Compressive Sensing encryption modes and their security

Abstract

Compressed Sensing may offer confidentiality with a good level of security that comes at limited extra costs. By this means, encryption can be added right into the sampling process. Previous proposals of Compressive Sensing encryption schemes are based on the randomness introduced by the sensing matrix. Once the matrix is fixed, the encryption becomes deterministic and therefore it can hardly be secure when encrypting more than a single signal. The work presented in this paper is built on the theoretical results on the secrecy of one-time Compressive Sensing encryption, and it proposes practical realizations, which extend this kind of encryption so that multiple signals may be encrypted under a single key. The confidentiality of the signal is thereby solely given by the inherent secrecy of the compressed measurements. In contrast to recent suggestions, the modes of operation defined in this paper are able to encrypt signals with different energy without exposing the signals energy to an eavesdropper. A general design for Compressive Sensing encryption modes is presented along with two realizations: one designed for parallel processing and another one that is self-synchronizing. The secrecy of the proposed modes is reduced to the secrecy of known and trusted cryptographic primitives. Compressive Sensing encryption modes are useful in a wide range of practical applications by providing a joint end-to-end encryption and compression that starts at the sensor level.