On the Judgement of Full-Period Sequences and a Novel Congruential Map with Double Modulus on Z(p^n)

作     者：Yongkui Li Jingbo Hu Yiyang Yu 

作者机构：Center for Nonlinear Complex SystemsDepartment of PhysicsSchool of Physics and AstronomyYunnan University Kunming 650091China School of Computer Science and TechnologyHubei University of Science and TechnologyXianning 437100China School of Electronic and Electrical EngineeringBaoji University of Arts and SciencesBaojiShaanxi 721016China 

出 版 物：《China Communications》 (中国通信（英文版）)

年 卷 期：2019年第16卷第5期

页      面：189-196页

核心收录：

学科分类：0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 

基　　金：supported in part by the National Natural Science Foundation of China(NSFC)(Grant Nos.11365023) the Science and Technology Program of Shaanxi Province(Grant Nos.2018GY-050) the Key Scientific Research Program of Department of Education of Shaanxi Province(Grant No.16JS008) the Key Projects of Baoji University of Arts and Sciences(Grant Nos.ZK2017037) 

主　　题：congruential map full-period maps generating sequences residue class rings chaos 

摘      要：This paper studies the judgement problem of full-period maps on Z(p^n) and proposes a novel congruential map with double modulus on Z(p^n). The full-period properties of the sequences generated by the novel map are studied completely. We prove some theorems including full-period judgement theorem on Z(p^n) and validate them by some numerical experiments. In the experiments, full-period sequences are generated by a full-period map on Z(p^n). By the binarization, full-period sequences are transformed into binary sequences. Then, we test the binary sequences with the NIST SP 800-22 software package and make the poker test. The passing rates of the statistical tests are high in NIST test and the sequences pass the poker test. So the randomness and statistic characteristics of the binary sequences are good. The analysis and experiments show that these full-period maps can be applied in the pseudo-random number generation(PRNG), cryptography, spread spectrum communications and so on.