混沌伪随机序列及其应用研究
摘要
随着计算机技术和网络技术的快速发展,信息安全成为了学术界和企业界共同关注的热点。以密码学为核心的信息安全领域中,随机序列扮演着非常重要的角色:密钥的生成、数字签名、认证和鉴别以及各种安全通信协议都离不开高质量的随机序列。正如著名的密码学家Bruce Schneier所说:“随机序列是谈论最少的密码学问题,但没有哪个问题比这个问题更重要”。从某种意义上讲,随机序列的安全性确定了整个安全体系的安全性。因此如何能够得到高质量的随机序列发生就成为了信息安全重点研究的问题。将混沌理论引入伪随机序列是当前国际非线性科学和信息科学两个学科交叉融合的热门前沿课题之一。本论文着重研究混沌伪随机序列发生器的设计与实现,并尝试将其用于保障信息的安全之中。
本论文中的主要贡献是:
①从多个方面对混沌理论基础作了详细的论述。给出了混沌的定义,描述了混沌运动的特征,并介绍了各种常见的混沌模型和混沌研究所需的判据与准则;
②介绍随机序列的相关理论,对目前信息安全中使用的随机序列发生器进行分析、归纳和总结,提出它们存在的问题:序列不够长、可以预测、产生的序列质量较差、速度较低、使用不方便等;
③对区间数目参数化分段线性混沌映射(SNP-PLCM)的密码学特性进行详细分析,并以此为基础,提出了一种基于区间数目参数化分段线性混沌映射的伪随机序列发生器。该发生器同时利用控制参数扰动策略和输出序列扰动策略避免数字化混沌系统的动力学特性退化。理论分析和仿真实验结果表明,该算法产生的伪随机序列具有理想的性能;
④混沌伪随机序列应用于S盒,提出了一种基于混沌序列的可度量动态S盒的设计方法。该方法利用区间数目参数化PLCM良好的密码特性产生的伪随机序列,然后用伪随机序列构造混沌动态S盒。数字分析结果表明,所设计的S盒有较高的非线性度和良好的严格雪崩特性;
⑤提出一种基于混沌动态S盒和非线性移位寄存器的快速序列密码算法,该算法利用混沌伪随机序列用来初始化非线性移位寄存器(NLFSR)、构造非线性移位寄存器的更新函数和混沌动态S盒。非线性移位寄存器每循环一次输出32比特密钥流。每输出21 6比特密钥流,混沌S k( i )盒动态更新一次,使得在安全和效率方面有一个比较好的折中点。实验结果表明该方法可以得到独立、均匀和长周期的密钥流序列,同时可以有效的克服混沌序列在有限精度实现时出现短周期和NLFSR每循环1次输出1比特密钥流的低效率问题;
⑥结合传统的Hash函数结构与混沌动态S盒,提出了一种基于混沌动态S盒的带密钥的Hash函数,该方法利用混沌动态S盒和函数查找表来生成具有混沌特性的Hash散列值,与现有的混沌Hash函数相比,该方法利用混沌动态S盒来提高系统的实时性能。结果表明该算法不仅具有很好的单向性,初值和密钥敏感性,而且实行的速度快,易于实现;
最后对论文工作进行了全面的总结,并对今后的研究方向进行了展望。
With the fast development of computer and Internet technology, Information security has become the common focus of both academia and enterprises. Cryptology is the core of information security and the random sequence has played a very important role in it. The key generation, digital signature, authentication and many kinds of communication protocol all need random sequence. Just as the famous expert of cryptology Bruce Schneier had pointed out that the random sequence is the problem which is discussed very less in cryptology, but it is the most important one in cryptology. In some case, the security of the random sequence decides the security of the system. So, how can we get high quality random sequence generator has become a very vital problem. In this thesis, we will study how to design high quality, fast, convenient random sequence generator. Currently, it is one of the hot promising reseachfields on the combination of nonlinear science and information science to apply chaos theory to pseudorandom sequence. In this dissertation, the design and implementation of chaotic pseudorandom sequence generator have been carefully studied and applied successfully to protect the security of information.
