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1.
布尔函数Walsh变换的非零取值个数 总被引:1,自引:0,他引:1
设Wf(y)(y∈F2^r)是布尔函数f:F2^r→F2的Walsh变换.Sf为Wf(y)≠0的y个数,S为所有Sf的并集(其中f过所有可能的布尔函数).决定集合S是通信和信息安全领域一个重要问题.本文利用群环工具给出研究这一问题的新方法.用这种方法以统一方式证明了[4]中的结果.并利用群环方法给出了关于集合S的一系列新结果. 相似文献
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概率方法在布尔函数相关免疫性研究中的应用 总被引:5,自引:0,他引:5
本文揭示了布尔函数的Walsh谱及“相关度”的概率实质,证明了Walsh谱的两条重要性质,正确地揭示了多维布尔向量函数的相关免疫性与其各分量的相关免疫性之间的关系;定义了布尔向量函数的Walsh变换及Walsh谱,并由此给出了与Xiao-Massey定理相应的判别条件。 相似文献
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冯克勤 《数学建模及其应用》2012,1(1):13-20
当前,密码学面临的一个挑战性问题是构造具有多种密码学性能的布尔函数,用来作为流密码和分组密码的密钥,以同时抵抗现有的多种破译和攻击方式。本文综述了近年来国内外在这方面的研究和进展。 相似文献
8.
本文给出了从可分图协方差矩阵的分布密度函数确定图精度矩阵分布密度函数的一般方法,得到了可分的Gaussian图模型中精度矩阵极大似然估计的分布密度函数表达式.当图协方差矩阵的分布密度分别服从超逆Wishart分布、超逆Г分布时,也得到了图精度矩阵分布密度函数的解析表达式. 相似文献
9.
《数学的实践与认识》2020,(2)
基于复合Mlinex损失函数,研究了指数威布尔分布的参数在先验分布为伽玛分布的B ayes估计,E-B ayes估计和多层Bayes估计.并用数值模拟的方法进行验证,结果表明三种估计方法的稳健性好,精确度较高. 相似文献
10.
《数学的实践与认识》2015,(18)
布尔函数线性Walsh谱和高阶Walsh谱的研究对构造能够抵抗线性逼近攻击和二次或较高次逼近攻击的密码函数发挥了重要作用.为了抵抗采样攻击,提出了布尔函数迹Walsh谱和迹Walsh循环谱概念,并给出该Walsh谱的一些简单性质.利用这一谱值的分布特性,可以很好地分析布尔函数的迹函数逼近问题,对序列密码采样攻击研究具有重要意义. 相似文献
11.
François Rodier 《Designs, Codes and Cryptography》2006,40(1):59-70
Boolean functions on the space
are not only important in the theory of error-correcting codes, but also in cryptography. In these two cases, the nonlinearity
of these functions is a main concept. Carlet, Olejár and Stanek gave an asymptotic lower bound for the nonlinearity of most
of them, and I gave an asymptotic upper bound which was strictly larger. In this article, I improve the bounds and get an
exact limit for the nonlinearity of most of Boolean functions. This article is inspired by a paper of G. Halász about the
related problem of real polynomials with random coefficients.
AMS Classification (2000) Primary: 11T71 · Secondary: 06E30 · 42A05 · 94C10 相似文献
12.
I. Strazdins 《Acta Appl Math》1997,46(2):147-167
In this paper we advance a practical solution of the classification problem of Boolean functions by the affine group – the largest group of linear transformations of variables. We show that the affine types (equivalence classes) can be arranged in a unique infinite sequence which contains all previous lists of types. The types are specified by their minimal representatives, spectral invariants, and stabilizer orders. A brief survey of the fundamental transformation groups is included. 相似文献
13.
Birger Strauch 《Mathematical Logic Quarterly》1997,43(4):510-524
We describe sets of partial Boolean functions being closed under the operations of superposition. For any class A of total functions we define the set ??(A) consisting of all partial classes which contain precisely the functions of A as total functions. The cardinalities of such sets ??(A) can be finite or infinite. We state some general results on ??(A). In particular, we describe all 30 closed sets of partial Boolean functions which contain all monotone and zero-preserving total Boolean functions. 相似文献
14.
