关于de Bruijn序列

本文对二元域上M序列的小项集合进行研究,给出了M序列的一些新的必要条件;对非奇布尔函数给出一种(基于小项集合的)编号表示,指出了M序列编号的若干特点;给出了本原M序列小项集合及剪接标号集合的一些性质;并对奇数阶自对偶反转M序列的小项构造和计数作了初步探讨,提出了一些分析和猜想。     

m序列的移位相加特性

讨论了m序列的移位相加特性,介绍了一种对给定的γ和η计算λ使序列三项式{ak η} {ak γ}={ak λ}成立的方法。无需给出m序列,只需通过产生m序列的本原多项式的互反多项式以及关于模p^n-1的分圆陪集就可以获得全部序列三项式。     

二元GMW序列Niho采样下的互相关性分析

GMW序列是一种线性复杂度很高的非线性序列,在直接序列扩频系统中有着很好的应用前景.通过证明级联二元GMW序列与其采样序列的互相关性在特定条下和构造级联GMW序列的幂无关,将二元GMW序列与其采样序列的互相关性与m序列联系起来.通过现有二元m序列在Niho采样下的互相关性研究结论,分析证明了级联二元GMW序列在Niho采样下的互相关性具有四值、五值、六值特性.     

确定周期为P n的二元序列k-错复杂度曲线的快速算法

设计了一个确定周期为P^n的二元序列k-错复杂度曲线的算法,这里p为素数,并且2是模P^2的一个本原根。该算法分别推广了魏-白-肖和魏-董-肖计算二元P^n周期序列线性复杂度与k-错复杂度的算法。     

确定周期为p~n的二元序列的k-错线性复杂度的一个算法

本文给出了确定周期为pn 的二元序列的k -错线性复杂度的一个算法 ,这里p为素数 ,2为模p2 的一个本原根     

确定周期为pn的二元周期序列的线性复杂度的一个快速算法

本文介绍了确定周期为ｐ ｎ 的二元周期序列的线性复杂度的一个快速算法,这里 ｐ 为素数,２为模 ｐ２的一个本原根。     

并元互补二元序列族

本文首先提出了并元加族的概念，然后研究了并元互补二元序列族与并元加族的关系和并元互二元序列族存在的条件，最后给出并元互补二元序列族的计算机搜索方法。     

一种新的二元互补序列偶的构造方法

本文研究了互补序列偶的构造问题,得到了一种新的二元互补序列偶的构造方法,即由N长二元序列偶和M长二元序列偶来构造MN长二元序列偶。这不仅拓宽了二元互补序列偶可构造的空间范围,更重要的是可以通过此种构造方法来构造更长的奇数长二元互补序列偶,弥补了原有的构造方法只能构造偶数长度的互补序列偶的不足,而且对研究奇数长二元互补序列偶也具有重要意义。     

确定周期为p^n的二元序列的k—错线性复杂度的一个算法

本文给出了确定周期为p^n的二元序列的k-错线性复杂度的一个算法，这里p为素数，2为模p2的一个本原根。     

二元周期序列互相关函数与相关性

移位寄存器序列的互相关函数用于密码研究与应用时,与传统的统计概念就不一致了。本文给出了二元周期序列互相关函数的几个等价定义,研究了互相关函数与概率统计中的相关性之间的相互关系。     

关于本原M序列的自相关函数

本文研究了本原M序列的自相关性能,首次获得了部份自相关函数的通解。这些通解的作用在于无需给出序列,只要知道反馈函数就可以获得相应的自相关函数值,大大降低了自相关函数的计算量。此外,还给出了自相关函数C(#em/em#)(n#em/em# 2n-1)的取值范围。     

基于免疫克隆算法的最优M序列搜索

二相编码脉冲压缩信号例如巴克码和M序列已经广泛应用于现代雷达系统中。二相编码波形设计中初始移位寄存器的选择是个关键技术，它直接决定了信号波形在满足最小峰值功率下能否具有最大脉压比。基于免疫学中的抗体克隆选择，提出了用免疫克隆算法（ICSA）来搜索M序列最优初始移位寄存器值。与标准遗传算法（SGA）和一种混合遗传算法（HGA）相比，文中提出的方法有效地战胜了早熟现象，得到了更优的搜索结果。实验结果证明了此算法的可行性和有效性。     

