基于混沌动态S盒的密码算法及其应用研究
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摘要
自从1989年英国数学家Matthews首次明确提出“混沌密码”的概念以来,数字化混沌密码技术受到了不同领域专家学者越来越多的关注。尤其是MD5、SHA-1等被成功“碰撞”后,使结合现代密码构造技术中的优秀思想或组件来设计安全数字混沌密码算法的研究成为了当前密码学领域一个极有潜力的研究方向。
本文主要同绕基于混沌动态S-Box的新型安全密码设计技术及其应用展开研究。在分析讨论了现有混沌密码算法存在问题的基础上,结合现代密码算法构造技术的优点设计了符合密码设计准则的单向Hash函数、可变长分组密码算法和图像加密算法,最后给出了基于混沌Hash函数的共献密钥协商协议和可认证的多秘密共享方案。具体来说,主要研究内容包括如下几个方面：
(1)对数字混沌密码算法的安全现状进行了深入分析,针对现有混沌密码算法构造中存在的浮点运算多、性能低的问题,研究了符合密码设计准则的单向、双向混沌动态S-Box的构造方法,为设计结合现代密码算法优点的安全快速混沌密码算法奠定基础。
(2)结合混沌系统与传统单向Hash函数设计方法的优点,在设计的混沌动态单向S-Box的基础上,提出了一种基于混沌动态单向S-Box的带秘密密钥的单向Hash函数构造方法。该方法用混沌S-Box替换和函数查找表来生成具有混沌特性的Hash摘要。与现有混沌Hash算法相比,新方案没有将原始数据直接参与混沌迭代,而是采用混沌动态S-Box替换来提高系统的实时性能。理论分析和实验结果表明：该方法不仅有很好单向性、初值和密钥敏感性,且有较大的密钥空间,易于实现。
(3)为了提高混沌分组密码算法的实现性能和安全强度,利用一维分段线性映射和Tent映射的混沌特性设计了一个可变长分组密码算法。算法实现过程中通过S盒替换来增强系统的混淆性,借助模加运算和移位操作来实现系统的雪崩特性。此外,明文相关的分组长度可以有效的抵御选择明文或选择密文攻击。研究表明：提出的基于混沌动态S盒的可变长分组密码算法不仅具有大的密钥空间还能有效抵御各种情景下的安全性攻击。
(4)分析讨论了现有空间混沌图像加密方案存在的运算效率低、扩散性差的问题,构造了一个选择明文攻击方案。在此基础上,提出了一种安全高效图像加密算法,该算法实现过程中借鉴现代密码算法构造中的优良思想,在像素置乱阶段动态生成混沌S盒群。像素替换阶段,非线性S盒查找表的使用减少了空间混沌迭代序列运算量,避免了过多的浮点运算带来的运算性能问题,同时,也在一定层度上缓解了数字化混沌密码算法存在的短周期、可预测问题,提高了系统的安全性能。该论文对提出方案进行了详细的雪崩特性测试、统计分析、信息熵和差分分析,各项理论分析和实验结果表明,提出方案运算效率高,有很好的差分性和大的密钥空间,能满足现有图像加密的各种安全特性。
(5)对现有混沌密码算法在密钥协商协议中的应用进行了深入研究。指出现有混沌密钥协商协议不仅容易遭受安全攻击,还不满足共献性,存在密钥控制,为此利用混沌Hash函数的单向性和抗碰撞性设计了一个基于混沌Hash函数的共献密钥协商方案,各种安全性分析证明,提出方案既满足共献性,消除了密钥控制,又能抵御现有攻击。
(6)通过对YCH系列多秘密共享方案的分析研究,指出它们在实现认证功能时存在公布数据多、通信和计算代价高、不利于计算能力弱的移动环境等缺陷,并在此基础上利用混沌Hash的高效性设计了适合于移动环境的防欺诈多秘密共享方案。与以往协议相比,该方案具有如下优点：a)计算性能高,较适合计算能力差的移动环境；b)实现原理简单；c)公布信息量少,通信代价低；d)长期秘密si可以重复使用,减少了秘密共享成本。
The research of digital chaotic ciphers has attracted more and more attention after British mathematician Matthews first definitely put forward the conception of chaotic encryption algorithm in 1989, especially MD5 and SHA-1 have been cracked. In addition, a lot of modern cipher construction techniques and components are excellent, so it is suggested combining with modern ciphers to construct secure chaotic cryptosystems.
This dissertation focuses on the design and application of chaotic ciphers based on chaotic dynamic S-Box, which involves the following aspects. First of all, this paper investigates the main problems of the chaotic ciphers faced. Secondly, it proposes some new chaotic cryptographic primitives, including a chaotic Hash function, a variable length block cipher and an image encryption scheme. Finally, it studies the proposed primitives in the application of security protocols. Specifically, the main achievements and originalities contained in this dissertation are as follows:
(1) Detailed analysis of the state-of-the-art techniques in chaotic cryptography is carried out. Chaos-based S-boxes are proposed to cut down floating-point calculations in the existing chaotic ciphers.
