Encryption based on compression can provide compression and encryption in a single step, in which redundancy is removed by compression and security is guaranteed by encryption. A novel secure arithmetic coding scheme based on interval exchanging is proposed in this paper, and it is applied to image encryption. It's found images can be transmitted securely on the Internet and the proposed algorithm dose not bring extra expense in terms of coding efficiency. Experimental results and security analyses indicate that the algorithm has good security strength as well as high encryption efficiency.