混沌密码算法及其在安全电子邮件系统中应用的研究
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摘要
混沌理论与常规密码学之间的广泛联系激起了越来越多的密码学研究者的兴趣,利用混沌系统构造密码算法成为信息安全领域的一个重要研究热点。一般来说,目前混沌密码大致可以分为两种,一种是面向无线通信的混沌保密通信系统(大多数是基于混沌同步技术);另一种是基于Internet的混沌密码系统,可称为数字化混沌密码。对于前一种混沌保密通信系统来说,由于现有的混沌同步技术抗噪声能力的局限性,使得这种系统在目前的实际应用中受到限制。而数字化混沌密码的应用,以常规密码学为基础,有可能扩展至常规密码学的所有领域,如对称密钥密码、非对称密钥密码(公钥密码)、单向函数、数字签名等,具有远大的应用前景。因此文中如未特别说明,所讲述的混沌密码均为数字化混沌密码。
在1990年至2000年左右,混沌密码主要集中于对称密码研究。其间涌现了大量的密码算法,同时也有大量的密码算法被分析和攻击。与此同时,混沌密码的设计和分析上均出现的一些新的方法,这为以后的混沌密码研究者提供了很好的借鉴。
从2000年以后,混沌密码的研究扩展至非对称密钥密码、单向函数算法以及数字签名算法等常规密码学领域,使得混沌密码的研究进入了一个新的发展阶段。本文关于混沌密码的研究主要包括以下几个方面的内容:混沌公钥密码的介绍与分析;基于外部密钥的混沌图像加密研究;混沌分组密码研究;混沌单向Hash函数研究以及基于混沌与椭圆曲线的数字签名研究。最后,提出并实现了一种应用了混沌密码的安全电子邮件系统。
本文的主要成果包括:
1.对最新出现的三种混沌公钥密码算法进行了介绍和分析。包括:基于Chebeshev混沌映射的类RSA和类ElGamal公钥密码;基于分布式动力系统加密(DDE: Distributed Dynamics Encryption)的一种混沌公钥密码,基于耦合映射格子通用同步(GSCML: Generalized Sychronization of Coupled Map Lattices)的混沌公钥密码。并对三种混沌非对称密钥算法进行了初步的分析,讨论了其安全性及其实际应用的可能性。
2.由于混沌系统的一些优良特点,基于混沌的图像加密正成为混沌密码应用的一个重要领域。由于混沌密钥保存和传递的不便以及混沌密钥空间设计的问题(混沌密码一般以系统参数或系统初始值为密钥),本文提出了基于外部密钥的混沌图像加密方案,并使用了单一混沌信号和复合混沌信号来分别具体实现。分析表明,该种算法具有良好的安全性和抵抗各种攻击的能力。
3.提出了一种新的基于混沌的分组密码算法。通过使用长的二进制分数来代表浮点分数值,并且通过一些变换来避免浮点运算,使得该算法不需要对混沌映射进行离散化就可以避免浮点运算。同时,根据Shannon的理论,在密码算法中设置了混淆与扩散过程;对密码算法的仿真和分析表明该密码算法具有良好的性能。
4.构建了基于迭代混沌系统的单向Hash函数的一般模型。对这类单向Hash函数构造的一般方法进行研究与分类,并对他们的安全性分析方法进行明确的阐述。在一般模型的基础上,构建了两种不同的基于迭代混沌系统的单向Hash函数,并对它们性能和安全性进行了评估。
5.提出了一种基于混沌与椭圆曲线的数字签名算法。在该算法中,利用混沌加密来增强椭圆曲线数字签名( ECDSA: Elliptic Curve Digital Signature Algorithm)的安全性。相对于ECDSA来说,新的数字签名算法能够抵抗单信息密钥泄漏攻击、重复使用单信息密钥攻击以及重复使用签名密钥等攻击。
6.在上述本文提出的基于混沌的分组密码算法、基于迭代混沌系统的单向Hash函数算法以及基于混沌与椭圆曲线的数字签名算法的基础上,提出了一种应用了混沌密码的安全电子邮件系统。应用与分析表明,混沌密码能够满足安全电子邮件系统实际应用的要求。
The broad relations between the chaos theory and the conventional cryptography have aroused interest of more and more researchers, and using chaotic system to construct cryptography algorithms becomes an important research hotspot in information security field. Generally, there are two kinds of chaotic communications. One is of chaotic secure communications for wireless application (most of them are based on chaos synchronization techniques), the other is digital chaotic cipher for Internet application. As for the first kind of communication systems, at present, their applications are restricted by their inability of tolerance on the noise. On the other hand, the digital chaotic cipher, which analog to the conventional cryptography, seems to be extended to all fields of cryptography, such as symmetric key cryptography, public key cryptography (asymmetric key cryptography), one-way hash function, digital signature, and so on. For this reason, the content in this dissertation are mainly on digital chaotic cipher except for some special comment.
