The 2-error Linear Complexity of 2n-Periodic Binary Sequences

Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of key sequences. For a random 2n-periodic binary sequence, the number of sequences with given 2-error linear complexityis provided. Then the expected 2-error linear complexity of a random 2n-periodic binary sequence is given.     

Linear complexity of quaternary sequences with odd period and low autocorrelation

Equivalence between two classes of quaternary sequences with odd period and best known autocorrelation are proved. A lower bound on the linear complexity of these sequences is presented. It is shown that the quaternary sequences have large linear complexity to resist Reeds and Sloane algorithm attack effectively.     

Computing the k-error joint linear complexity of binary periodic multisequences

Complexity measures for multisequences over finite fields, such as the joint linear complexity and the k-error joint linear complexity, play an important role in cryptology. In this paper we study a fast algorithm, presented by Venkateswarlu A, to computer the k-error joint linear complexity of a binary periodic multisequence. In this paper, the aim is mainly to complement the theoretical derivation and proof of the existing algorithm. Moreover, our algorithm reduces computation.     

THE APPLICATION OF LINEAR COMPLEXITY OF SEQUENCES TO LOWER BOUNDS ON THE MINIMUM DISTANCE OF CYCLIC CODES

Firstly,the Fourier transforms in finite fields and the concept of linear complexityof sequences are described.Then several known lower bounds on the minimum distance of cycliccodes are outlined.Finally,the minimum distance of cyclic codes is analyzed via linear complexityof sequences,and new theorems about the lower bounds are obtained.     

CONSTRUCTING AND ANALYZING A CLASS OF CONTROLLABLE SEQUENCES

By using m-sequence over the finite field GF(2m) of degree L to control m-sequence over GF(2m) of degree L, a class of periodic sequences with large linear complexity is constructed. The lower bounds of the linear complexity of these sequences are L((L +1)m-Lm).     

GAUSS PERIODS AND CYCLIC CODES FROM CYCLOTOMIC SEQUENCES OF SMALL ORDERS

Let p =ef +1 be an odd prime with positive integers e and f. In this paper, we calculate the values of Gauss periods of order e =3, 4, 6 over a finite field GF(q), where q is a prime with q≠p. As applications, several cyclotomic sequences of order e =3, 4, 6 are employed to construct a number of classes of cyclic codes over GF(q) with prime length. Under certain conditions, the linear complexity and reciprocal minimal polynomials of cyclotomic sequences are calculated, and the lower bounds on the minimum distances of these cyclic codes are obtained.     

A Fast Quantitative Analysis and Performance Estimation Method of SoC Bus Architectures

Various multi-layered bus architectures are now being used in the SoC industry. Reckless use of bus layers may result in low utilization of communication resource and waste silicon area. This paper introduces a quantitative analysis at the initial stage of SoC design. The time complexity is examined and it is found that their scale is the order of n to the power of n, or combinatorial, and thus the problem is NP-complete. The paper proposes some heuristic methods through in-depth investigation and applies them to each step of the exploration to reduce the time complexity. The exploration processes and the proposed methods are implemented as a software program and several experiments are performed. From the results, the performance of SNP turns out to be significantly enhanced and achieves 25% enhancement in comparison with a defacto standard bus, AXI. For time complexity, the reduction ratio goes down to 3.7× 10^-6.     

A NOVEL LINEAR DIFFERENTIAL SPACE-TIME MODULATION

Based on the Complex Orthogonal Linear Dispersion (COLD) code,a novel linear Differ- ential Space-Time Modulation (DSTM) design is proposed in this paper.Compared with the existing nonlinear DSTM schemes based on group codes,the proposed linear DSTM scheme is easier to design, enjoys full diversity and allows for a simplified differential receiver,which can detect the transmitted symbols separately.Furthermore,compared with the existing linear DSTM based on orthogonal design, our new construction can be applied to any number of transmit antennas.Similar to other algorithms, the proposed scheme also can be demodulated with or without channel estimates at the receiver,but the performance degrades approximately by 3dB when estimates are not available.     

On the Linear Complexity of a Class of Periodic Sequences Derived from Euler Quotients

In this paper, a family of binary sequences derived from Euler quotients with RSA modulus pq is introduced. Here two primes p and q are distinct and satisfy gcd(pq,(p-1)(q-1))=1. The linear complexities and minimal polynomials of the proposed sequences are determined. Besides, this kind of sequences is shown not to have correlation of order four although there exist some special relations by the properties of Euler quotients.     

