In this paper, we investigate the problem of efficient image data encryption and compression. Based on feedforward-feedback nonlinear dynamic filter (FFNDF) and employing random arithmetic coding, a novel image encryption scheme integrated with the set partitioning in hierarchical trees (SPIHT) has been proposed. The FFNDF is employed to generate pseudorandom sequences which determine the mapping the interval position in the process of arithmetic coding. By encoding the bits obtained from different passes in the SPIHT algorithm with adaptive random arithmetic coding, we obtain a flexible secure image compression coding scheme. Also, the scheme accommodates features of progressive coding of the SPIHT. Theoretical analysis and experimental results show that the scheme has good cryptographic security and perceptual security, and it does not affect the compression efficiency apparently. The efficiency and security of the encryption scheme makes it an ideal choice in various applications such as total encryption, selective encryption, conditional access.