###### Abstract  
Most of the image encryption schemes based on chaos have so far employed symmetric key cryptography, which leads to a situation where the key cannot be transmitted in public channels, thus limiting their extended application. Based on the elliptic curve cryptography (ECC), we proposed a public key image encryption method where the hash value derived from the plain image was encrypted by ECC. Furthermore, during image permutation, a novel algorithm based on different-sized block was proposed. The plain image was firstly divided into five planes according to the amount of information contained in different bits: the combination of the low 4 bits, and other four planes of high 4 bits respectively. Second, for different planes, the corresponding method of block partition was followed by the rule that the higher the bit plane, the smaller the size of the partitioned block as a basic unit for permutation. In the diffusion phase, the used hyperchaotic sequences in permutation were applied to improve the efficiency. Lots of experimental simulations and cryptanalyses were implemented in which the NPCR and UACI are 99.6124% and 33.4600% respectively, which all suggested that it can effectively resist statistical analysis attacks and chosen plaintext attacks. asymmetric encryption; elliptic curve cryptography; different-sized block permutation 202115691115691  
with delay and cascade. Meanwhile, bit-level permutation has been applied to some other algorithms. In [9], bits of the pixel were segmented into an odd group and an even group, and after that, the chaotic image was calculated by randomly swapping the two groups. A bit-level cyclic shift method was applied in [10] to enhance the effects of the permutation for the plain image. However, [PERSON] et al. [11] mentioned that when adopting nonlinear transformation directly, due to the narrow interval and unrich nonlinear dynamic behavior, some image encryption algorithms based on low-dimensional chaos systems bear security risks. To overcome this vital shortcoming, the hyperchaotic system was designed and realized for image encryption. Compared with chaotic system, the hyperchaotic system has stronger randomness that is more suitable for image encryption. In [12], because of the complicated dynamic properties, a four-dimensional (4D) hyperchaotic system was proposed to generate the key stream and control the further rotation and shift for rows and columns of each component of the plain color image. [PERSON] et al. [13] used a 2-dimensional compound homogeneous hyperchaotic system (CHHCS) in the process of permutation to obtain good effects. However, by using the chosen-plaintext attack, some encrypted images based on hyperchaotic system could still be successfully converted into the corresponding plain image without any error [14; 15]. In order to solve this weakness, plaintext was correlated with the chaotic key stream derived from the hyperchaotic sequences when generating the final encryption key stream, which enhanced the security under the chosen-plaintext attack [16]. However, with the improvement of security, the problem of time efficiency has also been exposed. Over the last several decades, there has been a sharp increase in the interest in promoting the time efficiency of hyperchaotic image encryption. By using the chaotic shift transform (CST), [PERSON] et al. [17] combined the processes of permutation and diffusion into one stage, which effectively enhanced the time efficiency. As an important part of the attempt to improve the time efficiency, block shuffling has raised much more attention in recent studies. The author of [18] presented the algorithm where the image was divided into 4 blocks, and after the replacement according to the pseudorandom sequences derived from the combination chaotic system, these subblocks are combined together. Another scheme proposed in [19] has divided each color constituent into the same sized blocks with the application of the substitution based on the paired S-box.