(2) Combined with the excellent thinking of traditional Hash function, a novel keyed one-way Hash function based on the designed chaotic dynamic S-Box is proposed. The new Hash function can give a chaotic Hash value by means of the look up table of functions and chaotic dynamic S-Box. Compared with the existing chaotic Hash functions, the new method improves computational performance of Hash system by using the chaotic dynamical S-Box substitution in place of iterating the original message directly in chaos system. Theoretical and experimental results show that the proposed Hash function has strong one way property, large key space, sensitivity to initial conditions and chaotic parameters.
(3) To overcome the dilemma between performance and security, a variable length block cipher (VLBC) based on piecewise linear chaotic map and Tent map is proposed. The new cryptosystem gains confusion by dynamic S-Box substitution and avalanche property by modular and cycle shift arithmetic. In addition, the plaintext determined block length can effectively resist chosen plaintext attack and chosen ciphertext attack. The security analysis demonstrates that the chaotic S-Box based VLBC not only has large key space but also can withstand the existing attacks.
(4) The diffusion and efficiency of the spatial chaotic based image cryptosystem are investigated. And then shows that the diffusion property of the spatial chaotic cryptosystem is too weak to withstand chosen plaintext attack. To improve the security, a novel image encryption scheme based a group of S-Boxes is proposed. The new scheme employs one spatial chaotic to shuffle the position of image pixels and build 4 S-Boxes dynamically, and then confuses the relationship between the cipher-image and the plain-image by utilizing a look-up table of S-Boxes, thereby significantly increasing the resistance to statistical and differential attacks. Theoretical and experimental results demonstrate that at the similar performance level, the proposed cryptosystem provides a secure way for image encryption and transmission.
(5) Based on careful security analysis of the chaotic key agreements, pointes out that none of these schemes can satisfy the contributory nature of key agreement. To fill the gaps, a secure contributory key agreement protocol based on chaotic Hash is proposed. The proposed scheme utilizes the chaotic Hash function to achieve the contributory nature and enhance its security. Cryptanalysis demonstrates that the proposed chaotic-Hash-based scheme can overcome all the current deficiencies.
(6) By analyzing current multi-secret sharing schemes, it pointes out that they are not adaptive the mobile condition. And then presents an improved chaotic Hash-based verifiable multi-secret sharing scheme on mobile devices e.g. cell phone and PDA. Compare with the existing verifiable multi-secret sharing schemes, the proposed scheme has the following strong points:a) more efficiency; b) the theory is simple and pellucid; c) fewer publishing data; d) the long-term secret si is reusable.
本文主要同绕基于混沌动态S-Box的新型安全密码设计技术及其应用展开研究。在分析讨论了现有混沌密码算法存在问题的基础上,结合现代密码算法构造技术的优点设计了符合密码设计准则的单向Hash函数、可变长分组密码算法和图像加密算法,最后给出了基于混沌Hash函数的共献密钥协商协议和可认证的多秘密共享方案。具体来说,主要研究内容包括如下几个方面：
(1)对数字混沌密码算法的安全现状进行了深入分析,针对现有混沌密码算法构造中存在的浮点运算多、性能低的问题,研究了符合密码设计准则的单向、双向混沌动态S-Box的构造方法,为设计结合现代密码算法优点的安全快速混沌密码算法奠定基础。
(2)结合混沌系统与传统单向Hash函数设计方法的优点,在设计的混沌动态单向S-Box的基础上,提出了一种基于混沌动态单向S-Box的带秘密密钥的单向Hash函数构造方法。该方法用混沌S-Box替换和函数查找表来生成具有混沌特性的Hash摘要。与现有混沌Hash算法相比,新方案没有将原始数据直接参与混沌迭代,而是采用混沌动态S-Box替换来提高系统的实时性能。理论分析和实验结果表明：该方法不仅有很好单向性、初值和密钥敏感性,且有较大的密钥空间,易于实现。
(3)为了提高混沌分组密码算法的实现性能和安全强度,利用一维分段线性映射和Tent映射的混沌特性设计了一个可变长分组密码算法。算法实现过程中通过S盒替换来增强系统的混淆性,借助模加运算和移位操作来实现系统的雪崩特性。此外,明文相关的分组长度可以有效的抵御选择明文或选择密文攻击。研究表明：提出的基于混沌动态S盒的可变长分组密码算法不仅具有大的密钥空间还能有效抵御各种情景下的安全性攻击。
(4)分析讨论了现有空间混沌图像加密方案存在的运算效率低、扩散性差的问题,构造了一个选择明文攻击方案。在此基础上,提出了一种安全高效图像加密算法,该算法实现过程中借鉴现代密码算法构造中的优良思想,在像素置乱阶段动态生成混沌S盒群。像素替换阶段,非线性S盒查找表的使用减少了空间混沌迭代序列运算量,避免了过多的浮点运算带来的运算性能问题,同时,也在一定层度上缓解了数字化混沌密码算法存在的短周期、可预测问题,提高了系统的安全性能。该论文对提出方案进行了详细的雪崩特性测试、统计分析、信息熵和差分分析,各项理论分析和实验结果表明,提出方案运算效率高,有很好的差分性和大的密钥空间,能满足现有图像加密的各种安全特性。
(5)对现有混沌密码算法在密钥协商协议中的应用进行了深入研究。指出现有混沌密钥协商协议不仅容易遭受安全攻击,还不满足共献性,存在密钥控制,为此利用混沌Hash函数的单向性和抗碰撞性设计了一个基于混沌Hash函数的共献密钥协商方案,各种安全性分析证明,提出方案既满足共献性,消除了密钥控制,又能抵御现有攻击。
(6)通过对YCH系列多秘密共享方案的分析研究,指出它们在实现认证功能时存在公布数据多、通信和计算代价高、不利于计算能力弱的移动环境等缺陷,并在此基础上利用混沌Hash的高效性设计了适合于移动环境的防欺诈多秘密共享方案。与以往协议相比,该方案具有如下优点：a)计算性能高,较适合计算能力差的移动环境；b)实现原理简单；c)公布信息量少,通信代价低；d)长期秘密si可以重复使用,减少了秘密共享成本。
