A novel asymmetric image encryption method is developed by integrating with hyper-chaotic system (HCS), deoxyribonucleic acid (DNA) level operation, Arnold transform (ART) and phase-truncated fractional Fourier transform (ptFrFT). In this method, all the initial values and/or control parameters of HCS, DNA, Arnold transform and ptFrFT are generated from a plaintext image by utilizing the SHA-256 hash algorithm, which are also taken as security keys for one-time pad. In this case, the plaintext is scrambled by ART and then encoded into a noise-like interim image using ptFrFT with two random phase masks as private keys obtained by HCS. Afterwards, the interim image is converted into the final ciphertext using DNA-level diffusion and scrambling. All these operations yield large enough key space and high sensitivity to the keys. Only if all the correct keys are employed, the useful information can be achieved. Some numerical results are demonstrated that the proposal has good security and strong robustness to different attacks.

通过与超混沌系统（HCS），脱氧核糖核酸（DNA）级操作，Arnold变换（ART）和相截断的分数阶Fourier变换（ptFrFT）集成，开发了一种新颖的不对称图像加密方法。在这种方法中，HCS，DNA，Arnold变换和ptFrFT的所有初始值和/或控制参数都是通过使用SHA-256哈希算法从纯文本图像生成的，SHA-256哈希算法也被用作一次性的安全密钥。在这种情况下，将纯文本用ART进行加扰，然后使用ptFrFT（带有两个随机相位掩码作为HCS获得的私钥）将其编码为类似噪声的临时图像。然后，使用DNA级别的扩散和加扰将临时图像转换为最终密文。所有这些操作都产生了足够大的键空间和对键的高灵敏度。只有使用所有正确的密钥，才能获得有用的信息。数值结果表明，该方案具有良好的安全性和针对不同攻击的鲁棒性。