Let n, s1, s2,..., sn be non-negative integers and M(s1, s2,...,sn) ={(a1, a2,..., a.)| ai is an integer and 0≤ai ≤si for each i}. In this paper, the cardinality of maximum trees of finite sequences in M(s1, s2,...,...Let n, s1, s2,..., sn be non-negative integers and M(s1, s2,...,sn) ={(a1, a2,..., a.)| ai is an integer and 0≤ai ≤si for each i}. In this paper, the cardinality of maximum trees of finite sequences in M(s1, s2,..., sn) sn) is obtained, which generalizes some of Frankl's results on families of finite sets with prescribed cardinalities for pairwise intersections.展开更多
Based on grow tree composite model, Finite Field Wavelet Grow Tree (FW-GT) was proposed in this paper. FW-GT is a novel framework to be used in data encryption enhancing data security. It is implemented by replacement...Based on grow tree composite model, Finite Field Wavelet Grow Tree (FW-GT) was proposed in this paper. FW-GT is a novel framework to be used in data encryption enhancing data security. It is implemented by replacement operator and wavelet operator. Forward integration and inverse decomposition of FW-GT are performed by replacement, inverse wavelets and its corresponding replacement, wavelet transforms. Replacement operator joined nonlinear factor, wavelet operator completed data transformation between lower dimensional space and higher dimensional space. FW-GT security relies on the difficulty of solving nonlinear equations over finite fields. By using FW-GT, high security of data could be obtained at the cost of low computational complexity. It proved FW-GT algorithm’s correctness in this paper. The experimental result and theory analysis shows the excellent performance of the algorithm.展开更多
文摘Let n, s1, s2,..., sn be non-negative integers and M(s1, s2,...,sn) ={(a1, a2,..., a.)| ai is an integer and 0≤ai ≤si for each i}. In this paper, the cardinality of maximum trees of finite sequences in M(s1, s2,..., sn) sn) is obtained, which generalizes some of Frankl's results on families of finite sets with prescribed cardinalities for pairwise intersections.
文摘Based on grow tree composite model, Finite Field Wavelet Grow Tree (FW-GT) was proposed in this paper. FW-GT is a novel framework to be used in data encryption enhancing data security. It is implemented by replacement operator and wavelet operator. Forward integration and inverse decomposition of FW-GT are performed by replacement, inverse wavelets and its corresponding replacement, wavelet transforms. Replacement operator joined nonlinear factor, wavelet operator completed data transformation between lower dimensional space and higher dimensional space. FW-GT security relies on the difficulty of solving nonlinear equations over finite fields. By using FW-GT, high security of data could be obtained at the cost of low computational complexity. It proved FW-GT algorithm’s correctness in this paper. The experimental result and theory analysis shows the excellent performance of the algorithm.
