改进伪随机序列随机性的一种新方法及应用

闵乐泉

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A New Approach for Improving Randomness of Pseudorandom Sequences with Applications

首发时间：2019-11-22

MIN Lequan ¹
MIN Lequan, Birth year-1951, Male，Professor and PhD-Supervisor. Main research：Chaos-based security communications, Roustness of the cellular neural network with applications,Virus infection dynamics with simulation. He was the director of 4 National Natural Science Foundation of China. He has coauthored to have published over 300 scientific papers.

1、Department of Information and Computer Science, School of Mathmatics and Physics, University of Science and Technology Beijing, Beijing 100083

Abstract：Pseudorandom number generators (PRNGs) are widely used in many fields, especially in cryptographic applications. Pseudorandom number sequences generated via a poor PRNG will lead to weak or guessable its keys, and leak the information which is prevented. Based on the Golomb's assumptions on idea pseudorandom sequences and FIPS 140-2 randomness test criteria, this paper first presents a new approach for improving the randomness of pseudorandom sequences. Second, using a generalized synchronization theorem, the Henon map, the logistic map and a tube map constructs a new 8-dimensional chaotic generalized synchronization system (8DCGSS). Then using the 8DCGSS designs a chaotic PRNG (CPRN). The keyspace of the CPRNG is larger than 21117. Finally, using the FIPS 140-2 randomness test and a generalized FIPS 140-2 randomness test measures the randomness of the keystreams generated via the CPRNG, the Matlab PRNG, the RC4 algorithm, and the m-sequence, and the improved keystreams in term of our approach. The results show that our approach are able to increase significantly the randomness of the keystreams generated by the four PRNGs.

keywords： Probability and statistics Improving randomness Golomb's assumptions Pseudorandom sequences Chaotic pseudorandom number generator RC4 algorithm m-Sequence FIPS 140-2 test

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改进伪随机序列随机性的一种新方法及应用

闵乐泉 ¹
MIN Lequan, Birth year-1951, Male，Professor and PhD-Supervisor. Main research：Chaos-based security communications, Roustness of the cellular neural network with applications,Virus infection dynamics with simulation. He was the director of 4 National Natural Science Foundation of China. He has coauthored to have published over 300 scientific papers.

1、北京科技大学数理学院信息与计算科学系

摘要：伪随机数发生器（PRNGs）应用于广泛的领域，特别是在密码学领域的应用。劣质的PRNGs将导致产生弱密钥或可猜出的密钥，从而泄露所隐藏的信息。基于Golomb关于理想伪随机序列的假设和FIPS 140-2 随机性检验准则，本文提出了一种改进伪随机序列随机性的新方法。利用广义同步定理，Henon映射，logstic 和立方映射构造了一个新的8维广义同步系统(8DCGSS)。然后用8DCGSS设计了一个混沌伪随机数发生器(CPRNG)。该CPRNG的密钥空间大于2^1117。作为应用，用FIPS 140-2 随机性检验准则和GFIPS 140-2 随机性检验准则分别对10000条由CPRNG，Matlab PRNG, RC4算法和m-序列产生的密钥流和利用本文算法改进的密钥流进行了检测。结果表明本文的算法可以显著地增加这四个PRNGs产生的密钥流的随机性。

关键词：概率论与数理统计 Golomb假设伪随机性改进伪随机序列混沌伪随机数发生器 RC4算法 m-序列 FIPS 140-2检测

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1. the National Natural Science Foundation of China（61074192）

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MIN Lequan. A New Approach for Improving Randomness of Pseudorandom Sequences with Applications[EB/OL]. Beijing:Sciencepaper Online[2019-11-22]. https://www.paper.edu.cn/releasepaper/content/201911-70.

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论文编号	201911-70
论文题目	改进伪随机序列随机性的一种新方法及应用
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