Herein, an asymmetric image encryption algorithm based on RSA cryptosystem and a fractional-order chaotic system is proposed. Its security depends on RSA algorithm. First, a pair of public and private keys is generated by RSA algorithm. Subsequently, a random message shown as plaintext key information is encrypted by the public key and RSA to achieve ciphertext key information. Next, a new transformation map is established to generate the initial key according to the ciphertext key information. Subsequently, the initial key is substituted into a fractional hyperchaotic system equation to calculate the keystream. Finally, permutation and diffusion operations are employed to encrypt a plain image to obtain the final cipher image. In the proposed algorithm, different keys for encryption and decryption are designed under an asymmetric architecture. The RSA algorithm and fractional chaotic system are combined to encrypt images; in particular, a fast algorithm for computing power multiplication is employed, which significantly improves the encryption effect and enhances the security. Simulation results show that the proposed algorithm is effective and applicable to image protection.

中文翻译：

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基于分数阶混沌系统和RSA公钥密码系统的非对称图像加密算法

在此，提出了一种基于RSA密码系统和分数阶混沌系统的非对称图像加密算法。它的安全性依赖于 RSA 算法。首先，通过 RSA 算法生成一对公钥和私钥。随后，显示为明文密钥信息的随机消息通过公钥和 RSA 加密，得到密文密钥信息。接下来，根据密文密钥信息建立新的变换映射，生成初始密钥。随后，将初始密钥代入分数超混沌系统方程以计算密钥流。最后，采用置换和扩散操作对普通图像进行加密以获得最终的密码图像。在所提出的算法中，用于加密和解密的不同密钥是在非对称架构下设计的。RSA算法和分数混沌系统相结合对图像进行加密；特别是采用了算力乘法的快速算法，显着提高了加密效果，增强了安全性。仿真结果表明，该算法是有效的，适用于图像保护。