Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely...Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.展开更多
Let R=Z/PkZ be the ring of integers modulo pk where p is a prime and k>1.Denote by n(r,m×n)tile number of m by n matrices with real rank r over R.In tile present paper.we compute n(r.m×n) and the number o...Let R=Z/PkZ be the ring of integers modulo pk where p is a prime and k>1.Denote by n(r,m×n)tile number of m by n matrices with real rank r over R.In tile present paper.we compute n(r.m×n) and the number of the orbits of Mm,n.(R)under GLm.(R)×GLm(R).where Mm.n(R) is the set of all m by n matrices over R.展开更多
The conventional ring signature schemes cannot address the scenario where the rank of members of the ring needs to be distinguished, for example, in electronically commerce application. To solve this problem, we prese...The conventional ring signature schemes cannot address the scenario where the rank of members of the ring needs to be distinguished, for example, in electronically commerce application. To solve this problem, we presented a Trusted Platform Module (TPM)-based threshold ring signature scheme. Employing a reliable secret Share Distribution Center (SDC), the proposed approach can authenticate the TPM-based identity rank of members of the ring but not track a specific member's identity. A subset including t members with the same identity rank is built. With the signing cooperation of t members of the subset, the ring signature based on Chinese remainder theorem is generated. We proved the anonymity and unforgeability of the proposed scheme and compared it with the threshold ring signature based on Lagrange interpolation polynomial. Our scheme is relatively simpler to calculate.展开更多
P-集合(packet sets)是由内P-集合X■(internal packet set X■)与外P-集合XF(outer packet set XF)构成的集合对;或者(X■,XF)是P-集合。P-集合具有动态特性(内P-集合具有内-动态特性,外P-集合具有外-动态特性)。P-集合在动态信息系统...P-集合(packet sets)是由内P-集合X■(internal packet set X■)与外P-集合XF(outer packet set XF)构成的集合对;或者(X■,XF)是P-集合。P-集合具有动态特性(内P-集合具有内-动态特性,外P-集合具有外-动态特性)。P-集合在动态信息系统的多个领域中获得了应用。在一类信息系统中,这类信息系统只具有内-动态特性,不具有外-动态特性。为了研究这类只有内-动态特性的信息系统,改进并简化P-集合,提出了半P-集合(half packet sets)。半P-集合是由内P-集合X■与有限普通集合X构成的集合对,或者(X■,X)是半P-集合,半P-集合具有内-动态特性。以及半P-集合与有限普通集合的关系,以及半P-集合与P-集合的关系。利用半P-集合给出信息内-真度与信息内-真度环的概念、信息内-真度环定理以及内-信息恢复-还原的内-真度准则与内-信息恢复-还原的特征系数准则。利用这些结果,给出内-真度环在内-信息恢复-还原中的应用。半P-集合是研究一类动态信息系统的一个新的数学方法与数学模型;半P-集合在一类信息系统应用中前景看好。展开更多
基金supported by the National Natural Science Foundation of China(12131015,12071422).
文摘Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.
文摘Let R=Z/PkZ be the ring of integers modulo pk where p is a prime and k>1.Denote by n(r,m×n)tile number of m by n matrices with real rank r over R.In tile present paper.we compute n(r.m×n) and the number of the orbits of Mm,n.(R)under GLm.(R)×GLm(R).where Mm.n(R) is the set of all m by n matrices over R.
基金Acknowledgements This work was supported by the National Basic Research Program of China under Crant No. 2007CB311100, Core Electronic Devices, High-end General Purpose Chips and Basic Software Products in China under Oant No. 2010ZX01037-001-001 Ph.D. Start-up Fund of Beijing University of Technology under Grants No. X0007211201101 and No. X00700054R1764, National Soft Science Research Program under Crant No. 2010GXQ5D317 and the National Natural Science Foundation of China underGrant No. 91018008 ,Opening Project of Key Lab of Information Network Security, Ministry of Public Security under Crant No. C11610, Opening Project of State Key Laboratory of Information Security （Institute of Sottware, Chinese Academy of Sciences） under Cxant No. 04-04-1.
文摘The conventional ring signature schemes cannot address the scenario where the rank of members of the ring needs to be distinguished, for example, in electronically commerce application. To solve this problem, we presented a Trusted Platform Module (TPM)-based threshold ring signature scheme. Employing a reliable secret Share Distribution Center (SDC), the proposed approach can authenticate the TPM-based identity rank of members of the ring but not track a specific member's identity. A subset including t members with the same identity rank is built. With the signing cooperation of t members of the subset, the ring signature based on Chinese remainder theorem is generated. We proved the anonymity and unforgeability of the proposed scheme and compared it with the threshold ring signature based on Lagrange interpolation polynomial. Our scheme is relatively simpler to calculate.
文摘P-集合(packet sets)是由内P-集合X■(internal packet set X■)与外P-集合XF(outer packet set XF)构成的集合对;或者(X■,XF)是P-集合。P-集合具有动态特性(内P-集合具有内-动态特性,外P-集合具有外-动态特性)。P-集合在动态信息系统的多个领域中获得了应用。在一类信息系统中,这类信息系统只具有内-动态特性,不具有外-动态特性。为了研究这类只有内-动态特性的信息系统,改进并简化P-集合,提出了半P-集合(half packet sets)。半P-集合是由内P-集合X■与有限普通集合X构成的集合对,或者(X■,X)是半P-集合,半P-集合具有内-动态特性。以及半P-集合与有限普通集合的关系,以及半P-集合与P-集合的关系。利用半P-集合给出信息内-真度与信息内-真度环的概念、信息内-真度环定理以及内-信息恢复-还原的内-真度准则与内-信息恢复-还原的特征系数准则。利用这些结果,给出内-真度环在内-信息恢复-还原中的应用。半P-集合是研究一类动态信息系统的一个新的数学方法与数学模型;半P-集合在一类信息系统应用中前景看好。
