On the secrecy of compressive cryptosystems under finite-precision representation of sensing matrices

In recent years, the Compressed Sensing (CS) framework has been shown to be an effective private key cryptosystem. If infinite precision is available, then it has been shown that spherical secrecy can be achieved. However, despite its theoretically proven secrecy properties, the only practically feasible implementations involve the use of Bernoulli sensing matrices. In this work, we show that different distributions employing a much larger finite alphabet can be considered. More in detail, we consider the use of quantized Gaussian sensing matrices and experimentally show that, besides being suitable for practical implementation, they can achieve higher secrecy with respect to Bernoulli sensing matrices. Furthermore, we show that this approach can be used to tune the secrecy of the CS cryptosystems based on the available machine precision.