In this paper, a novel double-image compression-encryption algorithm is proposed by combining Rossler hyperchaos and compressive sensing. In the proposed scheme, the sparse matrixes obtained by performing two-dimensional discrete wavelet transform on two plain images are first scrambled and compressed by index confusion and compressive sensing. Next, the compressed matrixes are linearly quantized, and then variable step length Josephus confusion and bitwise exclusive-OR operation are performed on them. The final noise-like cipher image is generated by hiding half of the encrypted image into the alpha channel of the other half of encrypted image. In order to realize "One cipher image corresponds to one key", a novel key generation mechanism is designed. Finally, the simulation analyses indicate that the proposed double-image encryption scheme has high transmission efficiency. Meanwhile, the average local information entropy of the cipher image is about 0.902 and the decryption quality is as high as 30 dB.