Propagation criteria and resiliency of vectorial Boolean functions are important
for cryptographic purpose (see [1–4, 7, 8, 10, 11, 16]). Kurosawa, Stoh [8] and Carlet [1]
gave a construction of Boolean functions satisfying PC(l) of order k from binary linear
or nonlinear codes. In this paper, the algebraic-geometric codes over GF(2m) are used to
modify the Carlet and Kurosawa-Satoh’s construction for giving vectorial resilient Boolean
functions satisfying PC(l) of order k criterion. This new construction is compared with
previously known results. 相似文献
15.
The interior and exterior functions of a Boolean function f were introduced in Makino and Ibaraki (Discrete Appl. Math. 69 (1996) 209–231), as stability (or robustness) measures of the f. In this paper, we investigate the complexity of two problems -INTERIOR and -EXTERIOR, introduced therein. We first answer the question about the complexity of -INTERIOR left open in Makino and Ibaraki (Discrete Appl. Math. 69 (1996) 209–231); it has no polynomial total time algorithm even if is bounded by a constant, unless P=NP. However, for positive h-term DNF functions with h bounded by a constant, problems -INTERIOR and -EXTERIOR can be solved in (input) polynomial time and polynomial delay, respectively. Furthermore, for positive k-DNF functions, -INTERIOR for two cases in which k=1, and and k are both bounded by a constant, can be solved in polynomial delay and in polynomial time, respectively. 相似文献
16.
在仿射等价类中找具有好的密码学性质的布尔函数 总被引:1,自引:0,他引:1
CHEN Wei-hong LI Na 《数学季刊》2005,20(4):395-400
The Boolean functions in an affine equivalence class are of the same algebraic degree and nonlinearity, but may satisfy different order of correlation immunity and propagation criterion. A method is presented in this paper to find Boolean functions with higher order correlation immunity or satisfying higher order propagation criterion in an affine equivalence class. 8 AES s-box functions are not better Boolean functions in their affine equivalence class. 相似文献
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Usually, local search methods are considered to be slow. In our paper, we present a simulated annealing-based local search algorithm for the approximation of Boolean functions with a proven time complexity that behaves relatively fast on randomly generated functions. The functions are represented by disjunctive normal forms (DNFs). Given a set of m uniformly distributed positive and negative examples of length n generated by a target function F(x
1,...,x
n), where the DNF consists of conjunctions with at most literals only, the algorithm computes with high probability a hypothesis H of length m · such that the error is zero on all examples. Our algorithm can be implemented easily and we obtained a relatively high percentage of correct classifications on test examples that were not presented in the learning phase. For example, for randomly generated F with n = 64 variables and a training set of m = 16384 examples, the error on the same number of test examples was about 19% on positive and 29% on negative examples, respectively. The proven complexity bound provides the basis for further studies on the average case complexity. 相似文献
18.
《代数通讯》2013,41(5):1805-1822
Abstract The concepts of Boolean metric space and convex combination are used to characterize polynomial maps A n ?→?A m in a class of commutative Von Neumann regular rings including p-rings, that we have called CFG-rings. In those rings, the study of the category of algebraic varieties (i.e., sets of solutions to a finite number of polynomial equations with polynomial maps as morphisms) is equivalent to the study of a class of Boolean metric spaces, that we call here CFG-spaces. 相似文献
19.
The strict avalanche criterion (SAC) was introduced by Webster and Tavares [10] in a study of cryptographic design criteria. This is an indicator for local property. In order to improve the global analysis of cryptographically strong functions, Zhang and Zheng [11] introduced the global avalanche characteristics (GAC). The sum-of-squares indicator related to the GAC is defined as
f
=
v
f
2(v), where
f
(v)=x (–1)
f
(x)f(x v). In this paper, we give a few methods to construct Boolean functions controlling five good cryptographic properties, namely balancedness, good local and GAC, high nonlinearity and high algebraic degree. We improve upon the results of Stanica [8] and Zhang and Zheng [11]. 相似文献
20.
Periodica Mathematica Hungarica - In our paper we study the usage of partially defined Boolean functions (PDBFs) for generating cryptographically strong Boolean functions. A PDBF can be considered... 相似文献