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中文摘要：
针对设计性能良好的伪随机数发生器的问题,提出了一个新的四维离散混沌系统。利用离散混沌广义同步定理构造了一个八维混沌广义同步（8D-CGS）系统,基于该8D-CGS通过一个实数域到整数域的变换设计了一个新的混沌伪随机发生器（CPRNG）,对其在密钥无扰动下产生的密钥流分别与在不同的密钥扰动下产生的密钥流及Matlab指令产生的密钥流进行相关系数和不同率的比较,两组比较结果的平均值分别为0.005 585 7和49.988 5%及0.005 877 3和49.982 8%,从而表明该CPRNG产生的密钥流几乎完全独立,不同率非常接近理想值50%。利用FIPS140-2和G FIPS 140-2检测标准分别对该CPRNG、RC4算法和ZUC算法产生的1 000个{0,1}序列进行检测,结果三组{0,1}序列均通过了FIPS 140-2标准,而分别有10、19和22个没有通过G FIPS 140-2标准,表明CPRNG通过率最高,且检测结果中的平均值和方差对比表明该CPRNG随机性能良好。
英文摘要：
Focusing on the design of a good pseudorandom number generator,a novel four-dimensional discrete chaotic system was proposed. Using the theorem of discrete chaotic generalized synchronization, an eight-dimensional chaotic generalized synchronization system（ 8D-CGS） was constructed. Based on the 8D-CGS and by transforming the real number set to the integer set,a novel chaotic pseudorandom number generator（ CPRNG） was designed. The undisturbed key stream was compared with the key streams produced by different key disturbation and Matlab commands respectively. The two groups of average correlation and different rate are 0. 005 585 7 and 49. 988 5%,and 0. 005 877 3 and 49. 982 8%. It shows that the key streams produced by the CPRNG almost independent absolutely and the different rate very close to the ideal value 50%. FIPS140-2 and G FIPS 140-2 test criterions were used to test the randomness of three 1 000 sequences of { 0,1 } generated respectively by the CPRNG,the RC4 algorithm and the ZUC algorithm. The results show that three { 0,1} sequences all pass the FIPS 140-2 test criterion and there are 10,19 and 22 sequences fail to pass the G FIPS 140-2 test criterion respectively,so the pass rate of the CPRNG is the highest. The means and variances of the tested results show that the CPRNG designed by this paper has promising randomness performance.
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