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.

翻译：基于云和分布式计算在现代控制系统中日益受到关注。然而，这些技术要求在并非完全可信的平台上执行计算，从而使得敏感控制相关数据的机密性面临风险。加密控制通过利用具有同态性质的现代密码系统来处理这一问题，这些系统允许在增加计算或通信开销（以及其他方面）的代价下实现安全评估。近年来，一种基于随机仿射变换的密码体制在加密控制领域引起了关注。其吸引力源于能够构造既提供安全保障又不受"传统"方法限制的同态映射。本文针对加密控制背景下的随机仿射变换进行了密码分析。为此，我们在一个广义框架下分析了该密码体制在实数域上的确定性与概率性变体，并采用密码学定义的安全性和攻击者模型。研究表明，确定性密码体制在已知明文攻击下会被破解，并不可避免地向攻击者泄露闭环系统的信息，这开辟了另一种攻击途径。对于概率性变体，可以实现密文的统计不可区分性，这使得成功攻击的可能性较低。我们通过研究概率性随机仿射变换密码的浮点实现完成分析，但遗憾的是，该分析表明若需要安全保证，该方案在实践中并不可行。