The following tasks have been accomplished in this dissertation:
①Chaos theory is introduced in detail from different aspects and views, the definition of chaos is presented, the characteristics of chaotic dynamics are described, and the criterion and rule of chaos are given.
②The relevant theory of random sequence is introduced, and theusual random sequence generators used in information security have been summarized, these generators' disadvantages, such as short period, predictability, bad quality, lower pace, inconvenience, are given.
③The piecewise linear chaotic map with a segment number parameter (SNP-PLCM) is analyzed in detail. Based on SNP-PLCM, a chaotic pseudorandom sequence generator is presented. The generator employs perturbation strategy of controls parameter and output sequences to avoid dynamical degradation of digital chaotic systems. Theoretical analysis and computer simulation results show that the chaotic pseudorandom sequence generator can get high quality sequences.
④A measurable dynamic S-box algorithm is proposed by use of chaotic pseudo- random sequences, and the performance of these S-boxes is analyzed mathematically. Theoretical analysis and computer test results show that this scheme has good security and performance.
⑤Based on chaotic pseudorandom sequence generator and non-linear feedback shift register (NLFSR), a fast streamer cipher is proposed. The approach is that chaotic pseudorandom sequence initializes NLFSR and constructs the update function of NLFSR, and chaotic dynamic S-boxes. The update function which is called once per round, manipulates the internal state to generate 64 bits of pseudorandom key stream. The chaotic dynamic S-box of the update function should be reconstructed at lease once for every 21 6 bit of key stream generated, that is, iteration 1024 times of chaotic system can produces 21 6 bits of pseudo-random key stream. The theoretical and numerical analyses show that the scheme can not only produce the independently and uniformly distributed key stream, but also can improve largely the period of chaotic sequence under the finite-precision circumstances and increase in efficiency.
⑥By combining the traditional iteration structure of Hash function with the dynamic S-boxes, a novel keyed Hash function is presented. The proposed approach can give a chaotic Hash value by means of the lookup table of functions and chaotic dynamic S-box. Compared with the existing chaotic Hash functions, this method improves computational performance of Hash system by using the chaotic S-box substitution. Theoretical and experimental results show that the proposed method has not only strong one way property, sensitivity to initial conditions and chaotic system’s parameters, but also high speed.
Finally, the research work of this dissertation is summarized, and the future reseach direction is indicated.
本论文中的主要贡献是:
①从多个方面对混沌理论基础作了详细的论述。给出了混沌的定义,描述了混沌运动的特征,并介绍了各种常见的混沌模型和混沌研究所需的判据与准则;
②介绍随机序列的相关理论,对目前信息安全中使用的随机序列发生器进行分析、归纳和总结,提出它们存在的问题:序列不够长、可以预测、产生的序列质量较差、速度较低、使用不方便等;
③对区间数目参数化分段线性混沌映射(SNP-PLCM)的密码学特性进行详细分析,并以此为基础,提出了一种基于区间数目参数化分段线性混沌映射的伪随机序列发生器。该发生器同时利用控制参数扰动策略和输出序列扰动策略避免数字化混沌系统的动力学特性退化。理论分析和仿真实验结果表明,该算法产生的伪随机序列具有理想的性能;
④混沌伪随机序列应用于S盒,提出了一种基于混沌序列的可度量动态S盒的设计方法。该方法利用区间数目参数化PLCM良好的密码特性产生的伪随机序列,然后用伪随机序列构造混沌动态S盒。数字分析结果表明,所设计的S盒有较高的非线性度和良好的严格雪崩特性;
⑤提出一种基于混沌动态S盒和非线性移位寄存器的快速序列密码算法,该算法利用混沌伪随机序列用来初始化非线性移位寄存器(NLFSR)、构造非线性移位寄存器的更新函数和混沌动态S盒。非线性移位寄存器每循环一次输出32比特密钥流。每输出21 6比特密钥流,混沌S k( i )盒动态更新一次,使得在安全和效率方面有一个比较好的折中点。实验结果表明该方法可以得到独立、均匀和长周期的密钥流序列,同时可以有效的克服混沌序列在有限精度实现时出现短周期和NLFSR每循环1次输出1比特密钥流的低效率问题;
⑥结合传统的Hash函数结构与混沌动态S盒,提出了一种基于混沌动态S盒的带密钥的Hash函数,该方法利用混沌动态S盒和函数查找表来生成具有混沌特性的Hash散列值,与现有的混沌Hash函数相比,该方法利用混沌动态S盒来提高系统的实时性能。结果表明该算法不仅具有很好的单向性,初值和密钥敏感性,而且实行的速度快,易于实现;
最后对论文工作进行了全面的总结,并对今后的研究方向进行了展望。
