Novel image compression–encryption hybrid algorithm based on key-controlled measurement matrix in compressive sensing

• An image encryption–compression hybrid algorithm based on CS and RPE is proposed.
• The security of the algorithm is ensured by the measurement matrices in CS.
• The key is shortened without treating the whole measurement matrix as the key.
• The random matrix in RPE is bound with the measurement matrix.

The existing ways to encrypt images based on compressive sensing usually treat the whole measurement matrix as the key, which renders the key too large to distribute and memorize or store. To solve this problem, a new image compression–encryption hybrid algorithm is proposed to realize compression and encryption simultaneously, where the key is easily distributed, stored or memorized. The input image is divided into 4 blocks to compress and encrypt, then the pixels of the two adjacent blocks are exchanged randomly by random matrices. The measurement matrices in compressive sensing are constructed by utilizing the circulant matrices and controlling the original row vectors of the circulant matrices with logistic map. And the random matrices used in random pixel exchanging are bound with the measurement matrices. Simulation results verify the effectiveness, security of the proposed algorithm and the acceptable compression performance.