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Imax=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.
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 hit-operation Iransformation is so small. Not all of the float number in[- 1,1 ] can be traversed by the standard 2nd hit-operation transformation just because the 1023- e is used as the shift number. The concept of transient data and 1 st 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 Iransformed 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 Imax = L under the computing precision L. The transformed sequence is uniform distributed which can be proved by X-verification.
出处
《电子学报》
EI
CAS
CSCD
北大核心
2015年第4期753-759,共7页
Acta Electronica Sinica
基金
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)
关键词
数字混沌
均匀性
暂态数据
暂态变换
digital chaotic
uniformity
transient data
transient aansformation
