Vienas iš svarbiausių šiuolaikinės kriptografijos uždavinių yra saugių vienkrypčių funkcijų paieška. Dabartiniai mokslininkai skiria šiam klausimui ypatingą demėsį. Šiame darbe yra nagrinėjama viena iš naujausių vienkrypčių funkcijų – matricinio laipsnio funkcija. Ši funkcija yra panaudota netiesinės algebrinės lygčių sistemos sudarymui. Pagrindinis demėsys darbe yra skirtas šios lygčių sistemos analizei bei jos praktiniam taikymui. Nustatysime ar matricinio laipsnio funkcija gali būti panaudota kriptografijoje. Taip pat nustatysime lygčių sistemos sprendinių skaičiaus priklausomybę nuo jos parametrų: matricų eilės m bei grupės Z_p parametro p. / Since the introduction of Diffie-Hellman key agreement protocol in 1976 computer technology has made a giant step forward. Nowadays there is not much time left before quantum computers will be in every home. However it was theoretically proven that discrete logarithm problem which is the basis for Diffie-Hellman protocol could be solved in polynomial time using such computers. Such possibility would make D-H protocol insecure. Thus cryptologists are searching for different ways to improve the security of the protocol by using hard problems. One of the ways to do so is to introduce secure one-way functions (OWF). In this paper a new kind of OWF called the matrix power function will be analyzed. Professor Eligijus Sakalauskas introduced this function in 2007 and later used this function to construct a Diffie-Hellman type key agreement protocol using square matrices. This protocol is not only based on matrix power function but also on commutative matrices which are defined in finite fields or rings. Thus an algebraic non-linear system of equations is formed. The security of this system will be analyzed. It will be shown that we can use matrix power function in cryptography. We will also be analyzing how does the solution of the system depend on system parameters: the order of matrices and a parameter p which defines a finite group Z_p. We will also briefly discuss the usage of this system in real life and the algebraic properties of the suggested OWF.

We describe heterogeneous multi-CPU and multi-GPU implementations of Jacobi's iterative method for the 2-D Poisson equation on a structured grid, in both single- and double-precision. Properly tuned, our best implementation achieves 98% of the empirical streaming GPU bandwidth (66% of peak) on a NVIDIA C1060. Motivated to find a still faster implementation, we further consider "wildly asynchronous" implementations that can reduce or even eliminate the synchronization bottleneck between iterations. In these versions, which are based on the principle of a chaotic relaxation (Chazan and Miranker, 1969), we simply remove or delay synchronization between iterations, thereby potentially trading off more flops (via more iterations to converge) for a higher degree of asynchronous parallelism. Our relaxed-synchronization implementations on a GPU can be 1.2-2.5x faster than our best synchronized GPU implementation while achieving the same accuracy. Looking forward, this result suggests research on similarly "fast-and-loose" algorithms in the coming era of increasingly massive concurrency and relatively high synchronization or communication costs.

<p>Hyperspectral reflectance data are utilised in many applications, where measured data are processed and converted into physical, chemical and/or biological properties of the target objects and/or processes being studied. It has been proven that crop reflectance data can be used to detect, characterise and quantify disease severity and plant density.</p><p>In this thesis, various methods were proposed and used for detection, characterisation and quantification of disease severity and plant density utilising data acquired by hand-held spectrometers. Following this direction, hyperspectral images provide both spatial and spectral information opening for more efficient analysis.</p><p>Hence, in this thesis, various surface water quality parameters of inland waters have been monitored using hyperspectral images acquired by airborne systems. After processing the images to obtain ground reflectance data, the analysis was performed using similar methods to those of the previous case. Hence, these methods may also find application in future satellite based hyperspectral imaging systems.</p><p>However, the large size of these images raises the need for efficient data reduction. Self organising and learning neural networks, that can follow and preserve the topology of the data, have been shown to be efficient for data reduction. More advanced variants of these neural networks, referred to as the weighted neural networks (WNN), were proposed in this thesis, such as the weighted incremental neural network (WINN), which can be used for efficient reduction, mapping and clustering of large high-dimensional data sets, such as hyperspectral images.</p><p>Finally, the analysis can be reversed to generate spectra from simpler measurements using multiple colour-filter mosaics, as suggested in the thesis. The acquired instantaneous single image, including the mosaic effects, is demosaicked to generate a multi-band image that can finally be transformed into a hyperspectral image.</p>

Hyperspectral reflectance data are utilised in many applications, where measured data are processed and converted into physical, chemical and/or biological properties of the target objects and/or processes being studied. It has been proven that crop reflectance data can be used to detect, characterise and quantify disease severity and plant density. In this thesis, various methods were proposed and used for detection, characterisation and quantification of disease severity and plant density utilising data acquired by hand-held spectrometers. Following this direction, hyperspectral images provide both spatial and spectral information opening for more efficient analysis. Hence, in this thesis, various surface water quality parameters of inland waters have been monitored using hyperspectral images acquired by airborne systems. After processing the images to obtain ground reflectance data, the analysis was performed using similar methods to those of the previous case. Hence, these methods may also find application in future satellite based hyperspectral imaging systems. However, the large size of these images raises the need for efficient data reduction. Self organising and learning neural networks, that can follow and preserve the topology of the data, have been shown to be efficient for data reduction. More advanced variants of these neural networks, referred to as the weighted neural networks (WNN), were proposed in this thesis, such as the weighted incremental neural network (WINN), which can be used for efficient reduction, mapping and clustering of large high-dimensional data sets, such as hyperspectral images. Finally, the analysis can be reversed to generate spectra from simpler measurements using multiple colour-filter mosaics, as suggested in the thesis. The acquired instantaneous single image, including the mosaic effects, is demosaicked to generate a multi-band image that can finally be transformed into a hyperspectral image.

科学研究費補助金 研究種目:総合研究(A) 課題番号:04302008 研究代表者:三井 斌友 研究期間:1992-1994年度