Security at the Analog-to-Information Interface Using Compressed Sensing

The random projection scheme entailed by CS can be seen as a means to provide a very simple, limited, but straightforward means of encryption when the random encoding matrix at its core is generated given a private key between two parties in a communication channel. Conversely, signal recovery can be seen as a decoder which, given the measurements, retrieves the intended message as it was encoded via CS. From the security point of view such a scheme is not perfectly secure, but comes for free with the use of CS. Thus, this chapter explores what are the achievable, even if limited, security properties of CS, with the idea that it could serve as a low-complexity cryptographic stage acting directly at the analog-to-information interface. The approach we will adopt is three-fold: we will characterize statistical attacks, known-plaintext attacks, and signal recovery performances for non-perfectly informed receivers. Leveraging this last point, we will discuss a concept of “multiclass” encryption in which several receiver classes are distinguished depending on the accuracy of their encoding matrix. This exploration is completed by several experiments, showing how such principles can be implemented to secure image and biosignal communications that use CS as a basic building block.