An Asymmetric Image Encryption Algorithm Based on a Fractional-Order Chaotic System and the RSA Public-Key Cryptosystem

摘要

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.