密码理论的若干关键技术研究
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摘要
随着计算机网络技术特别是Internet的迅猛发展，网络中传输和存储的电子数据的机密性、完整性和鉴别问题已成为人们关注的一个重要课题。密码技术是是信息安全的核心技术，自从Shannon奠定现代密码学基础以来，各国均在积极探索和开发具有自主知识产权的密码系统，从而保障信息化过程中的社会利益和国家利益。细胞自动机是时间、空间和状态均离散的动力学系统，其固有的组成单元的简单性、单元之间作用的局部性和信息处理的高度并行性，并表现出复杂的全局性等特点使得细胞自动机适合于密码学中的应用，被认为是密码技术自主化中最有希望的核心技术之一。
本文根据细胞自动机的研究现状，在流密码方面，提出了基于耦合可控细胞自动机和二维可控细胞自动机的高质量伪随机序列发生器；在对称密码方面，提出了基于耦合触发细胞自动机的加密算法和基于配对函数的对称加密算法；在公钥密码体制方面，提出了基于细胞自动机的公钥密码系统。
本文的主要研究工作和创新成果如下：
(1)提出了一种新的细胞自动机—耦合可控细胞自动机。根据耦合和可控细胞自动机的性质，提出了一种基于耦合可控细胞自动机伪随机序列发生方法。随机性测试表明，该伪随机序列发生器优于一维细胞自动机伪随机序列发生器，与二维细胞自动机伪随机序列发生器相当，同时它保留了一维细胞自动机的结构简单性。这种新的细胞自动机在对称密码学中有广泛地应用。
(2)提出了一种新的细胞自动机模型一二维梯形可控细胞自动机模型。根据二维可控细胞自动机的性质，提出了一种具有梯型结构的二维可控细胞自动机的伪随机序列发生方法。计算机模拟表明，具有梯型结构的二维可控细胞自动机伪随机序列发生器实现简单，产生的序列具有速度高、统计特性好等优点。
(3)根据耦合和触发细胞自动机的性质，采用相互作用的n个细胞自动机作为一个整体，构造出耦合触发细胞自动机加密系统。计算机仿真表明，该算法极大地提高了密钥空间，有效地阻止了蛮力攻击；同时加密时随机数的引入使得攻击者不可能获得唯一的明文密文对，从而有效地抵御了已知明文攻击和选择密文的攻击。
(4)提出了一种基于细胞自动机理论的公钥密码算法。该算法以n个1维可逆细胞自动机为私钥，由它们构造出的2维Moore型不可逆的细胞自动机为公钥组成公钥密码体制。该算法实现简单，易于VLSI实现，有效地解决了复杂密码算法在高速实时信息传输时带来的瓶颈现象。
(5)基于配对函数提出了一种对称加密算法，该算法采用了一次一密、多重算法对数据进行加密，密钥空间足够大，有效地防止了网络非法用户的唯明文攻击。该算法是一种安全性好、可靠性高、实用性强的数据加密算法。
With the development of the computer network technique, especially internet,problem of data confidentiality, integrity and authentication of electronic data hasalready become an important task. Cryptography is the kernel technology ofinformation security. From the foundation of morden cryptography, each ocountry inthe world has been exploring and developing the self-dependent techqiues ofcryptography to ensure benfits of society and contry during the process ofinformatization. Cellular automata(CA) is a discrete dynamic system composed of time,space and status, whose inherent characteristics of simplicity of component unit,locality of interaction, high parallelism of information processing as well ascomplicated dynamic property makes CA much suitable for cryptograph application.It becomes one of the most promising kernel techniques in the self-independentresearch of the cryptograph.
According to status quo of cellular automata, this paper presents two high qualitypseudo random generators based on controllable coupled and two-Dimensional CAwith a trapezoidal structure in stream cipher. From the view of symmetric encryption,two symmetric encryption algorithms based on coupled toggle cellular automata andpairing function is proposed.From the view of public-key cryptosystem,a public-keycryptosystem based on cellular automata is proposed.
