Abstract:

The research on chaotic cryptography mainly includes chaotic sequence cryptography, chaotic block cryptography, and chaotic public key cryptography. Chaotic sequence cryptography has the characteristics of simple software and hardware implementation, fast encryption and decryption processing speed, and no or only limited error propagation. The research achievements in the design of chaotic sequence ciphers are extremely fruitful, but their security analysis generally stays at the stage of statistical verification analysis, and there are few proofs and analyses of provable security or other conditional security. Therefore, proving the security of chaotic ciphers has become an urgent research gap in this field that needs to be filled. The research on chaotic block cipher is quite mature, but the overall structures used are generally limited by the types of cryptographic structures: Feistel structure, SPN structure, Lai-Massey, and others(mostly deformations and improvements of the basic structures). Therefore, building an innovative cryptographic architecture that breaks the traditional structures has become one of the key issues that chaotic block ciphers urgently need to solve. The research on chaotic public key cryptography is relatively weak. The chaotic public key cryptography algorithm that combines the unique cryptographic characteristics of chaotic systems with public key cryptography not only has theoretical research significance but also has practical application value. Chaos systems are also widely used in secure communication fields such as communication transmission, speech encryption, image encryption, and spread spectrum communication. The implementation of electrical and optical chaotic systems is simple, and their computational complexity does not significantly increase with the increase of key space. It can provide security protection for different scenarios such as wireless communication, physical layer link security, and application layer data security.

Key words: secure communication, chaotic system, chaotic sequence cryptography, chaotic block cryptography, chaos public key cryptography