Security analysis of the joint encryption and compressed sensing

This paper addresses the perfect secrecy analysis of the scenario for encryption via compressed sensing. In this system the measurement matrix is generated based on a secret seed and is considered as a shared secret key between sender and receiver. The knowledge of signal sparsity and shared secret key enables receiver to recover the original submitted signal. It was shown that the Shannon-sense perfect secrecy is not achievable in general in such an algorithm. Although, in this paper it is proven that a weaker sense perfect secrecy may be achieved under some assumptions. The mutual information between source and encrypted message sets is estimated to analyze the perfect secrecy problem in general for unknown statistical distribution over source message set. The numerical evidence is given to support theoretical results.