信息安全中伪随机序列的生成和性质及应用研究

Pseudo-random sequences are widely used in communication, cryptography, coding and other fields. Constructing pseudo-random sequences suitable for various applications has always been a hot topic in the theory of pseudo-random sequences.This project intends to study the construction, security and application of pseudo-random sequence in encoding, starting from several kinds of cyclotomic sequence and single-cycle T-function sequence. (1) The new generation of cyclotomic sequence will be represented and the complexity of sequences will be studied. Meanwhile, the 2-adic complexity of a class of almost complete Gauss integer sequence with period P^m-1 will be studied. (2) Maximum periodic pseudo-random sequence in finite field and cyclotomic field is constructed; pseudo-random sequence generator based on non-linear cryptographic function is designed and studied from the point of view of security index of generating sequence. (3) Design linear codes based on single circle T-function sequence and SLCE sequence will be studied, and the dimension, weight distribution, minimum distance of these codes will be discussed, as well as their applications in combination design, secret sharing and so on. The research results of this project are expected to promote the research of pseudo-random sequence theory and provide new components for communication and cryptography theory and application.

伪随机序列在通信、密码、编码等领域有广泛应用，构造适用于各应用领域的伪随机序列一直是伪随机序列理论研究热点。本项目拟以几类分圆序列和单圈T函数序列为研究切入点，利用有限域、代数数论和组合学的理论和方法，深入研究伪随机序列的构造、安全性以及在编码中的应用。(1)研究以SLCE序列为代表的分圆序列的生成，序列的复杂度等指标；研究一类周期为p^m-1的几乎完备高斯整数序列的2-adic复杂度．(2)构造有限域和分圆域上极大周期伪随机序列；设计基于非线性密码函数的伪随机序列生成器，从生成序列的安全性指标角度研究这种生成器的特性．(3)设计基于单圈T函数序列和SLCE等分圆序列的线性码，研究其维数、重量分布、极小距离等指标，遴选性质优良的码，研究其在组合设计、秘密共享等方面的应用。本项目的研究结果有望促进伪随机序列理论研究，为通信和密码理论和应用提供新的部件。

伪随机序列在通信、密码、编码等领域有广泛应用，构造适用于各应用领域的伪随机序列一直是伪随机序列理论研究热点。本项目以几类分圆序列和单圈T函数序列为基础序列，利用有限域、代数数论和组合学的理论和方法，深入研究了伪随机序列的构造、安全性以及在编码中的应用。(1) 研究了以SLCE序列为代表的分圆序列的生成，序列的复杂度等指标；(2) 研究了一类周期为p^m-1的几乎完备高斯整数序列的2-adic复杂度；(3) 构造了有限域和分圆域上极大周期伪随机序列；设计了基于非线性密码函数的伪随机序列生成器，从生成序列的安全性指标角度研究这种生成器的特性；(4)设计了几类线性码，研究其维数、重量分布、极小距离等指标，遴选性质优良的码，研究其在组合设计、秘密共享等方面的应用。本项目的研究结果有望促进伪随机序列理论研究，为通信和密码理论和应用提供新的部件。

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