Improved Modular Division Implementation with the Akushsky Core Function

The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.

POSIT vs. Floating Point in Implementing IIR Notch Filter by Enhancing Radix-4 Modified Booth Multiplier

The increased demand for better accuracy and precision and wider data size has strained current the floating point system and motivated the development of the POSIT system. The POSIT system supports flexible formats and tapered precision and provides equivalent accuracy with fewer bits. This paper examines the POSIT and floating point systems, comparing the performance of 32-bit POSIT and 32-bit floating point systems using IIR notch filter implementation. Given that the bulk of the calculations in the filter are multiplication operations, an Enhanced Radix-4 Modified Booth Multiplier (ERMBM) is implemented to increase the calculation speed and efficiency. ERMBM enhances area, speed, power, and energy compared to the POSIT regular multiplier by 26.80%, 51.97%, 0.54%, and 52.22%, respectively, without affecting the accuracy. Moreover, the Taylor series technique is adopted to implement the division operation along with cosine arithmetic unit for POSIT numbers. After comparing POSIT with floating point, the accuracy of POSIT is 92.31%, which is better than floating point’s accuracy of 23.08%. Moreover, POSIT reduces area by 21.77% while increasing the delay. However, when the ERMBM is utilized instead of the POSIT regular multiplier in implementing the filter, POSIT outperforms floating point in all the performance metrics including area, speed, power, and energy by 35.68%, 20.66%, 31.49%, and 45.64%, respectively.

Low latency Montgomery multiplier for cryptographic applications

In this modern era, data protection is very important. To achieve this, the data must be secured using either public-key or private-key cryptography (PKC). PKC eliminates the need of sharing key at the beginning of communication. PKC systems such as ECC and RSA is implemented for different security services such as key exchange between sender, receiver and key distribution between different network nodes and authentication protocols. PKC is based on computationally intensive finite field arithmetic operations. In the PKC schemes, modular multiplication (MM) is the most critical operation. Usually, this operation is performed by integer multiplication (IM) followed by a reduction modulo M. However, the reduction step involves a long division operation that is expensive in terms of area, time and resources. Montgomery multiplication algorithm facilitates faster MM operation without the division operation. In this paper, low latency hardware implementation of the Montgomery multiplier is proposed. Many interesting and novel optimization strategies are adopted in the proposed design. The proposed Montgomery multiplier is based on school-book multiplier, Karatsuba-Ofman algorithm and fast adders techniques. The Karatsuba-Ofman algorithm and school-book multiplier recommends cutting down the operands into smaller chunks while adders facilitate fast addition for large size operands. The proposed design is simulated, synthesized and implemented using Xilinx ISE Design Suite by targeting different Xilinx FPGA devices for different bit sizes (64-1024). The proposed design is evaluated on the basis of computational time, area consumption, and throughput. The implementation results show that the proposed design can easily outperform the state of the art

INVESTIGATION OF RISKS OF INFLUENCE OF THE RESULTS OF THE OPERATION DIVISION ON THE QUALITY OF PSEUDO-RANDOM VALUE GENERATORS EMBEDDED IN THE SOFTWARE

The article is devoted to certain approaches that concerned a checking random values obtained from the generator of random (pseudorandom) values. The article provides the results of a practical research of the numbers which are obtained during the division operation. The research was directed to find out the ratio of even and odd numbers in a quotients and remainders in the results of performing of the division operation. The analysis was carried out due to the fact that the remainder and quotient of division is widely used in various algorithms of software tools intended for generating random and pseudorandom values (numbers). The results of the research, which are given in this scientific publication, confirm the existence of prerequisites for the outputting by the generator of pseudorandom values such values (numbers) which will not fully meet the criteria. First of all, it is a criterion which concerns parity and oddity of the numbers which can be outputted by generator of random and pseudorandom values. The authors propose to explore parity and oddity using two methods. The first method is based on Pearson's squared test (chi-squared test). It allows you to find out the presence and admissibility of deviation of the sequence of values obtained empirically, with theoretical (predicted) values. In this case, the level of accuracy is chosen depending on the requirements for the software product as a whole and the generator of random (pseudorandom) values in particular. The second method is based on the long series test (long sequences test), which determines the permissible number of even or odd values that follow each other. In this case, the number of allowed such sequences depends on the number of results obtained during a series of experiments. The proposed approaches are recommended for software products planning and testing which is supposed to be used by the Ministry of Defense of Ukraine.

Quantum Circuit Design of Toom 3-Way Multiplication

In classical computation, Toom–Cook is one of the multiplication methods for large numbers which offers faster execution time compared to other algorithms such as schoolbook and Karatsuba multiplication. For the use in quantum computation, prior work considered the Toom-2.5 variant rather than the classically faster and more prominent Toom-3, primarily to avoid the nontrivial division operations inherent in the latter circuit. In this paper, we investigate the quantum circuit for Toom-3 multiplication, which is expected to give an asymptotically lower depth than the Toom-2.5 circuit. In particular, we designed the corresponding quantum circuit and adopted the sequence proposed by Bodrato to yield a lower number of operations, especially in terms of nontrivial division, which is reduced to only one exact division by 3 circuit per iteration. Moreover, to further minimize the cost of the remaining division, we utilize the unique property of the particular division circuit, replacing it with a constant multiplication by reciprocal circuit and the corresponding swap operations. Our numerical analysis shows that the resulting circuit indeed gives a lower asymptotic complexity in terms of Toffoli depth and qubit count compared to Toom-2.5 but with a large number of Toffoli gates that mainly come from realizing the division operation.

effectiveness of the problem solving method on learning outcomes of the English course for room division operation during the COVID-19 pandemic

This study aims to determine how much effective problem-solving methods are in the third semester of English learning outcomes in the Hospitality Study Program, Tourism Department, Bali State Polytechnic during the Covid-19 pandemic. The background in this study is the lack of student enjoyment in English, inappropriate learning strategies, and the lack of developing student creativity in the learning process. This type of research is quantitative research. Data collection techniques using observation, tests, and documentation. Participants consisted of 60 (29 male and 31 female) third-semester students of the Diploma 3 Program, Hospitality, Bali State Polytechnic, 2020/2021 academic year. The data were collected through a classroom action-based research procedure starting from planning, acting, observing, and reflecting. Through the quasi-experimental design, the collected data were analyzed using paired t-tests and mixed design ANCOVA to identify any significant improvement after the administration of the action. Furthermore, the qualitative data were analyzed based on the results of observations during the giving of the action and the results of the questionnaire.