Main contributions of this dissertation are summarized as follows:
(1) A novel cellular automata(CA)-coupling and controllable CA(CCCA) isproposed in this paper. According to character of CCCA, a pseudo random generatingmethod based on CCCA is presented. Randomness test results on CCCApseudorandom number generators (PRNGs) show that they are better thanone-dimensional CA PRNGs and can be comparable to two-dimensional ones.Meanwhile it keeps the structure simplicity of one-dimensional CA. This novel CCCAis widely used in symmetrical cryptography.
(2) A novel cellular automata(CA)- two-Dimensional controllable CA with atrapezoidal structure is proposed in this paper. According to characteristics oftwo-Dimensional controllable CA, a pseudo random generating method based ontwo-Dimensional controllable CA with a trapezoidal structure is presented. Simulationdemonstrates that pseudo random bit sequence generator based on the two- dimensional controllable CA with a trapezoidal structure is easily implemented, andcan generate high speed bit sequence and excellent statistical properties.
(3) According to characters of coupled and toggle cellular automata, a novelcryptography system is constructed based on coupled toggle cellular automata, usingthe interaction with n cellular automatas. Computer simulation indicates thatcryptosystem can greatly enlarge the key space and effectively resist brute attack; Inthe meantime, the import of random numbers makes that attacker can not obtain uniqueplaintext and corresponding ciphertext, which effectively resists known-plain attackand chosn-cipher attack.
(4) A public-key cryptosystem based on cellular automata is proposed. Thisalgorithm employs n one-dimensional reversible cellular automata as secret key, andthe two-dimensional Moore-neighbor irreversible cellular automata constructed byabove cellular automata is taken as the public-key. Both of these keys compose thepublic-key cryptosystem. This algorithm can be implemented simply and is suitable ofimplementation with VLSI, which efficiently solves the bottle-neck phenomenonbrought by the complicated encryption algorithm during the high speed and real timeinformation transmission.
(5) According to characters of pairing function, a kind of symmetric encryptionalgorithm based on pairing function is proposed. This algorithm encrypts data byone-time one-key and multiple encryption, its key space is big to enough and defendseffectively ciphertext-only attack of network's illicit users. This algorithm is a dataencryption of safety, reliability and practial.
本文根据细胞自动机的研究现状，在流密码方面，提出了基于耦合可控细胞自动机和二维可控细胞自动机的高质量伪随机序列发生器；在对称密码方面，提出了基于耦合触发细胞自动机的加密算法和基于配对函数的对称加密算法；在公钥密码体制方面，提出了基于细胞自动机的公钥密码系统。
本文的主要研究工作和创新成果如下：
(1)提出了一种新的细胞自动机—耦合可控细胞自动机。根据耦合和可控细胞自动机的性质，提出了一种基于耦合可控细胞自动机伪随机序列发生方法。随机性测试表明，该伪随机序列发生器优于一维细胞自动机伪随机序列发生器，与二维细胞自动机伪随机序列发生器相当，同时它保留了一维细胞自动机的结构简单性。这种新的细胞自动机在对称密码学中有广泛地应用。
(2)提出了一种新的细胞自动机模型一二维梯形可控细胞自动机模型。根据二维可控细胞自动机的性质，提出了一种具有梯型结构的二维可控细胞自动机的伪随机序列发生方法。计算机模拟表明，具有梯型结构的二维可控细胞自动机伪随机序列发生器实现简单，产生的序列具有速度高、统计特性好等优点。
(3)根据耦合和触发细胞自动机的性质，采用相互作用的n个细胞自动机作为一个整体，构造出耦合触发细胞自动机加密系统。计算机仿真表明，该算法极大地提高了密钥空间，有效地阻止了蛮力攻击；同时加密时随机数的引入使得攻击者不可能获得唯一的明文密文对，从而有效地抵御了已知明文攻击和选择密文的攻击。
(4)提出了一种基于细胞自动机理论的公钥密码算法。该算法以n个1维可逆细胞自动机为私钥，由它们构造出的2维Moore型不可逆的细胞自动机为公钥组成公钥密码体制。该算法实现简单，易于VLSI实现，有效地解决了复杂密码算法在高速实时信息传输时带来的瓶颈现象。
(5)基于配对函数提出了一种对称加密算法，该算法采用了一次一密、多重算法对数据进行加密，密钥空间足够大，有效地防止了网络非法用户的唯明文攻击。该算法是一种安全性好、可靠性高、实用性强的数据加密算法。