With the fast development of computer and Internet technology, Information security has become the common focus of both academia and enterprises. Cryptology is the core of information security and the random sequence has played a very important role in it. The key generation, digital signature, authentication and many kinds of communication protocol all need random sequence. Just as the famous expert of cryptology Bruce Schneier had pointed out that the random sequence is the problem which is discussed very less in cryptology, but it is the most important one in cryptology. In some case, the security of the random sequence decides the security of the system. So, how can we get high quality random sequence generator has become a very vital problem. In this thesis, we will study how to design high quality, fast, convenient random sequence generator. Currently, it is one of the hot promising reseachfields on the combination of nonlinear science and information science to apply chaos theory to pseudorandom sequence. In this dissertation, the design and implementation of chaotic pseudorandom sequence generator have been carefully studied and applied successfully to protect the security of information.
The following tasks have been accomplished in this dissertation:
①Chaos theory is introduced in detail from different aspects and views, the definition of chaos is presented, the characteristics of chaotic dynamics are described, and the criterion and rule of chaos are given.
②The relevant theory of random sequence is introduced, and theusual random sequence generators used in information security have been summarized, these generators' disadvantages, such as short period, predictability, bad quality, lower pace, inconvenience, are given.
③The piecewise linear chaotic map with a segment number parameter (SNP-PLCM) is analyzed in detail. Based on SNP-PLCM, a chaotic pseudorandom sequence generator is presented. The generator employs perturbation strategy of controls parameter and output sequences to avoid dynamical degradation of digital chaotic systems. Theoretical analysis and computer simulation results show that the chaotic pseudorandom sequence generator can get high quality sequences.
④A measurable dynamic S-box algorithm is proposed by use of chaotic pseudo- random sequences, and the performance of these S-boxes is analyzed mathematically. Theoretical analysis and computer test results show that this scheme has good security and performance.
⑤Based on chaotic pseudorandom sequence generator and non-linear feedback shift register (NLFSR), a fast streamer cipher is proposed. The approach is that chaotic pseudorandom sequence initializes NLFSR and constructs the update function of NLFSR, and chaotic dynamic S-boxes. The update function which is called once per round, manipulates the internal state to generate 64 bits of pseudorandom key stream. The chaotic dynamic S-box of the update function should be reconstructed at lease once for every 21 6 bit of key stream generated, that is, iteration 1024 times of chaotic system can produces 21 6 bits of pseudo-random key stream. The theoretical and numerical analyses show that the scheme can not only produce the independently and uniformly distributed key stream, but also can improve largely the period of chaotic sequence under the finite-precision circumstances and increase in efficiency.
⑥By combining the traditional iteration structure of Hash function with the dynamic S-boxes, a novel keyed Hash function is presented. The proposed approach can give a chaotic Hash value by means of the lookup table of functions and chaotic dynamic S-box. Compared with the existing chaotic Hash functions, this method improves computational performance of Hash system by using the chaotic S-box substitution. Theoretical and experimental results show that the proposed method has not only strong one way property, sensitivity to initial conditions and chaotic system’s parameters, but also high speed.
Finally, the research work of this dissertation is summarized, and the future reseach direction is indicated.
引文
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