For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characteri...For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characterize the Kondratiev space of random test function, in which space it is convenient to study random distribution,random partial differential equation and other problems.展开更多
Investigated the properties of LUCas sequence(LUC), the paper proposed a new variant of (probabilistic) public-key encryption scheme. Security analysis of the proposed encryption schemes shows that its one-wayness is ...Investigated the properties of LUCas sequence(LUC), the paper proposed a new variant of (probabilistic) public-key encryption scheme. Security analysis of the proposed encryption schemes shows that its one-wayness is equivalent to partial LUC discrete logarithm problem in ZN, and for the proposed probabilistic encryption scheme, its semantic security is equivalent to decisional LUC Diffie-Hellman problem in ZN. At last, the efficiency of the proposed schemes is briefly analyzed.展开更多
Let Z/（p^e） be the integer residue ring modulo p^e with p an odd prime and integer e ≥ 3. For a sequence a over Z/（p^e）, there is a unique p-adic decomposition a- = a-0 ＋a-1 .p ＋… ＋ a-e-l .p^e-1 where each a-...Let Z/（p^e） be the integer residue ring modulo p^e with p an odd prime and integer e ≥ 3. For a sequence a over Z/（p^e）, there is a unique p-adic decomposition a- = a-0 ＋a-1 .p ＋… ＋ a-e-l .p^e-1 where each a-i can be regarded as a sequence over Z/（p）, 0 ≤ i ≤ e - 1. Let f（x） be a primitive polynomial over Z/（p^e） and G＇（f（x）,p^e） the set of all primitive sequences generated by f（x） over Z/（p^e）. For μ（x） ∈ Z/（p）[x] with deg（μ（x）） ≥ 2 and gad（1 ＋ deg（μ（x））,p- 1） = 1, setφe-1 （x0, x1,… , xe-1） = xe-1. [μ（xe-2） ＋ ηe-3（x0, X1,…, xe-3）] ＋ ηe-2（x0, X1,…, xe-2） which is a function of e variables over Z/（p）. Then the compressing mapφe-1 ： G＇（f（x）,p^e） → （Z/（p））^∞ ,a-→φe-1（a-0,a-1, … ,a-e-1） is injective. That is, for a-,b-∈ G＇（f（x）,p^e）, a- = b- if and only if φe-1 （a-0,a-1, … ,a-e-1） = φe-1（b-0, b-1,… ,b-e-1）. As for the case of e = 2, similar result is also given. Furthermore, if functions φe-1 and ψe-1 over Z/（p） are both of the above form and satisfy φe-1（a-0,a-1,…,a-e-1）=ψe-1（b-0, b-1,… ,b-e-1） for a-,b-∈G＇（f（x）,p^e）, the relations between a- and b-, φe-1 and ψe-1 are discussed展开更多
A new method, referred to as the full-recurrent-decimal-sequences (FRDS) method, is proposed to generate the pseudorandom integer strings and the pseudorandom sequences. The pseudorandom integer strings properties and...A new method, referred to as the full-recurrent-decimal-sequences (FRDS) method, is proposed to generate the pseudorandom integer strings and the pseudorandom sequences. The pseudorandom integer strings properties and the run-length properties of the FRDS-sequences are investigated . By transformation, a new kind of pseudorandom sequences with optimal auto-correlation functions is suggested.展开更多
In Chinese, Mathematics is “数学”, i.e. Numbers （数） Knowledge （学）. Human identifies us ourselves from the whole one of the Universe by means of numbers, and numbers are equal object status identities, and numb...In Chinese, Mathematics is “数学”, i.e. Numbers （数） Knowledge （学）. Human identifies us ourselves from the whole one of the Universe by means of numbers, and numbers are equal object status identities, and numbers counting means repetition, i.e. the process or time dimension. Given a series of n numbers, a1 , a2 , … , an , n∈N, i.e. the n objects of status, and a general formula a（i） for ordering all of the number terms by i （i=1 to n） can be generated, which shows a process of counting, and from sequencing to progression, some properties are extracted.展开更多
基金Supported by Nature Science Foundation of Hainan Province (Grant No. 118MS040,2018CXTD338)NSF of Higher Education Institutions of Hainan Province (Grant No. Hnky2018ZD-6)National Natural Science Foundation of China (Grant No. 11861029)。
文摘For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characterize the Kondratiev space of random test function, in which space it is convenient to study random distribution,random partial differential equation and other problems.
基金Supported by the 973 State Key Project of China (No.G1999035803)the National Natural Science Foundation of China (No.69931010).
文摘Investigated the properties of LUCas sequence(LUC), the paper proposed a new variant of (probabilistic) public-key encryption scheme. Security analysis of the proposed encryption schemes shows that its one-wayness is equivalent to partial LUC discrete logarithm problem in ZN, and for the proposed probabilistic encryption scheme, its semantic security is equivalent to decisional LUC Diffie-Hellman problem in ZN. At last, the efficiency of the proposed schemes is briefly analyzed.
基金Supported by the National Natural Science Foundation of China(60673081)863 Program(2006AA01Z417)
文摘Let Z/（p^e） be the integer residue ring modulo p^e with p an odd prime and integer e ≥ 3. For a sequence a over Z/（p^e）, there is a unique p-adic decomposition a- = a-0 ＋a-1 .p ＋… ＋ a-e-l .p^e-1 where each a-i can be regarded as a sequence over Z/（p）, 0 ≤ i ≤ e - 1. Let f（x） be a primitive polynomial over Z/（p^e） and G＇（f（x）,p^e） the set of all primitive sequences generated by f（x） over Z/（p^e）. For μ（x） ∈ Z/（p）[x] with deg（μ（x）） ≥ 2 and gad（1 ＋ deg（μ（x））,p- 1） = 1, setφe-1 （x0, x1,… , xe-1） = xe-1. [μ（xe-2） ＋ ηe-3（x0, X1,…, xe-3）] ＋ ηe-2（x0, X1,…, xe-2） which is a function of e variables over Z/（p）. Then the compressing mapφe-1 ： G＇（f（x）,p^e） → （Z/（p））^∞ ,a-→φe-1（a-0,a-1, … ,a-e-1） is injective. That is, for a-,b-∈ G＇（f（x）,p^e）, a- = b- if and only if φe-1 （a-0,a-1, … ,a-e-1） = φe-1（b-0, b-1,… ,b-e-1）. As for the case of e = 2, similar result is also given. Furthermore, if functions φe-1 and ψe-1 over Z/（p） are both of the above form and satisfy φe-1（a-0,a-1,…,a-e-1）=ψe-1（b-0, b-1,… ,b-e-1） for a-,b-∈G＇（f（x）,p^e）, the relations between a- and b-, φe-1 and ψe-1 are discussed
文摘A new method, referred to as the full-recurrent-decimal-sequences (FRDS) method, is proposed to generate the pseudorandom integer strings and the pseudorandom sequences. The pseudorandom integer strings properties and the run-length properties of the FRDS-sequences are investigated . By transformation, a new kind of pseudorandom sequences with optimal auto-correlation functions is suggested.
文摘In Chinese, Mathematics is “数学”, i.e. Numbers （数） Knowledge （学）. Human identifies us ourselves from the whole one of the Universe by means of numbers, and numbers are equal object status identities, and numbers counting means repetition, i.e. the process or time dimension. Given a series of n numbers, a1 , a2 , … , an , n∈N, i.e. the n objects of status, and a general formula a（i） for ordering all of the number terms by i （i=1 to n） can be generated, which shows a process of counting, and from sequencing to progression, some properties are extracted.
