THE RUNTIME ANALYSIS OF COMPUTATION OF MODULAR EXPONENTIATION

Context. Providing the problem of fast calculation of the modular exponentiation requires the development of effective algorithmic methods using the latest information technologies. Fast computations of the modular exponentiation are extremely necessary for efficient computations in theoretical-numerical transforms, for provide high crypto capability of information data and in many other applications. Objective – the runtime analysis of software functions for computation of modular exponentiation of the developed programs based on parallel organization of computation with using multithreading. Method. Modular exponentiation is implemented using a 2k-ary sliding window algorithm, where k is chosen according to the size of the exponent. Parallelization of computation consists in using the calculation of the remainders of numbers raised to the power of 2i modulo, and their further parallel multiplications modulo. Results. Comparison of the runtimes of three variants of functions for computing the modular exponentiation is performed. In the algorithm of parallel organization of computation with using multithreading provide faster computation of modular exponentiation for exponent values larger than 1K binary digits compared to the function of modular exponentiation of the MPIR library. The MPIR library with an integer data type with the number of binary digits from 256 to 2048 bits is used to develop an algorithm for computing the modular exponentiation with using multithreading. Conclusions. In the work has been considered and analysed the developed software implementation of the computation of modular exponentiation on universal computer systems. One of the ways to implement the speedup of computing modular exponentiation is developing algorithms that can use multithreading technology on multi-cores microprocessors. The multithreading software implementation of modular exponentiation with increasing from 1024 the number of binary digit of exponent shows an improvement of computation time with comparison with the function of modular exponentiation of the MPIR library.

Software komputer

Komputer merupakan mesin yang memproses data menjadi suatu informasi. Komputer digunakan users untuk meningkatkan hasil kerja dan memecahkan berbagai masalah. Yang menjadi pemroses data atau pemecah masalah itu adalah software atau perangkat lunak. Bentuk terkecil dari perangkat lunak adalah operasi aritmatik (+, -, :, x) dan logika (AND, OR, >, <, =). Dari operasi dasar ini disusun program atau perangkat lunak. Tingkat pemrosesan yang di kerjakan perangkat lunak pun dari machine-like, mulai berubah seperti human-like. Di dalam teori informasi, di susun hirarki informasi, mulai dari data/ fakta, kemudian setelah proses seleksi dan pengurutan menjadi sesuatu yang berguna menjadi informasi. Informasi yang di susun secara sistematis dengan suatu alur logika tertentu menjadi knowledge. Dan pada akhirnya gabungan knowledge yang di gabung dari berbagai sisi guna membangun wisdom. Data yang di proses pun telah banyak berubah, yang semula hanya berupa data bilangan dan karakter merambah ke audio visual (bunyi, suara, gambar, film). Sejauh perkembangan hingga saat ini, seluruh proses menggunakan format data digital dengan satuan bit (binary digit).

Pengenalan software komputer

Komputer merupakan mesin yang memproses data menjadi suatu informasi. Komputer digunakan users untuk meningkatkan hasil kerja dan memecahkan berbagai masalah. Yang menjadi pemroses data atau pemecah masalah itu adalah software atau perangkat lunak. Bentuk terkecil dari perangkat lunak adalah operasi aritmatik (+, -, :, x) dan logika (AND, OR, >, <, =). Dari operasi dasar ini disusun program atau perangkat lunak. Tingkat pemrosesan yang di kerjakan perangkat lunak pun dari machine-like, mulai berubah seperti human-like. Di dalam teori informasi, di susun hirarki informasi, mulai dari data/ fakta, kemudian setelah proses seleksi dan pengurutan menjadi sesuatu yang berguna menjadi informasi. Informasi yang di susun secara sistematis dengan suatu alur logika tertentu menjadi knowledge. Dan pada akhirnya gabungan knowledge yang di gabung dari berbagai sisi guna membangun wisdom. Data yang di proses pun telah banyak berubah, yang semula hanya berupa data bilangan dan karakter merambah ke audio visual (bunyi, suara, gambar, film). Sejauh perkembangan hingga saat ini, seluruh proses menggunakan format data digital dengan satuan bit (binary digit).

VLSI Implementation of Digital Filter using Novel RTSD Adder and Booth Multiplier

Finite Impulse Response (FIR) filters are most important element in signal processing and communication. Area and speed optimization are the essential necessities of FIR filter design. This work looks at the design of Finite Impulse Response (FIR) filters from an arithmetic perspective. Since the fundamental arithmetic operations in the convolution equations are addition and multiplication, they are the objectives of the design analysis. For multiplication, Booth encoding is utilized in order to lessen the quantity of partial products. Consequently, considering carry-propagation free addition strategies should improve the addition operation of the filter. The redundant ternary signed-digit (RTSD) number framework is utilized to speedup addition in the filter. The redundant ternary representation utilizes more bits than required to denote the single binary digit because of which most numbers have several representations. This special behavior of RTSD allows the addition along with the absence of typical carry propagation. Xilinx ISE design suite 14.5 is used for the design and validation of proposed method. From the implementation result, the proposed design of FIR filter is compared with other conventional techniques to show the better performance by means of power, area and delay.

Data: The Given

What is data, and how does it matter for international law? This chapter examines the material nature of the binary digit—the bit—to show three characteristics that mark it out as an object of governance. First, data as ‘thing’ must be distinguished from data as ‘medium’. Second, bits make everything countable. Third, with digitalization, there is no avoiding manipulation—there is no ‘authentic’ original: the technology has no unmediated state. Bits turn out to be an extraordinarily versatile referential technology, whose very ease of creation, storage, and reproducibility encourages proliferation while blurring the distinction between things (‘objects’) and facts (‘knowledge’). The chapter then turns to a principal material means by which data today cross borders: transoceanic cables. Overall, the chapter addresses the novel concerns contemporary material forms of data production and storage raise for international legal subjectivity and jurisdiction.