八维广义同步系统在伪随机数发生器中的应用

该文提出一类4维离散系统。利用系统平衡点处 Jacobi 矩阵的特征值来分析系统在平衡点处的稳定性，建立了一个判别这类系统为周期或混沌的定理。依据该定理构造了一个新的4维离散系统。该系统具有正的Lyapunov指数，数值模拟显示该系统的动力学行为具有混沌特性。结合该系统和系统广义同步定理构造了一个8维广义同步混沌系统。利用该系统构造了一个16 bit混沌伪随机数发生器 (CPRNG)，其密钥空间大于21245。利用FIPS 140-2 检测/广义FIPS 140-2检测判别标准分别检测由CPRNG, Narendra RBG, RC4 PRNG和ZUC PRNG生成的1000个长度为20000 bit的密钥流的随机性。检测结果表明，分别有100%/99%, 100%/82.9%, 99.9%/ 98.8%和100%/97.9%密钥流通过FIPS 140-2检测/广义FIPS 140-2 检测标准。数值仿真显示不同密钥流之间有平均50.004%不同码。结果说明设计的伪随机数发生器有好的随机性，可以抵抗穷尽攻击。该文提出的CPRNG为密码安全的研究与发展提供了新的工具。

Application of 8-dimensional Generalized Synchronization System in Pseudorandom Number Generator

This paper proposes a class of 4-Dimensional Discrete Systems (4DDSs). Using the eigenvalues of Jacobian matrix of the system at the equilibrium, the?stability of the system at the equilibrium is analyzed. A theorem is set up, which is used to determine whether the class systems are periodic or chaotic. Based on the theorem, a 4DDS is constructed. The 4DDS has positive Lyapunov exponent. Numerical simulations show that the dynamic behaviors of the 4DDS have chaotic attractor characteristics as they expects. Combining the 4DDS with Generalized Synchronization (GS) theorem, an 8-Dimensional GS Chaotic System (8DGSCS) is designed. Using this system, this paper designs a 16 bit string Chaotic Pseudo Random Number Generator (CPRNG). Theoretically the key space of the CPRNG is larger than 21245. The FIPS 140-2 test suit/Generalized FIPS 140-2 test suit are used to test the randomness of the 1000-key streams consisting of 20000 bit generated by the CPRNG, Narendra RBG, RC4 PRNG and ZUC PRNG, respectively. The results show that there are 100%/99%, 100%/ 82.9%, 99.9%/98.8% and 100%/97.9% key streams passing the FIPS 140-2 test suit/Generalized FIPS 140-2 test suit, respectively. Numerical simulations show that the different key-streams have 50.004% different codes. The results show that the generated CPRNG has good randomness properties, can better resist the brute attack. The designed CPRNG provides a novel tool for the research and development of cryptography.