As the basic cryptographic structure for multivariate quadratic quasigroup (MQQ) scheme, MQQ has been one of the latest tools in designing MQ cryptosystem. There have been several construction methods for MQQs in the ...
详细信息
As the basic cryptographic structure for multivariate quadratic quasigroup (MQQ) scheme, MQQ has been one of the latest tools in designing MQ cryptosystem. There have been several construction methods for MQQs in the literature, however, the algorithm for judging whether quasigroups of any order are MQQs over Galois fields is still lacking. To this end, the objective of this paper is to establish a necessary and sufficient condition for a given quasigroup of order p(kd) to be an MQQ over GF(p(k)). Based on this condition, we then propose an algorithm to justify whether or not a given quasigroup in the form of multiplication table of any order pkd is an MQQ over GF(p(k)), and generate the d Boolean functions of the MQQ if the quasigroup is an MQQ. As a result, we can obtain all the MQQs over GF(p(k)) in theory using the proposed algorithm. Two examples are provided to illustrate the validity of our method.
As the basic cryptographic structure for MQQ scheme, multivariate quadratic quasigroup (MQQ) has been one of the latest tools in designing cryptographic system. However, it is limited to the operation over GF(2) and l...
详细信息
As the basic cryptographic structure for MQQ scheme, multivariate quadratic quasigroup (MQQ) has been one of the latest tools in designing cryptographic system. However, it is limited to the operation over GF(2) and lacks the general understanding. In this paper, we propose a necessary and sufficient condition to verify whether a given quasigroup of any order pi'd is a bilinear MQQ over GF(pk), which shows checking whether an arbitrary quasigroup is bilinear MQQ is equivalent to solving a simple matrix equation. Based on this newly established condition, a deterministic algorithm is proposed to judge whether or not a given quasigroup is bilinear MQQ, and to generate bilinear MQQ if it is. Two examples are given to show the validity of our results.
We present a recursive generating algorithm for unrestricted permutations which is based on both the decomposition of a permutation as a product of transpositions and that as a union of disjoint cycles. It generates p...
详细信息
We present a recursive generating algorithm for unrestricted permutations which is based on both the decomposition of a permutation as a product of transpositions and that as a union of disjoint cycles. It generates permutations at each recursive step and slight modifications of it produce generating algorithms for Bell permutations and involutions. Further refinements yield algorithms for these classes of permutations subject to additional restrictions: a given number of cycles or/and fixed points. We obtain, as particular cases, generating algorithms for permutations counted by the Stirling numbers of the first and second kind, even permutations, fixed-point-free involutions and derangements. All of these algorithms run in constant amortized time. (C) 2009 Published by Elsevier Ltd
Real-world networks are often compared to random graphs to assess whether their topological structure could be a result of random processes. However, a simple random graph in large scale often lacks social structure b...
详细信息
Real-world networks are often compared to random graphs to assess whether their topological structure could be a result of random processes. However, a simple random graph in large scale often lacks social structure beyond the dyadic level. As a result we need to generate clustered random graph to compare the local structure at higher network levels. In this paper a generalized version of Gleeson's algorithm G(V-s, V-T, E-s, E-T, S, T) is advanced to generate a clustered random graph in large-scale which persists the number of vertices | V|, the number of edges |E| and the global clustering coefficient C-A as in the real network and it works successfully for nine large-scale networks. Our new algorithm also has advantages in randomness evaluation and computation efficiency when compared with the existing algorithms.
In this article, we define the binary codes of tournament matrices in the class T(R) and give unique construction algorithms for matrices which have minimum and maximum binary codes. By introducing a generating algori...
详细信息
In this article, we define the binary codes of tournament matrices in the class T(R) and give unique construction algorithms for matrices which have minimum and maximum binary codes. By introducing a generating algorithm with an order we show that all matrices in class T(R) can be sorted uniquely between matrices with minimum and maximum binary codes. (C) 2014 Elsevier B.V. All rights reserved.
In a recent article [W.M.B. Dukes, M.F. Flanagan, I Mansour, V. Vajnovszki, Combinatorial Gray codes for classes of pattern avoiding permutations, Theoret. Comput. Sci. 396 (2008) 35-49], Dukes, Flanagan, Mansour and ...
详细信息
In a recent article [W.M.B. Dukes, M.F. Flanagan, I Mansour, V. Vajnovszki, Combinatorial Gray codes for classes of pattern avoiding permutations, Theoret. Comput. Sci. 396 (2008) 35-49], Dukes, Flanagan, Mansour and Vajnovszki present Gray codes for several families of pattern avoiding permutations. In their Gray codes two consecutive objects differ in at most four or five positions, which is not optimal. In this paper, we present a unified construction in order to refine their results (or to find other Gray codes). In particular, we obtain more restrictive Gray codes for the two Wilf classes of Catalan permutations of length n: two consecutive objects differ in at most two or three positions which is optimal for n odd. Other refinements have been found for permutation sets enumerated by the numbers of Schroder, Pell, even index Fibonacci numbers and the central binomial coefficients. A general efficient generating algorithm is also given. (C) 2009 Elsevier B.V. All rights reserved.
In this paper we study the problem of the whole mirror duplication-random loss model in terms of pattern avoiding permutations. We prove that the class of permutations obtained with this model after a given number p o...
详细信息
In this paper we study the problem of the whole mirror duplication-random loss model in terms of pattern avoiding permutations. We prove that the class of permutations obtained with this model after a given number p of duplications of the identity is the class of permutations avoiding the alternating permutations of length 2(p) + 1. We also compute the number of duplications necessary and sufficient to obtain any permutation of length n. We provide two efficient algorithms to reconstitute a possible scenario of whole mirror duplications from identity to any permutation of length n. One of them uses the well-known binary reflected Gray code (Gray, 1953) [10]. Other relative models are also considered. (C) 2010 Elsevier B.V. All rights reserved.
A Gray code for a combinatorial class is a method for listing the objects in the class so that successive objects differ in some prespecified, small way, typically expressed as a bounded Hamming distance. In a previou...
详细信息
A Gray code for a combinatorial class is a method for listing the objects in the class so that successive objects differ in some prespecified, small way, typically expressed as a bounded Hamming distance. In a previous work, the authors of the present paper showed, among other things, that the m-ary Reflected Gray Code Order yields a Gray code for the set of restricted growth functions. Here we further investigate variations of this order relation, and give the first Gray codes and efficient generating algorithms for bounded restricted growth functions.
AbstractA practical methodology is presented for the exact combinatory evaluation of 2‐way cross‐classifications. The combinatory distribution is based on a test‐statistic relating to the information content of an ...
详细信息
AbstractA practical methodology is presented for the exact combinatory evaluation of 2‐way cross‐classifications. The combinatory distribution is based on a test‐statistic relating to the information content of an observed table. Several examples of exact evaluation accompany this present
In 1970 Freeman suggested the following criteria which the chain code of a line must meet [1], [2]: 1) at most two basic directions are present and these can differ only by unity, modulo eight, 2) one of these values ...
详细信息
In 1970 Freeman suggested the following criteria which the chain code of a line must meet [1], [2]: 1) at most two basic directions are present and these can differ only by unity, modulo eight, 2) one of these values always occurs singly, 3) successive occurrences of the principal direction occurring singly are as uniformly spaced as possible. In this correspondence we give the following: 1) an algorithm presentation of Freeman"s three properties about the chain code of a line and the proof that it is also the algorithm recognizing whether a chain code is the chain code of a line, 2) the proof of the equivalence of the above presentation and Rosenfeld"s chord property [3].
暂无评论