整数剩余类环上压缩导出序列分布性质的研究

In the middle of 1980s, Zeng Kencheng, Dai Zongduo and Huang Minqiang from China and Kuzmin and Nechaev from Soviet Union presented compressing sequences derived from primitive sequences over rings, which were regarded as a class of nonlinear sequences, and they independently proved that the highest level sequences preserve all the information of the original primitive sequences over the rings. After that, these nonlinear sequences draw much attention all over the world, and many results have been obtained. Especially, after the eSTREAM project, cryptographers prefer to use nonlinear sequence block to design stream ciphers. The research on compressing sequences may provide some references for designing stream ciphers. This project focuses on the distribution properties of compressing sequences. Our research includes the following. First we want to find more injective compressing maps, and then give more details about these maps to tell under which conditions these maps are local entropy-preservation and even local entropy-preservation with some related sequence. At last, we study the minimal distinguishable length of compressing sequences and hope that we can get some nontrivial results.

二十世纪八十年代中期，我国学者曾肯成、戴宗铎和黄民强以及前苏联学者Kuzmin和Nechaev分别提出了环上本原序列压缩导出序列这一非线性序列模型，并且他们各自独立证明了最高权位序列具有保熵性，即本原序列相等当且仅当最高权位序列相等。由于这一重要的密码学性质，这类非线性序列的研究吸引了国内外广泛的关注，并且取得了大量的成果。特别是在eSTREAM计划之后，密码设计者趋向于采用非线性驱动部件来设计流密码，对该类序列的研究或许能为密码设计提供一些参考。本项目主要研究压缩序列的分布性质，内容包括以下几个方面，首先寻找更多具有保熵性的压缩映射，其次对具有保熵性的压缩映射进行深入的分析，给出其具有局部保熵性，甚至是具有在某特定序列控制下的局部保熵性的等价条件，最后我们研究压缩序列的最小可区分长度，希望能在这一重要的困难问题上有突破。

二十世纪八十年代中期，我国学者曾肯成、戴宗铎和黄民强以及前苏联学者Kuzmin和Nechaev分别提出了环上本原序列压缩导出序列这一非线性序列模型，并且他们各自独立证明了最高权威序列具有保熵性。这类非线性序列的研究吸引了国内外广泛的关注，并且取得了大量的成果。本项目给出了大量新的保熵映射，并且给出了一类保熵映射压缩导出的序列具有局部保熵性的等价条件，这些结果提供了大量的保熵压缩序列，并且加深了我们对此类序列的认识。