Fundamenta Informaticae - Volume 145, issue 2

Authors: Han, Huiting | Tang, Chunming | Lou, Yu | Xu, Maozhi

Article Type: Research Article

Abstract: Maximum distance separable (MDS) codes introduce MDS matrices which not only have applications in coding theory but also are of great importance in the design of block ciphers. It has received a great amount of attention. In this paper, we first introduce a special generalization of circulant matrices called block circulants with circulant blocks, which can be used to construct MDS matrices. Then we investigate some interesting and useful properties of this class of matrices and prove that their inverse matrices can be implemented efficiently. Furthermore, we present some 4 × 4 and 8 × 8 efficient MDS matrices of …this class which are suitable for MDS diffusion layer. Compared with previous results, our construction provides better efficiency for the implementation of both the matrix and the its inverse matrix. Show more

Keywords: MDS matrix, diffusion layers, InvMixcolumn, Mixcolumn, circulant matrix

DOI: 10.3233/FI-2016-1349

Citation: Fundamenta Informaticae, vol. 145, no. 2, pp. 111-124, 2016

Authors: Nagy, Benedek | Lukić, Tibor

Article Type: Research Article

Abstract: In this paper, we consider the binary tomography reconstruction problem. A new approach is proposed what exploits a possibility provided by the natural structure of the triangular grid, which is not available in the case of the classical square grid. In contrast to the square grid, in the case of the triangular grid information need for the reconstruction of the unknown image is increasing when not only one, but two projections are used by lanes. In this way, the number of Δ and ∇ shaped pixels per lane can be determined. We propose this type of projection approach and call …it dense projections. The reconstruction is based on three projection directions by the lane directions of the grid (they are analogous to row and column directions on the square grid). Our algorithm is deterministic and uses energy minimization technique to find (near) optimal solution in a reasonable time. The experimental evaluation of the new method, using regular hexagon shaped test images, is given. Comparison with reconstructions based on the square grid is also considered. Show more

Keywords: tomography, triangular grid, dense projection approach, energy minimization, approximate solution

DOI: 10.3233/FI-2016-1350

Citation: Fundamenta Informaticae, vol. 145, no. 2, pp. 125-141, 2016

Authors: Pomykała, Jacek

Article Type: Research Article

Abstract: In the paper we investigate the set of odd, squarefree positive integers n that can be factored completely in polynomial time O (log6+ɛ n ), given the prime decomposition of orders ordn b for b ≤ logη n , (η > 2), which is closely related to DLPC problem. We prove that the number of n ≤ x that may not be factored in deterministic time O (log6+ɛ n ), is at most (η − 2)−1 x (log x )−c (η −2) , for some c …> 0 and arbitrary ɛ > 0. Show more

Keywords: factoring algorithms, Z*n-generating sets, Dirichlet characters, smooth numbers, discrete logarithm problem for composite numbers, large sieve estimates

DOI: 10.3233/FI-2016-1351

Citation: Fundamenta Informaticae, vol. 145, no. 2, pp. 143-150, 2016

Authors: Song, Yinglei | Qu, Junfeng | Xu, Ying | Cai, Liming

Article Type: Research Article

Abstract: In this paper, we develop a novel graph theoretic approach for protein threading. In order to perform the protein sequence-structure alignment in threading both efficiently and accurately, we develop a graph model to describe the tertiary structure of a protein family and the alignment between a sequence and a family can be efficiently computed with a dynamic programming algorithm when the tree width of the graph model is a small integer. Our experiments show that this new approach is significantly faster than existing tools for threading and can achieve comparable prediction accuracy.

Keywords: protein threading, graph theoretic approach, dynamic programming

DOI: 10.3233/FI-2016-1352

Citation: Fundamenta Informaticae, vol. 145, no. 2, pp. 151-170, 2016

Authors: Tian, Miaomiao | Huang, Liusheng

Article Type: Research Article

Abstract: Identity-based signature is an important technique for light-weight authentication. Recently, many efforts have been made to construct identity-based signatures over lattice assumptions since they would remain secure in future quantum age. In this paper we present a new identity-based signature scheme from lattice problems. This scheme is more efficient than other lattice-based identity-based signature schemes in terms of both computation and communication complexities. We prove its security in the random oracle model under short integer solution assumption that is as hard as approximating several worst-case lattice problems. We also extend the scheme to an identity-based message recovery signature scheme that …has better performance. Show more

Keywords: identity-based signature, lattice, performance, message recovery

DOI: 10.3233/FI-2016-1353

Citation: Fundamenta Informaticae, vol. 145, no. 2, pp. 171-187, 2016

Authors: Yang, Hong-ying | Liang, Lin-lin | Li, Yong-wei | Wang, Xiang-yang

Article Type: Research Article

Abstract: Moments and moment invariants have become a powerful tool in image processing owing to their image description capability and invariance property. But, conventional methods are mainly introduced to deal with the binary or gray-scale images, and the only approaches for color image always have poor color image description capability. Based on Exponent moments (EMs) and quaternion, we introduced the quaternion Exponent moments (QEMs) for describing color images in this paper, which can be seen as the generalization of EMs for gray-level images. It is shown that the QEMs can be obtained from the EMs of each color channel. We derived …and analyzed the rotation, scaling, and translation (RST) invariant property of QEMs. We also discussed the problem of color image retrieval using QEMs. Experimental results are provided to illustrate the efficiency of the proposed color image descriptors. Show more

Keywords: Color image, quaternion, Exponent moments, quaternion Exponent moments, geometric invariance, color image retrieval

DOI: 10.3233/FI-2016-1354

Citation: Fundamenta Informaticae, vol. 145, no. 2, pp. 189-205, 2016

Authors: Zeng, Zhi-Fang | Liu, Jian-Guo | Jiang, Yan | Nie, Bin

Article Type: Research Article

Abstract: Describing the dispersion decreasing fiber, a variable-coefficient nonlinear Schrödinger equation is hereby under investigation. Three transformations have been obtained from such a equation to the known standard and cylindrical nonlinear Schrödinger equations with the relevant constraints on the variable coefficients presented, which turn out to be more general than those previously published in the literature. Meanwhile, several families of exact dark-soliton-like and bright-soliton-like solutions are constructed. Also, we obtain some similarity solutions, which can be illustrated in terms of the elliptic and the second Painlevé transcendent equations.

Keywords: symbolic computation, nonlinear Schrödinger equation, similarity solutions, soliton-like solutions

DOI: 10.3233/FI-2016-1355

Citation: Fundamenta Informaticae, vol. 145, no. 2, pp. 207-219, 2016