From about 1990 to 2000, chaos-based ciphers were developed, and symmetric key cryptography was the main research target. Many ciphers presented were analyzed and attacked. At the same time, there were some methods proposed to design and analysis of digital chaos-based ciphers, which provide good references for researchers.
After 2000, the research of the chaos-based cipher is extended to asymmetric cipher, one-way hash function and some other fields of conventional cryptography, this means that the chaotic cipher has developed to a new stage.
Our contributions in this dissertation involve the following aspects: review and analysis on chaos-based public key cryptography, research on chaos-based image encryption algorithm with external keys, research on chaos-based block cipher, research on one-way hash function based on iterated chaotic systems and digital signature based on chaotic systems and elliptic curves. In the last chapter, we propose a secure E-mail system that uses chaos-based cryptography.
The main contributions contained in this dissertation include:
1. An overall introduction of three new chaos-based public key cryptography algorithms is given in this dissertation. They include: RSA-like and ElGamal-like public key cryptography based on Chebeshev chaotic map, public key cryptography based on DDE and public key cryptography based on GSCML. Based on the introduction of the three algorithms, we have the analysis of them and the discussion of possibility of their applications.
2. For the advantages of the characteristics of chaotic systems, the research on chaos-based image encryption/decryption is becoming an important application filed of chaos-based cryptography. Usually, a chaotic cipher uses system parameters or initial values or both of them as the secret key, so the storage and transformation of the secret chaotic key are inconvenient and the design of key space is also a problem. We propose a chaos-based image encryption/decryption algorithm with external keys, and two different methods are presented by using a single chaotic system and mixed chaotic systems, respectively. Analysis shows that they have good security and can resist many kinds of attacks.
3. A novel block cipher based on chaotic systems is presented. It needs not discretize the chaotic maps, but uses long binary fractions and some other transformations to avoid float operations. At the same time, according to Shannon’s theory, diffusion and confusion are used in the algorithm for improving the security of the cipher. Simulation and analysis show that the new block cipher has a good performance.
4. A general model of one-way hash function based on iterated chaotic systems is constructed. The general construction method of this kind of one-way hash function is studied and classified, and the analysis methods for their security are also described. Based on the general model, we construct two one-way hash functions based on iterated chaotic systems, and their performance and security are also evaluated.
5. A digital signature based on chaotic systems and elliptic curves is presented, in which chaos-based cipher is used to strength the security of ECDSA. Compared to ECDSA, the proposed algorithm can resist single message leak-out attack, repeat use of single message key attack and repeat use of signature key attack.
6. By use of the above-mentioned results of research on chaos-based block cipher, one-way hash function based on iterated chaotic systems and digital signature based on chaotic systems and elliptic curves, we propose a secure E-mail system. The application and analysis show that chaos-based cipher can fulfill the requirements of the real application.
在1990年至2000年左右,混沌密码主要集中于对称密码研究。其间涌现了大量的密码算法,同时也有大量的密码算法被分析和攻击。与此同时,混沌密码的设计和分析上均出现的一些新的方法,这为以后的混沌密码研究者提供了很好的借鉴。
从2000年以后,混沌密码的研究扩展至非对称密钥密码、单向函数算法以及数字签名算法等常规密码学领域,使得混沌密码的研究进入了一个新的发展阶段。本文关于混沌密码的研究主要包括以下几个方面的内容:混沌公钥密码的介绍与分析;基于外部密钥的混沌图像加密研究;混沌分组密码研究;混沌单向Hash函数研究以及基于混沌与椭圆曲线的数字签名研究。最后,提出并实现了一种应用了混沌密码的安全电子邮件系统。
本文的主要成果包括:
1.对最新出现的三种混沌公钥密码算法进行了介绍和分析。包括:基于Chebeshev混沌映射的类RSA和类ElGamal公钥密码;基于分布式动力系统加密(DDE: Distributed Dynamics Encryption)的一种混沌公钥密码,基于耦合映射格子通用同步(GSCML: Generalized Sychronization of Coupled Map Lattices)的混沌公钥密码。并对三种混沌非对称密钥算法进行了初步的分析,讨论了其安全性及其实际应用的可能性。
2.由于混沌系统的一些优良特点,基于混沌的图像加密正成为混沌密码应用的一个重要领域。由于混沌密钥保存和传递的不便以及混沌密钥空间设计的问题(混沌密码一般以系统参数或系统初始值为密钥),本文提出了基于外部密钥的混沌图像加密方案,并使用了单一混沌信号和复合混沌信号来分别具体实现。分析表明,该种算法具有良好的安全性和抵抗各种攻击的能力。
3.提出了一种新的基于混沌的分组密码算法。通过使用长的二进制分数来代表浮点分数值,并且通过一些变换来避免浮点运算,使得该算法不需要对混沌映射进行离散化就可以避免浮点运算。同时,根据Shannon的理论,在密码算法中设置了混淆与扩散过程;对密码算法的仿真和分析表明该密码算法具有良好的性能。
4.构建了基于迭代混沌系统的单向Hash函数的一般模型。对这类单向Hash函数构造的一般方法进行研究与分类,并对他们的安全性分析方法进行明确的阐述。在一般模型的基础上,构建了两种不同的基于迭代混沌系统的单向Hash函数,并对它们性能和安全性进行了评估。
5.提出了一种基于混沌与椭圆曲线的数字签名算法。在该算法中,利用混沌加密来增强椭圆曲线数字签名( ECDSA: Elliptic Curve Digital Signature Algorithm)的安全性。相对于ECDSA来说,新的数字签名算法能够抵抗单信息密钥泄漏攻击、重复使用单信息密钥攻击以及重复使用签名密钥等攻击。
