Computer Arithmetics of Multi-Digits Numbers in Sequential and Parallel Calculation Models

V.K. Zadiraka

A.M. Tereshchenko

A.V. Anisimov

О.М. Khimich

Affiliation:

V.M.Glushkov Institute of Cybernetics of the NAS of Ukraine

Project: Scientific book

Year: 2021

Publisher: PH "Naukova Dumka"

Pages: 134

DOI:

ISBN: 978-966-00-1748-1

Language: Ukrainian

How to Cite:

Zadiraka, V.K., Tereshchenko, A.M. (2021). Computer Arithmetics of Multi-Digits Numbers in Sequential and Parallel Calculation Models. Kyiv, Naukova Dumka. 134 p. [in Ukraine].

Abstract:

The monograph investigates the existing and proposes new algorithms efficient in terms of speed and memory for the implementation of basic asymmetric cryptographic transformations for different computational models. The complexity of the algorithm for implementing the operation of adding multi-digit numbers with the prediction of the hyphen is analyzed. An algorithm for implementing the operation of adding multi-digit numbers in a parallel computational model is presented. New algorithms for the implementation of the multi-digit multiplication operation by the standard method in a column, the Karatsuba–Ofman method, on the basis of cyclic convolution and fast Fourier transform are considered. The complexity of multi-digit multiplication algorithms for sequential and parallel computational models is analyzed. Algorithms for implementing the operation of calculating a multi-bit balance in a sequential computational model are considered. A new algorithm for implementing the modular multiplication operation for a parallel computational model is proposed.
Intended for specialists in the field of computer arithmetic, as well as for researchers, graduate students and university students interested in algorithms for implementing arithmetic operations with multi-digit numbers.

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