混沌密码理论研究与应用新进展

doi:10.3969/j.issn.1671-1122.2024.02.004

摘要/Abstract

摘要：

混沌密码研究主要包括混沌序列密码、混沌分组密码和混沌公钥密码。混沌序列密码具有软硬件实现简单、加解密处理速度快、没有或只有有限的错误传播等特点。混沌序列密码的设计方面研究成果极为丰硕，但其安全性分析一般停留在统计性验证分析阶段，而对可证明安全性或其他有条件安全性的证明和分析很少，因此证明混沌序列密码的安全性已成为该领域亟需填补的空白。混沌分组密码的研究颇为成熟，但其整体结构一般受限于Feistel结构、SPN结构、Lai-Massey结构及其变形结构。因此，构建突破传统结构的创新性密码架构成为混沌分组密码亟待解决的关键问题之一。混沌公钥密码的研究相对薄弱，利用混沌系统特有的密码特性和公钥密码系统相结合的混沌公钥密码算法不仅具有理论研究意义，而且具有实际应用价值。混沌系统也被广泛应用于通信传输、语音加密、图像加密和扩频通信等保密通信领域。电、光混沌系统实现简便，其计算复杂性不会随着密钥空间的增大而明显增大，能够为无线通信、物理层链路安全、应用层数据安全等不同场景提供安全保护。

关键词: 保密通信, 混沌系统, 混沌序列密码, 混沌分组密码, 混沌公钥密码

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

中图分类号:

TP309

赵耿, 马英杰, 董有恒. 混沌密码理论研究与应用新进展[J]. 信息网络安全, 2024, 24(2): 203-216.

ZHAO Geng, MA Yingjie, DONG Youheng. New Progress in Research and Application of Chaotic Cryptography Theory[J]. Netinfo Security, 2024, 24(2): 203-216.

图/表 1

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算法	优点	缺点
文献[10,11]	各格子间产生能量传递，系统在空间和时间上都会出现混沌现象	易受回归映射和相空间重构攻击，存在弱混沌，格子输出的分岔图中均存在周期窗口
文献[12]	分数阶混沌映射作为底层映射，提高了系统复杂度，采用非线性耦合方案，提高了能量传输速度	系统的分岔图存在周期窗口，存在弱混沌现象
文献[13,14]	采用动态耦合参数和非线性耦合方案，提高了能量传递速度	未很好地解决弱混沌和周期窗口问题，输出序列分布未得到很好的均匀化，回归映射集中在抛物线附近
文献[15]	采用混合线性—非线性耦合方案，提高了能量传递速度	在某些控制参数下一些格子处于弱混沌状态
文献[16]	采用随机耦合方案，极大加快了能量传递速度，提高了系统的复杂度	随机耦合过程无法复现，适用场景有限
文献[17-21]	使用ECA控制耦合和扰动，有良好的复杂性、遍历性、非周期性和不可预测性，能够抵抗回归映射攻击，采用动态非线性耦合方案，极大加快了能量传递速度	底层映射函数计算复杂性在一定程度上影响系统的运算速度