Using Normal Form of Matrices over Finite Fields to Construct Cartesian Authentication Codes

In this paper, one construction of Cartesian authentication codes from the normal form of matrices over finite fields are presented and its size parameters are computed. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the P I and P S , which denote the largest probabilities of a successful impersonation attack and of a successful substitution attack respectively, of these codes are also computed.

Normal Bases and Their Dual-Bases over Finite Fields

In this paper, we prove the following results： 1） A normal basis N over a finite field is equivalent to its dual basis if and only if the multiplication table of N is symmetric; 2） The normal basis N is self-dual if and only if its multiplication table is symmetric and Tr（α^2） = 1, where α generates N; 3） An optimal normal basis N is self-dual if and only if N is a type-Ⅰ optimal normal basis with q = n = 2 or N is a type-Ⅱ optimal normal basis.

ON THE COMPLEXITY OF THE NORMAL BASES VIA PRIME GAUSS PERIOD OVER FINITE FIELDS

A formula on the complexity of the normal bases generated by prime Gauss period overfinite fields is presented in terms of cyclotomic numbers.Then,the authors determine explicitly thecomplexity of such normal bases and their dual bases in several cases where the related cyclotomicnumbers have been calculated.Particularly,the authors find several series of such normal bases withlow complexity.

A New Criterion on k-Normal Elements over Finite Fields

The notion of normal elements for finite fields extension was generalized as k-normal elements by Huczynska et al.(2013).Several methods to construct k-normal elements were presented by Alizadah et al.(2016)and Huczynska et al.(2013),and the criteria on k-normal elements were given by Alizadah et al.(2016)and Antonio et al.(2018).In the paper by Huczynska,S.,Mullen,G.,Panario,D.and Thomson,D.(2013),the number of k-normal elements for a fixed finite field extension was calculated and estimated.In this paper the authors present a new criterion on k-normal elements by using idempotents and show some examples.Such criterion was given for usual normal elements before by Zhang et al.(2015).

On the Existence for Some Special Primitive Elements in Finite Fields

Let F_q be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive elementα∈ F_(q^n) such that α + α^(-1)is also primitive or α + α^(-1)is primitive and α is a normal element of F_(q^n) over F_q.

On the Index of Finite Determinacy of Vector Fields with Resonances

In this paper we study normal forms for a class of germs of 1-resonant vector fields on R^n with mutually different eigenvalues which may admit extraneous resonance relations. We give an estimation on the index of finite determinacy from above as well as the essentially simplified polynomial normal forms for such vector fields. In the case that a vector field has a zero eigenvalue, the result leads to an interesting corollary, a linear dependence of the derivatives of the hyperbolic variables on the central variable.

On Existence of Primitive Normal Elements of Cubic Form over Finite Fields

For a prime p and a positive integer k,let q=p^(k) and F_(q)^(n) be the extension field of F_(q).We derive a sufficient condition for the existence of a primitive element α in F_(q)^(n) such that α^(3)-α+1 is also a primitive element of F_(q)^(n) ,a sufficient condition for the existence of a primitive normal element a in F_(q)^(n) over F_(q) such that α(3)-α+1 is a primitive element of F_(q)^(n) ,and a suficient condition for the existence of a primitive normal element a in F_(q)^(n) over F_(q) such that а^(3)-а+1 is also a primitive normal element of F_(q)^(n) over F_(q).

类氢He^(+)在白矮星磁场范围赖曼系吸收谱的研究

采用发展的(Finite-basis-size)方法用(B-splines)基在典型的磁化白矮星强磁场中计算了类氢离子He^(+)的离散光谱。涉及到的磁场范围为2.35~2350 MG。计算共涉及9个磁化原子态,包含3种对称性0^(+)、0-和(-1)^(+),计算了8种电偶极跃迁的波长、振子强度和跃迁速率。此8种电偶极跃迁分别为10^(+)→ν0-(ν=1-4)和10^(+)→ν(-1)^(+)(ν=1-4)。计算结果显示此8种电偶极跃迁的波长均分布在紫外区域,当磁感应强度γ=0.2a.u时10^(+)→4(-1)^(+)跃迁属于弱跃迁。计算结果可作为天体物理的参考数据。

基于多项式基的Camellia算法S盒硬件优化

该文提出一种基于不可约多项式的Camellia算法S盒的代数表达式,并给出了该表达式8种不同的同构形式。然后,结合Camellia算法S盒的特点,基于理论证明给出一种基于多项式基的S盒优化方案,此方法省去了表达式中的部分线性操作。相对于同一种限定门的方案,在中芯国际(SMIC)130 nm工艺库中,该文方案减少了9.12%的电路面积;在SMIC 65 nm工艺库中,该文方案减少了8.31%的电路面积。最后,根据Camellia算法S盒设计中的计算冗余,给出了2类完全等价的有限域的表述形式,此等价形式将对Camellia算法S盒的优化产生积极影响。

On Primitive Optimal Normal Elements of Finite Fields

Let q be a prime or prime power and Fq^n the extension of q elements finite field Fq with degree n （n 〉 1）. Davenport, Lenstra and School proved that there exists a primitive element α ∈ Fq^n such that α generates a normal basis of Fq^n over Fq. Later, Mullin, Gao and Lenstra, etc., raised the definition of optimal normal bases and constructed such bases. In this paper, we determine all primitive type I optimal normal bases and all finite fields in which there exists a pair of reciprocal elements α and α^-1 such that both of them generate optimal normal bases of Fq^n over Fq. Furthermore, we obtain a sufficient condition for the existence of primitive type II optimal normal bases over finite fields and prove that all primitive optimal normal elements are conjugate to each other.