6.在上述本文提出的基于混沌的分组密码算法、基于迭代混沌系统的单向Hash函数算法以及基于混沌与椭圆曲线的数字签名算法的基础上,提出了一种应用了混沌密码的安全电子邮件系统。应用与分析表明,混沌密码能够满足安全电子邮件系统实际应用的要求。
The broad relations between the chaos theory and the conventional cryptography have aroused interest of more and more researchers, and using chaotic system to construct cryptography algorithms becomes an important research hotspot in information security field. Generally, there are two kinds of chaotic communications. One is of chaotic secure communications for wireless application (most of them are based on chaos synchronization techniques), the other is digital chaotic cipher for Internet application. As for the first kind of communication systems, at present, their applications are restricted by their inability of tolerance on the noise. On the other hand, the digital chaotic cipher, which analog to the conventional cryptography, seems to be extended to all fields of cryptography, such as symmetric key cryptography, public key cryptography (asymmetric key cryptography), one-way hash function, digital signature, and so on. For this reason, the content in this dissertation are mainly on digital chaotic cipher except for some special comment.
From about 1990 to 2000, chaos-based ciphers were developed, and symmetric key cryptography was the main research target. Many ciphers presented were analyzed and attacked. At the same time, there were some methods proposed to design and analysis of digital chaos-based ciphers, which provide good references for researchers.
After 2000, the research of the chaos-based cipher is extended to asymmetric cipher, one-way hash function and some other fields of conventional cryptography, this means that the chaotic cipher has developed to a new stage.
Our contributions in this dissertation involve the following aspects: review and analysis on chaos-based public key cryptography, research on chaos-based image encryption algorithm with external keys, research on chaos-based block cipher, research on one-way hash function based on iterated chaotic systems and digital signature based on chaotic systems and elliptic curves. In the last chapter, we propose a secure E-mail system that uses chaos-based cryptography.
The main contributions contained in this dissertation include:
1. An overall introduction of three new chaos-based public key cryptography algorithms is given in this dissertation. They include: RSA-like and ElGamal-like public key cryptography based on Chebeshev chaotic map, public key cryptography based on DDE and public key cryptography based on GSCML. Based on the introduction of the three algorithms, we have the analysis of them and the discussion of possibility of their applications.
2. For the advantages of the characteristics of chaotic systems, the research on chaos-based image encryption/decryption is becoming an important application filed of chaos-based cryptography. Usually, a chaotic cipher uses system parameters or initial values or both of them as the secret key, so the storage and transformation of the secret chaotic key are inconvenient and the design of key space is also a problem. We propose a chaos-based image encryption/decryption algorithm with external keys, and two different methods are presented by using a single chaotic system and mixed chaotic systems, respectively. Analysis shows that they have good security and can resist many kinds of attacks.
3. A novel block cipher based on chaotic systems is presented. It needs not discretize the chaotic maps, but uses long binary fractions and some other transformations to avoid float operations. At the same time, according to Shannon’s theory, diffusion and confusion are used in the algorithm for improving the security of the cipher. Simulation and analysis show that the new block cipher has a good performance.
4. A general model of one-way hash function based on iterated chaotic systems is constructed. The general construction method of this kind of one-way hash function is studied and classified, and the analysis methods for their security are also described. Based on the general model, we construct two one-way hash functions based on iterated chaotic systems, and their performance and security are also evaluated.
5. A digital signature based on chaotic systems and elliptic curves is presented, in which chaos-based cipher is used to strength the security of ECDSA. Compared to ECDSA, the proposed algorithm can resist single message leak-out attack, repeat use of single message key attack and repeat use of signature key attack.
6. By use of the above-mentioned results of research on chaos-based block cipher, one-way hash function based on iterated chaotic systems and digital signature based on chaotic systems and elliptic curves, we propose a secure E-mail system. The application and analysis show that chaos-based cipher can fulfill the requirements of the real application.
引文
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