisms
that do not suffer from the restrictions of ``conventional'' approaches.
  This paper provides a cryptanalysis of random affine transformations in the
context of encrypted control. To this end, a deterministic and probabilistic
variant of the cipher over real numbers are analyzed in a generalized setup,
where we use cryptographic definitions for security and attacker models. It is
shown that the deterministic cipher breaks under a known-plaintext attack, and
unavoidably leaks information of the closed-loop, which opens another angle of
attack. For the probabilistic variant, statistical indistinguishability of
ciphertexts can be achieved, which makes successful attacks unlikely. We
complete our analysis by investigating a floating point realization of the
probabilistic random affine transformation cipher, which unfortunately suggests
the impracticality of the scheme if a security guarantee is needed.