The research of digital chaotic ciphers has attracted more and more attention after British mathematician Matthews first definitely put forward the conception of chaotic encryption algorithm in 1989, especially MD5 and SHA-1 have been cracked. In addition, a lot of modern cipher construction techniques and components are excellent, so it is suggested combining with modern ciphers to construct secure chaotic cryptosystems.
This dissertation focuses on the design and application of chaotic ciphers based on chaotic dynamic S-Box, which involves the following aspects. First of all, this paper investigates the main problems of the chaotic ciphers faced. Secondly, it proposes some new chaotic cryptographic primitives, including a chaotic Hash function, a variable length block cipher and an image encryption scheme. Finally, it studies the proposed primitives in the application of security protocols. Specifically, the main achievements and originalities contained in this dissertation are as follows:
(1) Detailed analysis of the state-of-the-art techniques in chaotic cryptography is carried out. Chaos-based S-boxes are proposed to cut down floating-point calculations in the existing chaotic ciphers.
(2) Combined with the excellent thinking of traditional Hash function, a novel keyed one-way Hash function based on the designed chaotic dynamic S-Box is proposed. The new Hash function can give a chaotic Hash value by means of the look up table of functions and chaotic dynamic S-Box. Compared with the existing chaotic Hash functions, the new method improves computational performance of Hash system by using the chaotic dynamical S-Box substitution in place of iterating the original message directly in chaos system. Theoretical and experimental results show that the proposed Hash function has strong one way property, large key space, sensitivity to initial conditions and chaotic parameters.
(3) To overcome the dilemma between performance and security, a variable length block cipher (VLBC) based on piecewise linear chaotic map and Tent map is proposed. The new cryptosystem gains confusion by dynamic S-Box substitution and avalanche property by modular and cycle shift arithmetic. In addition, the plaintext determined block length can effectively resist chosen plaintext attack and chosen ciphertext attack. The security analysis demonstrates that the chaotic S-Box based VLBC not only has large key space but also can withstand the existing attacks.
(4) The diffusion and efficiency of the spatial chaotic based image cryptosystem are investigated. And then shows that the diffusion property of the spatial chaotic cryptosystem is too weak to withstand chosen plaintext attack. To improve the security, a novel image encryption scheme based a group of S-Boxes is proposed. The new scheme employs one spatial chaotic to shuffle the position of image pixels and build 4 S-Boxes dynamically, and then confuses the relationship between the cipher-image and the plain-image by utilizing a look-up table of S-Boxes, thereby significantly increasing the resistance to statistical and differential attacks. Theoretical and experimental results demonstrate that at the similar performance level, the proposed cryptosystem provides a secure way for image encryption and transmission.
(5) Based on careful security analysis of the chaotic key agreements, pointes out that none of these schemes can satisfy the contributory nature of key agreement. To fill the gaps, a secure contributory key agreement protocol based on chaotic Hash is proposed. The proposed scheme utilizes the chaotic Hash function to achieve the contributory nature and enhance its security. Cryptanalysis demonstrates that the proposed chaotic-Hash-based scheme can overcome all the current deficiencies.
(6) By analyzing current multi-secret sharing schemes, it pointes out that they are not adaptive the mobile condition. And then presents an improved chaotic Hash-based verifiable multi-secret sharing scheme on mobile devices e.g. cell phone and PDA. Compare with the existing verifiable multi-secret sharing schemes, the proposed scheme has the following strong points:a) more efficiency; b) the theory is simple and pellucid; c) fewer publishing data; d) the long-term secret si is reusable.
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