一种混沌伪随机序列均匀化普适算法的改进

doi:10.3969/j.issn.0372-2112.2015.04.018

电子学报 ›› 2015, Vol. 43 ›› Issue (4): 753-759.DOI: 10.3969/j.issn.0372-2112.2015.04.018

一种混沌伪随机序列均匀化普适算法的改进

李佩玥¹, 石俊霞², 郭嘉亮¹, 陈雪¹, 杨怀江¹

1. 中国科学院长春光学精密机械与物理研究所应用光学国家重点实验室, 吉林长春 130033;
2. 中国科学院长春光学精密机械与物理研究所, 吉林长春 130033

收稿日期:2014-01-28 修回日期:2014-08-07 出版日期:2015-04-25
- 通讯作者:
- 石俊霞
- 作者简介:
- 李佩玥 男,1985年6月出生于吉林磐石,博士,助理研究员,主要研究方向:混沌密码学、网络安全、精密驱动与控制技术.E-mail:lipy@sklao.ac.cn
- 基金资助:
- 国家重点基础研究发展计划973项目基金 (No.2007CB311201); 吉林省科技发展计划 (No.20130522120JH)

Improvement of a Universal Algorithm for Uniformization of Chaotic Pseudo-Random Sequences

LI Pei-yue¹, SHI Jun-xia², GUO Jia-liang¹, CHEN Xue¹, YANG Huai-jiang¹

1. State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin 130033, China;
2. Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin 130033, China

Received:2014-01-28 Revised:2014-08-07 Online:2015-04-25 Published:2015-04-25
- Supported by:
- Foundation of National Program on Key Basic Research Project of China (973 Program) (No.2007CB311201); Science and Technology Development Project of Jilin Province (No.20130522120JH)

摘要/Abstract

摘要：

为了分析盛利元等所述算法的安全性与普适性,从信息论的角度提出了单轮迭代信息损失量和动力学系统平均信息损失速度的概念,分析结果表明,第二类比特位变换的单轮迭代信息损失量为12比特,标准第二类比特位变换的单轮迭代信息损失量与指数e有关,存在信息损失量较小的可能性,将1023-e作为移位位数,使得标准第二类比特位变换无法遍历[-1,1]区间内的所有浮点数.进一步提出了暂态数据和第一类暂态变换的概念,并对文献[14]中所述算法进行了改进,改进后算法能够将任意混沌输出序列转换为至[0,1]区间内的浮点数,转换过程的信息损失量为L-1比特,接近有限计算精度为L时的最大信息损失速度I_max=L,且通过χ检验可证明转换后的混沌输出序列服从均匀分布.

关键词: 数字混沌, 均匀性, 暂态数据, 暂态变换

Abstract:

In order to analyze the security and universality of the arithmetic proposed by Sheng et al,the concept of information loss in single iteration and average speed of information loss in dynamic system is proposed based on information theory.It is shown that the information loss of the 2nd bit-operation transformation is 12 bits,and which of the standard 2nd bit-operation transformation is related to the exponent e.It is possible that the information loss of the 2nd bit-operation transformation is so small.Not all of the float number in[-1,1]can be traversed by the standard 2nd bit-operation transformation just because the 1023-e is used as the shift number.The concept of transient data and 1st transient transformation is proposed further,and the arithmetic proposed in literature[14]is improved as well.The output sequence of random digital chaotic system can be transformed as float number in[0,1]by the improved arithmetic.The information loss of this transformation is L-1 bits,which is approached to the maximum speed of information loss I_max=L under the computing precision L.The transformed sequence is uniform distributed which can be proved by χ-verification.

Key words: digital chaotic, uniformity, transient data, transient transformation

中图分类号:

李佩玥, 石俊霞, 郭嘉亮, 等. 一种混沌伪随机序列均匀化普适算法的改进[J]. 电子学报, 2015, 43(4): 753-759.

LI Pei-yue, SHI Jun-xia, GUO Jia-liang, et al. Improvement of a Universal Algorithm for Uniformization of Chaotic Pseudo-Random Sequences[J]. Acta Electronica Sinica, 2015, 43(4): 753-759.

参考文献

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一种混沌伪随机序列均匀化普适算法的改进

Improvement of a Universal Algorithm for Uniformization of Chaotic Pseudo-Random Sequences

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