共查询到18条相似文献,搜索用时 140 毫秒
1.
有限域上的置换多项式在密码学,编码理论和序列设计等领域中有着广泛的应用.至今,对于置换多项式的研究已取得一系列的进展,研究者提出利用AGW准则、分段函数等来构造和证明置换,而对于置换多项式的分类仅有少数几种被提出,因此构造不同类型的置换多项式是一个值得研究的问题.本文利用迹函数和线性化多项式构造了一类有限域上具有特殊形式的无限类置换多项式.首先,我们对一类线性化多项式和一类二次齐次多项式进行讨论,当其存在线性转换时,给出其需要满足的条件.进一步地,当这两类多项式存在0-线性转换时,我们利用这两类函数构造出了有限域上具有特殊形式的两类置换多项式. 相似文献
2.
3.
有限域上高次剩余码的生成多项式都是多项式[xn-1]的因式。针对多项式[xn-1]在有限域上分解的困难性,给出了三元域[F3]上三次和四次剩余码的幂等生成元表达式。利用计算机软件求解这些幂等生成元与[xn-1]最大公因式就可得到三次和四次剩余码生成多项式而不用分解[xn-1]。 相似文献
4.
有限域上高次剩余码的生成多项式都是多项式[xn-1]的因式。针对多项式[xn-1]在有限域上分解的困难性,给出了二元域[F2]上三次和四次剩余码的幂等生成元表达式。利用计算机软件求解该幂等生成元与[xn-1]最大公因式就可得到三次和四次剩余码生成多项式而不用分解[xn-1]。 相似文献
5.
6.
AGW准则和分段方法是构造有限域上置换多项式的两种主要方法。介绍有限域上置换多项式在密码学和编码理论中的应用,总结利用AGW准则和分段方法构造有限域上置换多项式和逆置换的研究进展,阐述置换多项式存在的问题,并对下一步研究工作进行展望。 相似文献
7.
文章首先分析了张青坡等人中提出的多项式形式的E1Gamal签名体制的安全缺陷,然后基于有限域上多项式的性质,提出了有限域上多项式形式代理保护代理签名方案;新的签名方案中,利用多项式进行签名权利的委托,并由改进的有限域上的多项式形式的E1Gamal签名体制生成代理签名。新方案的安全性基于离散对数的难解性。 相似文献
8.
9.
曹阳 《计算机与数字工程》2015,(3):462-464
结合ECC密码体制优点和有限域上离散对数问题,提出了一种基于混沌映射的混合安全双向认证密钥协商协议。协议基于有限域上切比雪夫多项式的半群特性,运用ECC密码算法隐藏通信双方产生的有限域上切比雪夫多项式值,实现了通信双方双向认证,避免了Bergamo攻击,抵抗了中间人攻击、重放攻击,保证了密钥协商的安全性。理论上分析表明,该协议不仅具有强安全性,而且具有高效性特点。 相似文献
10.
11.
We consider the problem of fast computation of the Fourier transform over a finite field by decomposing an arbitrary polynomial into a sum of linearized polynomials. Examples of algorithms for the Fourier transform with complexity less than that of the best known analogs are given. 相似文献
12.
This paper presents a linearized polynomial mixed-integer programming model (PMIPM) for the integration of process planning and scheduling problem. First, the integration problem is modeled as a PMIPM in which some of the terms are of products of up to three variables, of both binary and continuous in nature. Then, an equivalent linearized model is derived from the polynomial model by applying certain linearization techniques. Although the linearized models have more variables and constraints than their polynomial counterparts, they are potentially solvable to the optimum in comparison to their equivalent polynomial models. Experiments show that the linearized model possesses certain characteristics that are absent from other models in the literature, and provides a fundamental framework for further research in this area. 相似文献
13.
《Journal of Symbolic Computation》2001,31(1-2):19-36
The paper focuses on the deterministic complexity of factoring polynomials over finite fields assuming the extended Riemann hypothesis (ERH). By the works of Berlekamp (1967, 1970) and Zassenbaus (1969), the general problem reduces deterministically in polynomial time to finding a proper factor of any squarefree and completely splitting polynomial over a prime field Fp. Algorithms are designed to split such polynomials. It is proved that a proper factor of a polynomial can be found deterministically in polynomial time, under ERH, if its roots do not satisfy some stringent condition, called super square balanced. It is conjectured that super square balanced polynomials do not exist. 相似文献
14.
The problem is studied of testing for stability a class of real polynomials in which the coefficients depend on a number of variable parameters in a multilinear way. We show that the testing for real unstable roots can be achieved by examining the stability of a finite number of corner polynomials (obtained by setting parameters at their extreme values), while checking for unstable complex roots normally involves examining the real solutions of up to m + 1 simultaneous polynomial equations, where m is the number of parameters. When m = 2, this is an especially simple task. 相似文献
15.
Timo von Oertzen 《Algorithmica》2006,46(1):119-136
In this paper we give an efficient algorithm to find symbolically correct zeros of a polynomial f ∈ R[X] which can be represented
by square roots. R can be any domain if a factorization algorithm over R[X] is given, including finite rings or fields, integers,
rational numbers, and finite algebraic or transcendental extensions of those. Asymptotically, the algorithm needs O(Tf(d2)) operations in R, where Tf(d) are the operations for the factorization algorithm over R[X] for a polynomial of degree d. Thus, the algorithm has polynomial
running time for instance for polynomials over finite fields or the rationals. We also present a quick test for deciding whether
a given polynomial has zeros expressible by square roots and describe some additional methods for special cases. 相似文献
16.
We present a symbolic algorithm to solve for the zeros of a polynomial vector field equivariant with respect to a finite subgroup of O (n). We prove that the module of equivariant. polynomial maps for a finite matrix group is Cohen-Macaulay and give an algorithm to compute a fundamental basis. Equivariant normal forms are easily computed from this basis. We use this basis to transform the problem of finding the zeros of an equivariant map to the problem of finding zeros of a set of invariant polynomials. Solving for the values of fundamental polynomial invariants at the zeros effectively reduces each group orbit of solutions to a single point. Our emphasis is on a computationally effective algorithm and we present our techniques applied to two examples. 相似文献
17.
《Journal of Symbolic Computation》1994,17(3):237-258
In this paper, we provide an account of several new techniques for computing the primitive idempotents of a commutative artinian algebra over a finite field. Examples of such algebras include the center of a finite group algebra or any finite dimensional quotient of a polynomial ring. The computational methods described are applicable in fairly general situations and the algorithms presented are easily programmed. Both pseudocode and operation counts are provided. As an application, the problem of factoring polynomials over finite fields is discussed. 相似文献
18.
I.K. Rystsov 《Information Processing Letters》1983,16(3):147-151
Kozen (1977) proved that the emptiness problem for regular languages intersection is polynomial complete. In this paper we show that many other problems concerning deterministic finite state automata are polynomial complete and therefore intractable for solution. On the other hand, simplified versions of these problems can be solved in polynomial time by deterministic algorithms. This work is a part of the research on automata theory carried out at the Institute of Cybernetics headed by academician V.M. Glushkov. 相似文献