A New Family of Quaternary Sequences with Low Correlation and Large Linear Span

Based on quadratic functions, a new family of quaternary sequences of period 2＂ - 1 is presented for n = em with arbitrary rn. The new family is proved to have low correlation and large linear span.     

随机周期序列☆错线性复杂度的期望上界

周期序列的k错线性复杂度是衡量流密码系统的安全性能的一个重要指标。本文给出了周期序列k错线性复杂度上界的一个更强的结果,从而给出了几种不同情形下随机周期序列k错线性复杂度的期望的上界。特别地,还给出了周期N=pv,随机周期序列满足一定条件时1错线性复杂度的期望更紧的结果。     

On the expected value of the linear complexity and the k-errorlinear complexity of periodic sequences

Rueppel (1986) conjectured that periodic binary sequences have expected linear complexity close to the period length N. In this paper, we determine the expected value of the linear complexity of N-periodic sequences explicitly and confirm Rueppel's conjecture for arbitrary finite fields. Cryptographically strong sequences should not only have a large linear complexity, but also the change of a few terms should not cause a significant decrease of the linear complexity. This requirement leads to the concept of the k-error linear complexity of N-periodic sequences. We present a method to establish a lower bound on the expected k-error linear complexity of N-periodic sequences based on the knowledge of the counting function 𝒩_N,₀(c), i.e., the number of N-periodic sequences with given linear complexity c. For some cases, we give explicit formulas for that lower bound and we also determine 𝒩_N,0(c)     

Cross-sectional TEM and KOH-Etch Studies of Extended Defects in 3C-SiC <Emphasis Type="Italic">p</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">n</Emphasis> Junction Diodes Grown on 4H-SiC Mesas

This article presents cross-sectional transmission electron microscopy and molten-potassium hydroxide etching studies of (111) 3C-SiC diodes which we previously reported to be free of forward-voltage drift despite abundant electroluminescent linear features presumed to be defects. Our results show that the majority of linear features are stacking faults lying in inclined {111} planes. Additionally, high densities of isolated etch pits (10⁶–10⁸ cm⁻²) are observed in 3C films grown on stepped 4H mesas, while 3C films nucleated on step-free 4H mesas exhibited orders of magnitude fewer etch pits and stacking faults. Defect formation mechanisms whose impetuses are steps on the 4H-SiC pregrowth mesa are discussed.     

k-error linear complexity of q-ary sequence of period p2

Based on element statistics in a matrix,a new efficient computing method for computing the k-error linear complexity of q-ary sequence of period p²was proposed,where p,q were odd primes and q modulo p²was primitive.A general result and a concrete proof were showed.To verify the correctness of the result,two kinds of q-ary sequence of period p²were illustrated.Because the new method does not need iterative calculation and when it is implemented by program and compared with existing algorithms,the results show that the proposed new algorithm is significantly more efficient in calculating k-error linear complexity of q-ary sequence of period p².     

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。     

单圈T函数输出序列的稳定性研究

k-错线性复杂度是衡量序列稳定性的重要指标,该文对单圈T函数按位输出序列的k-错线性复杂度进行了深入研究,利用序列线性复杂度的多项式求解法和Chan Games算法,分析得到了当输入规模n=2tt时,单圈T函数按位输出序列k-错线性复杂度的分布,并进一步给出了该序列的k-错线性复杂度曲线。     

单圈T函数输出序列k-错线性复杂度研究

该文对单圈T函数输出序列的k-错线性复杂度进行了深入研究,利用多项式理论和Chan Games算法,分析得到了当n=2t时,单圈T函数输出序列线性复杂度的n个下降点及其对应位置的k-错线性复杂度,并给出了k-错线性复杂度的分布和k-错线性复杂度曲线。     

k-error linear complexity of binary cyclotomic generators

In terms of the discrete Fourier transforms,the k-error linear complexities over F₂were discussed for Legendre,Ding-Helleseth-Lam,and Hall's sextic residue sequences of odd prime period p.More precisely,the 1-error linear complexities of these sequences were determined.Then,with some special restrictions of the order of 2 modulo p,partial results on their k-error linear complexities (k≥2) were proved.     

二元周期序列的k错误线性复杂度

随着k的增大,序列k错误线性复杂度的值会从线性复杂度递减到0.对于周期为2的方幂的二元序列,Kurosawa讨论了线性复杂度和k错误线性复杂度的关系,给出了使得序列的k错误线性复杂度严格小于序列的线性复杂度最小的k值.本文利用多项式的权重关系给出了使得序列k错误线性复杂度再次减小的最小k值.