Towards constant-time probabilistic root finding for code-based cryptography

In code-based cryptography, deterministic algorithms are used in the root-finding step of the decryption process. However, probabilistic algorithms are more time efficient than deterministic ones for large fields. These algorithms can be useful for long-term security where larger parameters are relevant. Still, current probabilistic root-finding algorithms suffer from time variations making them susceptible to timing side-channel attacks. To prevent these attacks, we propose a countermeasure to a probabilistic root-finding algorithm so that its execution time does not depend on the degree of the input polynomial but on the cryptosystem parameters. We compare the performance of our proposed algorithm to other root-finding algorithms already used in code-based cryptography. In general, our method is faster than the straightforward algorithm in Classic McEliece. The results also show the range of degrees in larger finite fields where our proposed algorithm is faster than the Additive Fast Fourier Transform algorithm.

Fast Analysis of Broadband Electromagnetic Scattering Characteristics of Electrically Large Targets using Precorrected Fast Fourier Transform Algorithm based on Near Field Matrix Interpolation Method

In this paper, a new method is proposed to analyze the broadband electromagnetic characteristics of electrically large targets by combining the precorrected-FFT algorithm (P-FFT) with the near-field matrix interpolation technique. The proposed method uses the precorrected-FFT algorithm to reduce the storage and accelerate the matrix vector product of the far field. In order to make the precorrected-FFT algorithm can calculate the broadband characteristics of electrically large targets more quickly, the matrix interpolation method is used to interpolate the near-field matrix of the precorrected-FFT algorithm to improve the efficiency of calculation. The numerical results obtained validate the proposed method and its implementation in terms of accuracy and runtime performance.

Mobile image processing system based on the Raspberry Pi 4 platform

The article presents an image processing system based on the Raspberry Pi (RPi) platform. At the beginning of the article, the basic assumptions and purpose of the system are discussed. The following section presents the structure and operation of the system. The window application managing the system and allowing to perform contextual and spectral transformations on images as well as the measurement of parameters such as image processing time and mean square error (MSE) was discussed. The transformations performed were based both on ready formulas contained in the OpenCV library and the author's implementations, including the function implementing the Fast Fourier Transform algorithm radix-2. Examples of transformations were presented along with their usefulness. In the end, the development potential of the created system is presented and its application in specific solutions is proposed.

DEVELOPMENT OF A MEASUREMENT SYSTEM AND SOFTWARE PRODUCT TO COLLECT AND ANALYSE ELECTRICITY QUALITY PARAMETERS

In the real operating conditions of electrical networks, there are modes of operation characterised by deviations of their parameters from their nominal values. Of particular importance for the operation of electrical equipment are variations in the amplitude and frequency of the supply voltage. The permissible and limit deviations of these parameters are regulated in accordance with national standards. To calculate the main power quality parameters it is not sufficient to know only the methods of their calculation. Additional algorithms are needed to determine fundamental harmonic voltages and frequencies. Such a method is the discrete Fourier transform. This algorithm is designed for signal analysis. However, this algorithm was not widely used in calculating Fourier coefficients in modern software packages. The reason is that it takes much time and computer resources to determine the Fourier coefficients which reduces the attractiveness of this approach. For this reason, it is advisable to use the fast Fourier transform algorithm. This algorithm uses the periodicity properties of the trigonometric function, which allows reducing the number of multiplication operations. The results of using the fast Fourier transform algorithm are similar to the discrete Fourier algorithm, but the number of operations required for calculation is several times less. At the same time, fast and discrete Fourier transform algorithms can give quite a significant error in determining the frequency estimate. This deviation is related to multiplicity of time between signal measurements and its period. If the period of the analogue signal is a multiple of the sampled signal measurement distance, an additional Quin method must be used to reduce the error in determining the frequency of the main signal. In this regard, the development of algorithms and software complex for automated measurement systems of electrical power quality indicators using digital data acquisition and processing devices in real time is an urgent task.

Application of two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for 4k fixed format digital image of satellite data in frequency domain processing

Currently, digital images in the format Full HD (1920 * 1080 pixels) and 4K (4096 * 3072) are widespread. This article will consider the option of processing a similar image in the frequency domain. As an example, take a snapshot of the earth's surface. The discrete Fourier transform will be computed using a two-dimensional analogue of the Cooley-Tukey algorithm and in a standard way by rows and columns. Let us compare the required number of operations and the results of a numerical experiment. Consider the examples of image filtering.