With the development of the computer network technique, especially internet,problem of data confidentiality, integrity and authentication of electronic data hasalready become an important task. Cryptography is the kernel technology ofinformation security. From the foundation of morden cryptography, each ocountry inthe world has been exploring and developing the self-dependent techqiues ofcryptography to ensure benfits of society and contry during the process ofinformatization. Cellular automata(CA) is a discrete dynamic system composed of time,space and status, whose inherent characteristics of simplicity of component unit,locality of interaction, high parallelism of information processing as well ascomplicated dynamic property makes CA much suitable for cryptograph application.It becomes one of the most promising kernel techniques in the self-independentresearch of the cryptograph.
According to status quo of cellular automata, this paper presents two high qualitypseudo random generators based on controllable coupled and two-Dimensional CAwith a trapezoidal structure in stream cipher. From the view of symmetric encryption,two symmetric encryption algorithms based on coupled toggle cellular automata andpairing function is proposed.From the view of public-key cryptosystem,a public-keycryptosystem based on cellular automata is proposed.
Main contributions of this dissertation are summarized as follows:
(1) A novel cellular automata(CA)-coupling and controllable CA(CCCA) isproposed in this paper. According to character of CCCA, a pseudo random generatingmethod based on CCCA is presented. Randomness test results on CCCApseudorandom number generators (PRNGs) show that they are better thanone-dimensional CA PRNGs and can be comparable to two-dimensional ones.Meanwhile it keeps the structure simplicity of one-dimensional CA. This novel CCCAis widely used in symmetrical cryptography.
(2) A novel cellular automata(CA)- two-Dimensional controllable CA with atrapezoidal structure is proposed in this paper. According to characteristics oftwo-Dimensional controllable CA, a pseudo random generating method based ontwo-Dimensional controllable CA with a trapezoidal structure is presented. Simulationdemonstrates that pseudo random bit sequence generator based on the two- dimensional controllable CA with a trapezoidal structure is easily implemented, andcan generate high speed bit sequence and excellent statistical properties.
(3) According to characters of coupled and toggle cellular automata, a novelcryptography system is constructed based on coupled toggle cellular automata, usingthe interaction with n cellular automatas. Computer simulation indicates thatcryptosystem can greatly enlarge the key space and effectively resist brute attack; Inthe meantime, the import of random numbers makes that attacker can not obtain uniqueplaintext and corresponding ciphertext, which effectively resists known-plain attackand chosn-cipher attack.
(4) A public-key cryptosystem based on cellular automata is proposed. Thisalgorithm employs n one-dimensional reversible cellular automata as secret key, andthe two-dimensional Moore-neighbor irreversible cellular automata constructed byabove cellular automata is taken as the public-key. Both of these keys compose thepublic-key cryptosystem. This algorithm can be implemented simply and is suitable ofimplementation with VLSI, which efficiently solves the bottle-neck phenomenonbrought by the complicated encryption algorithm during the high speed and real timeinformation transmission.
(5) According to characters of pairing function, a kind of symmetric encryptionalgorithm based on pairing function is proposed. This algorithm encrypts data byone-time one-key and multiple encryption, its key space is big to enough and defendseffectively ciphertext-only attack of network's illicit users. This algorithm is a dataencryption of safety, reliability and practial.
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