Vanishing Ideals of Projective Spaces over Finite Fields and a Projective Footprint Bound

We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these generators form a universal Gr¨obner basis of the ideal. Further we give a projective analogue for the so-called footprint bound, and a version of it that is suitable for estimating the number of rational points of projective algebraic varieties over finite fields. An application to Serre’s inequality for the number of points of projective hypersurfaces over finite fields is included.

Low-complexity multiplexer-based normal basis multiplier over GF（2^m）

We present a new normal basis multiplication scheme using a multiplexer-based algorithm. In this algorithm, the proposed multiplier processes in parallel and has a multiplexer-based structure that uses MUX and XOR gates instead of AND and XOR gates. We show that our multiplier for type-1 and type-2 normal bases saves about 8% and 16%, respectively, in space complexity as compared to existing normal basis multipliers. Finally, the proposed architecture has regular and modular con-figurations and is well suited to VLSI implementations.

有限域上的k-型高斯正规基及其对偶基

正规基在有限域的许多应用领域中有广泛应用:编码理论、密码学、信号传送等.Z.X.Wan等(Finite Fields and Their Applications,2007,13(4):411-417.)给出了Fqn在Fq上的Ⅰ型最优正规基的对偶基的复杂度为:3n-3(q为偶数)或3n-2(q为奇数).这是一类类似于k-型高斯正规基的低复杂度正规基.最近,廖群英等(四川大学学报:自然科学版,2010,47(6):1221-1224.)给出了2-型高斯正规基的对偶基及其复杂度.在此基础上,给出了一般的k-型高斯正规基N的对偶基以及当n≥k≥1时,N的复杂度的一个上界.进而证明了当k=3时,此上界可达到,并由此给出了所有(弱)自对偶的k-型高斯正规基.

核主泵屏蔽电机温度场研究

核主泵屏蔽电机是核电站的重要组成部分,其安全稳定的运行对核岛一次回路系统来说非常重要。针对核主泵屏蔽电机内发热与冷却的复杂性以及核主泵屏蔽电机工作在高温高压条件下的特点,以一台5 500 kW核主泵屏蔽电机为例,根据流体力学及传热学理论,建立三维流体场与三维温度场耦合的求解域物理模型,采用有限体积法计算额定工况下电机的温度分布。通过计算揭示了核主泵屏蔽电机内温度的分布规律,并分析了其原因,可为核主泵屏蔽电机的冷却结构设计以及更大容量核主泵屏蔽电机温度场的准确计算提供理论依据。

有限域上与k-型高斯正规基相关的自对偶正规基

设q为素数p的方幂,n为正整数,Fqn是q元有限域Fq的n次扩域,α∈Fqn生成Fqn在Fq上的k-型高斯正规基.给出了存在a,b∈Fq使得β=a+bα生成Fqn在Fq上自对偶正规基,以及存在a,b∈Fq,使得a+bα和a+bαn2生成Fqn在Fq上互为对偶的正规基的等价刻划.

有限域上的k-型高斯正规基的对偶基及其乘法表

设q为素数的方幂,N是F qn在F q上的k-型高斯正规基.得到了k型高斯正规基的几个性质,并利用这些性质给出了N的对偶基的简洁证明,以及N与其对偶基乘法表对应元素之间的关系.

基于节点电荷电位有限元法的油纸绝缘结构极性反转电场分析

基于电荷–电位有限元法分析换流变压器的油纸绝缘结构极性反转电场,该方法可以直接得到节点电位和节点电荷。对各个时刻节点电荷进行处理,提出得到电荷密度的方法。通过提取一类边界上的节点面电荷密度,可以准确地计算出第一类边界上的法向电场强度,从而可以更好地指导绝缘强度设计。通过一个有解析解的双层有损同轴绝缘结构模型,验证了方法的有效性。最后,分析了一个换流变压器阀侧绕组典型绝缘结构的极性反转电场变化过程。

有限域上一类自对偶正规基的乘法表与复杂度

设有限域F qn在F q上高斯正规基N的生成元α的线性组合β=a+bα(a,b∈F q)生成的自对偶正规基为B.给出了N和B的乘法表之间的关系,并由此得到N为最优正规基时,B的复杂度的准确计算公式.

二元域上对称循环矩阵的非退化性

齐次旋转对称布尔函数与F2n在F2上的一类特殊正规基有着密切的联系,这类正规基的存在性依赖于二元域F2上n×n对称循环矩阵的可逆性.利用有限域上多项式的性质给出了F2上一类n×n对称循环矩阵的行列式计算公式,并由此得到一类特殊的可逆对称循环矩阵.

110kV劣化瓷质悬式绝缘子空间电场研究

输电线路运行的绝缘子发生劣化时,其周围空间电场相对正常状态会发生局部畸变,因此比较和分析绝缘子劣化前后的电场分布特性,可以识别出劣化绝缘子。文章通过有限元仿真软件建立110 kV瓷质悬式绝缘子的1:1有限元电场仿真模型,得到绝缘子串性能良好时的电场分布参考曲线;通过改变绝缘子串劣化位置和程度,获得劣化状态下绝缘子串的空间电场分布变化曲线。仿真结果表明:绝缘子串劣化区域的轴向电场强度显著降低,其中零值绝缘子比低值绝缘子的下降程度更为突出;另外随着测量距离的增大,劣化绝缘子造成的电场畸变逐渐减弱。在高压实验大厅搭建绝缘子空间电场实验平台,用光学电场传感器测量了绝缘子串在不同情况下的轴向电场并通过“直线归一法”对测量数据进行了处理,试验结果表明:劣化绝缘子附近的轴向电场显著减小,与仿真结果一致。因此,测量空间电场可以实现劣化绝缘子的带电检测。