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.

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	1. A New Approach for Improving Randomness of Pseudorandom Sequences with Applications
	MIN Lequan
	Mathematics 17 November 2019
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	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.
	TO cite this article:MIN Lequan. A New Approach for Improving Randomness of Pseudorandom Sequences with Applications[OL].[17 November 2019] http://en.paper.edu.cn/en_releasepaper/content/4749989


	2. Reinterpret the concept of measurement uncertainty
	Ye Xiaoming
	Mathematics 19 July 2018
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	Abstract:The existing definition of uncertainty actually violates a basic mathematical concept: the variance of a constant with a definite value is 0. Therefore, various interpretations of uncertainty concept are actually specious. From the perspective of probability theory, this paper will point out the key trouble of existing concept, and fully prove that the uncertainty is actually the evaluation value of probability interval of an error and expresses the possible degree that the measured quantity value is close to the true value, instead of the dispersion of measured quantity value. This will lead to a comprehensive change in the interpretation method of measurement theory.
	TO cite this article:Ye Xiaoming. Reinterpret the concept of measurement uncertainty[OL].[19 July 2018] http://en.paper.edu.cn/en_releasepaper/content/4745739

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	3. Interpretations of measurement error theory based on new concepts
	Ye Xiaoming
	Mathematics 04 November 2017
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	Abstract:In several previously published papers, the author proposed a new thinking of measurement theory based on error non-classification philosophy. Based on the new concepts, this paper re-interprets the basic principle of measurement error theory completely from the perspective of mathematics, re-proves the concept logic of error classification and the dispersion concept of uncertainty in existing measurement theory are actually incorrect, and gives a new interpretation method for error evaluation principle and measurement uncertainty concept. Its core ideas are, standard deviation is the evaluation of the probable range of an error instead of the dispersion of a measurement result, and any error has a standard deviation to evaluate its probable range.
	TO cite this article:Ye Xiaoming. Interpretations of measurement error theory based on new concepts[OL].[ 4 November 2017] http://en.paper.edu.cn/en_releasepaper/content/4741855


	4. Moderate deviations for estimators under an exponentiallystochastic differentiability condition
	GAO Fu-qing,LIU Qiao-jing
	Mathematics 16 May 2017
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	Abstract:We introduce an exponentially stochastic differentiability condition to study moderate deviations for M-estimators. Under the condition, a moderate deviation principle is established. Some sufficient conditions of the exponentially stochastic differentiability and examples are also given.
	TO cite this article:GAO Fu-qing,LIU Qiao-jing. Moderate deviations for estimators under an exponentiallystochastic differentiability condition[OL].[16 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4735018


	5. Large deviation analysis for a Poisson model on thecoverage problem
	GAO Fu-qing,ZHAO Xin-qiu
	Mathematics 16 May 2017
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	Abstract:Mao and Lindsay proposed a Poisson model for the coverageproblem and studied the Good-Turing estimators associated with themodel. The Poisson model provides a simplified framework forinferring any general abundance-$mathcal K$ coverage. In thispaper, we prove that the Good-Turing estimators satisfy largedeviation principle and moderate deviation principle, which yieldrates of convergence and a useful method for constructing asymptoticconfidence intervals.
	TO cite this article:GAO Fu-qing,ZHAO Xin-qiu. Large deviation analysis for a Poisson model on thecoverage problem[OL].[16 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4735015


	6. Explicit estimate for convergence rates of continuous time markov chains (I)
	HOU Zhenting,ZHANG Zhuo,YAN Zhenhai
	Mathematics 16 May 2017
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	Abstract:justifying In this paper, we give explicit estimate on the rate of convergence of the transition probabilities to the stationary distribution for a class of exponential ergodic Markov chains. Our results are different from earlier estimates using coupling theory and from estimates using stochastically monotone. The estimates show a noticeable improvement on existing results if Markov chains contain instantaneous state or nonconservative state. The method of proof uses existing result of discrete time Markov chain, together with $h-$ skeleton. We apply this results, Ray-Knight compactification and $mbox{It}hat{o}$ excursion theory to two examples: a class of singular Markov chains and Kolmogorov matrix. In addition, we apply the Ray-Knight compactification, $mbox{It}hat{o}$ excursion theory and explicit estimate for convergence rates of continuous time markov chains to two examples: a class of singular Markov chains and Kolmogorovmatrix.
	TO cite this article:HOU Zhenting,ZHANG Zhuo,YAN Zhenhai. Explicit estimate for convergence rates of continuous time markov chains (I) [OL].[16 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4734375


	7. The Invalidity of the Log-Sobolev Inequality on thePath Space of Compound Poisson Processes
	DENG Chang-Song
	Mathematics 15 May 2017
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	Abstract:By using a formula for random shifts on the path space of compound Poissonprocess, a natural Dirichlet form of jump type is defined. The generator of the Dirichlet formis formulated. Moreover, the log-Sobolev inequality is disproved.
	TO cite this article:DENG Chang-Song. The Invalidity of the Log-Sobolev Inequality on thePath Space of Compound Poisson Processes[OL].[15 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4734040


	8. General $F$-Sobolev TypeInequalities for Symmetric Forms
	DENG Chang-Song
	Mathematics 15 May 2017
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	Abstract:Using Cheeger's isoperimetric constants, weestablish weak $F$-Sobolev, $F$-Sobolev, and super$F$-Sobolev inequalities for general symmetric forms.
	TO cite this article:DENG Chang-Song. General $F$-Sobolev TypeInequalities for Symmetric Forms[OL].[15 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4734043


	9. Absolute Continuity of the Law of Solutions to SPDEs Driven by White Noise with Coefficients Depending on the Past of the Solutions
	YANG Xue
	Mathematics 08 May 2017
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	Abstract:In this paper, we consider stochastic partial differential equations driven by space-time white noise. The coefficients are nonlinear and depend on the past of the solution. We prove, under reasonable conditions, that the law of the solution admits a density with respect to Lebesgue measure.
	TO cite this article:YANG Xue. Absolute Continuity of the Law of Solutions to SPDEs Driven by White Noise with Coefficients Depending on the Past of the Solutions[OL].[ 8 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4733521


	10. on existence and uniqueness of invariant measures of multivalued stochastic differential equations with jumps
	GUAN Yue,WU Jing
	Mathematics 25 April 2017
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	Abstract:The ergodicity of multivalued stochastic differential equations with L'evy jumps when the coefficients are non-Lipschitz continuous by proving that the transition semigroup is strongly Feller and irreducible, and that it admits a unique invariant measure. This is obtained through an $L^2$-convergence result, Girsanov's theorem, coupling method combined and a stopping argument.
	TO cite this article:GUAN Yue,WU Jing. on existence and uniqueness of invariant measures of multivalued stochastic differential equations with jumps[OL].[25 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4726595

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