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 st...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.展开更多
<正> The performance of individual pseudo-random sequence, generated by some mechanism, is often not ideal. The asymptotic performance of the addition (in the sense (mod p) of a large number of such individual s...<正> The performance of individual pseudo-random sequence, generated by some mechanism, is often not ideal. The asymptotic performance of the addition (in the sense (mod p) of a large number of such individual sequences is studied and the necessary and sufficient condition under which the resulting sequence may converge to genuine randomness is obtained.展开更多
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)+1 种基金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)
文摘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.
基金Project supported by the National Natural Science Foundation of China,the UPGC of Hong Kong,Hong Kong Baptist University and SRCU.
文摘<正> The performance of individual pseudo-random sequence, generated by some mechanism, is often not ideal. The asymptotic performance of the addition (in the sense (mod p) of a large number of such individual sequences is studied and the necessary and sufficient condition under which the resulting sequence may converge to genuine randomness is obtained.