基于VHDL语言M序列密码系统设计的新方法

文章介绍了用M序列为密钥序列的序列密码系统的优越性，提出了采用VHDL语言来设计这种序列密码系统的新方法。和现有的其他方法比较，该方法具有硬件实现容易，处理速度快，实时性好，密钥管理方便。体积小等特点。     

多位全状态移位型计数器的实现

M序列信号可以模拟白噪声，广泛应用于扩频通信、数字加密、数字系统测试等领域。如果能够将移位型计数器的全部状态加以利用，实现All States Sequence信号，则既可以实现同步计数，还可拓宽移位型计数器的应用领域。     

Minimal Complete Primitives for Secure Multi-Party Computation

The study of minimal cryptographic primitives needed to implement secure computation among two or more players is a fundamental question in cryptography. The issue of complete primitives for the case of two players has been thoroughly studied. However, in the multi-party setting, when there are n > 2 players and t of them are corrupted, the question of what are the simplest complete primitives remained open for t n/3. (A primitive is called complete if any computation can be carried out by the players having access only to the primitive and local computation.) In this paper we consider this question, and introduce complete primitives of minimal cardinality for secure multi-party computation. The cardinality issue (number of players accessing the primitive) is essential in settings where primitives are implemented by some other means, and the simpler the primitive the easier it is to realize. We show that our primitives are complete and of minimal cardinality possible for most cases.     

Ternary pseudorandom signal design for uniform excitation and reduced effect of nonlinear distortion

Ternary pseudorandom signals with uniform spectra are useful for system identification, particularly during prototyping when actuators are rather primitive. To reduce the effect of nonlinear distortion on the linear estimate, the signal should have harmonic multiples of two and three suppressed. No analytical method is currently available for the design of such signals, while optimisation cannot guarantee an optimal solution. An analytical method that guarantees optimality is introduced in which the pseudorandom signal, generated from a Galois field, is designed based on a primitive version of the signal having suitable harmonic properties and a sparse spectrum with multiple periodicity.     

An approximation to the weight distribution of binary linear codes

Binary primitive BCH codes form a large class of powerful error-correcting codes. The weight distributions of primitive BCH codes are unknown except for some special classes, such as the single, double, triple error-correcting codes and some very low-rate primitive BCH codes. However, asymptotic results for the weight distribution of a large subclass of primitive BCH codes have been derived by Sidel'nikov. These results provide some insight into the weight structure of primitive BCH codes. Sidel'nikov's approach is improved and applied to the weight distribution of any binary linear block code. Then Sidel'nikov's results on the weight distributions of binary primitive BCH codes are improved and it is shown that the weights of a binary primitive code have approximate binomial distribution.     

Oblivious Transfers and Privacy Amplification

Oblivious transfer (OT) is an important primitive in cryptography. In chosen one-out-of-two string OT, a sender offers two strings, one of which the other party, called the receiver, can choose to read, not learning any information about the other string. The sender on the other hand does not obtain any information about the receivers choice. We consider the problem of reducing this primitive to OT for single bits. Previous attempts to doing this were based on self-intersecting codes. We present a new technique for the same task, based on so-called privacy amplification. It is shown that our method has two important advantages over the previous approaches. First, it is more efficient in terms of the number of required realizations of bit OT, and second, the technique even allows for reducing string OT to (apparently) much weaker primitives. An example of such a primitive is universal OT, where the receiver can adaptively choose what type of information he wants to obtain about the two bits sent by the sender subject to the only constraint that some, possibly very small, uncertainty must remain about the pair of bits.     

本原σ-LFSR序列的迹表示及其应用

σ-LFSR是一基于字的LFSR模型,它的设计充分利用了现代CPU特点,可很好地应用于设计适合快速软件实现的序列密码算法中。而在实际应用中,本原σ-LFSR序列具有最核心的作用。该文分析了本原σ-LFSR序列的产生条件,利用其迭代关系式和有限域的迹函数,给出了它的具体表达式,从而得到本原σ-LFSR序列的迹表示;其次由本原σ-LFSR序列的迹表示,给出了一个σ-LFSR序列为本原的充要条件。它们为进一步研究本原σ-LFSR序列提供了新的工具。     

Two applications of cyclotomic cosets to certain BCH codes (Corresp.)

A more accurate designed distance bound is given for a subclass of narrow-sense primitive Bose-Chaudhuri-Hocquenghem (BCH) codes for which Mann has found the number of information digits. It is also determined when two consecutive odd integers are in the same cyclotomic coset.