Optimization of Multidigit Multiplication Based on Discrete (Fourier, Cosine, Sine) Transforms in the Parallel Computing Model
Abstract The authors consider the multidigit multiplication operation, on whose speed the speed of asymmetric cryptographic software and hardware depends. Algorithms for implementing the multiplication of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are proposed. Du...
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| Autor*in: |
Zadiraka, V. K. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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© Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Enthalten in: Cybernetics and systems analysis - Springer US, 1992, 58(2022), 4 vom: Juli, Seite 619-639 |
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volume:58 ; year:2022 ; number:4 ; month:07 ; pages:619-639 |
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10.1007/s10559-022-00495-6 |
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| 520 | |a Abstract The authors consider the multidigit multiplication operation, on whose speed the speed of asymmetric cryptographic software and hardware depends. Algorithms for implementing the multiplication of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are proposed. Due to the use of DCT and DST, the calculations for the real and imaginary parts of the discrete Fourier transform (DFT) of a real even-length signal are separated, which allows translating the complex-number calculations to real-number calculations. The operations of the algorithm are replaced in order to preserve symmetry in the real or imaginary parts of the multidigit numbers, which allows the use of DCT and DST of lower length N / 2 + 1 and increases the possibility of parallelizing in multidigit multiplication. | ||
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10.1007/s10559-022-00495-6 doi (DE-627)OLC2079835807 (DE-He213)s10559-022-00495-6-p DE-627 ger DE-627 rakwb eng 000 VZ Zadiraka, V. K. verfasserin aut Optimization of Multidigit Multiplication Based on Discrete (Fourier, Cosine, Sine) Transforms in the Parallel Computing Model 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract The authors consider the multidigit multiplication operation, on whose speed the speed of asymmetric cryptographic software and hardware depends. Algorithms for implementing the multiplication of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are proposed. Due to the use of DCT and DST, the calculations for the real and imaginary parts of the discrete Fourier transform (DFT) of a real even-length signal are separated, which allows translating the complex-number calculations to real-number calculations. The operations of the algorithm are replaced in order to preserve symmetry in the real or imaginary parts of the multidigit numbers, which allows the use of DCT and DST of lower length N / 2 + 1 and increases the possibility of parallelizing in multidigit multiplication. multidigit multiplication multidigit arithmetic asymmetric cryptography discrete cosine transform discrete sine transform discrete Fourier transform fast Fourier algorithm Tereshchenko, A. M. aut Enthalten in Cybernetics and systems analysis Springer US, 1992 58(2022), 4 vom: Juli, Seite 619-639 (DE-627)131081225 (DE-600)1112963-3 (DE-576)029167868 1060-0396 nnns volume:58 year:2022 number:4 month:07 pages:619-639 https://doi.org/10.1007/s10559-022-00495-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 58 2022 4 07 619-639 |
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10.1007/s10559-022-00495-6 doi (DE-627)OLC2079835807 (DE-He213)s10559-022-00495-6-p DE-627 ger DE-627 rakwb eng 000 VZ Zadiraka, V. K. verfasserin aut Optimization of Multidigit Multiplication Based on Discrete (Fourier, Cosine, Sine) Transforms in the Parallel Computing Model 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract The authors consider the multidigit multiplication operation, on whose speed the speed of asymmetric cryptographic software and hardware depends. Algorithms for implementing the multiplication of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are proposed. Due to the use of DCT and DST, the calculations for the real and imaginary parts of the discrete Fourier transform (DFT) of a real even-length signal are separated, which allows translating the complex-number calculations to real-number calculations. The operations of the algorithm are replaced in order to preserve symmetry in the real or imaginary parts of the multidigit numbers, which allows the use of DCT and DST of lower length N / 2 + 1 and increases the possibility of parallelizing in multidigit multiplication. multidigit multiplication multidigit arithmetic asymmetric cryptography discrete cosine transform discrete sine transform discrete Fourier transform fast Fourier algorithm Tereshchenko, A. M. aut Enthalten in Cybernetics and systems analysis Springer US, 1992 58(2022), 4 vom: Juli, Seite 619-639 (DE-627)131081225 (DE-600)1112963-3 (DE-576)029167868 1060-0396 nnns volume:58 year:2022 number:4 month:07 pages:619-639 https://doi.org/10.1007/s10559-022-00495-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 58 2022 4 07 619-639 |
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10.1007/s10559-022-00495-6 doi (DE-627)OLC2079835807 (DE-He213)s10559-022-00495-6-p DE-627 ger DE-627 rakwb eng 000 VZ Zadiraka, V. K. verfasserin aut Optimization of Multidigit Multiplication Based on Discrete (Fourier, Cosine, Sine) Transforms in the Parallel Computing Model 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract The authors consider the multidigit multiplication operation, on whose speed the speed of asymmetric cryptographic software and hardware depends. Algorithms for implementing the multiplication of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are proposed. Due to the use of DCT and DST, the calculations for the real and imaginary parts of the discrete Fourier transform (DFT) of a real even-length signal are separated, which allows translating the complex-number calculations to real-number calculations. The operations of the algorithm are replaced in order to preserve symmetry in the real or imaginary parts of the multidigit numbers, which allows the use of DCT and DST of lower length N / 2 + 1 and increases the possibility of parallelizing in multidigit multiplication. multidigit multiplication multidigit arithmetic asymmetric cryptography discrete cosine transform discrete sine transform discrete Fourier transform fast Fourier algorithm Tereshchenko, A. M. aut Enthalten in Cybernetics and systems analysis Springer US, 1992 58(2022), 4 vom: Juli, Seite 619-639 (DE-627)131081225 (DE-600)1112963-3 (DE-576)029167868 1060-0396 nnns volume:58 year:2022 number:4 month:07 pages:619-639 https://doi.org/10.1007/s10559-022-00495-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 58 2022 4 07 619-639 |
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10.1007/s10559-022-00495-6 doi (DE-627)OLC2079835807 (DE-He213)s10559-022-00495-6-p DE-627 ger DE-627 rakwb eng 000 VZ Zadiraka, V. K. verfasserin aut Optimization of Multidigit Multiplication Based on Discrete (Fourier, Cosine, Sine) Transforms in the Parallel Computing Model 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract The authors consider the multidigit multiplication operation, on whose speed the speed of asymmetric cryptographic software and hardware depends. Algorithms for implementing the multiplication of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are proposed. Due to the use of DCT and DST, the calculations for the real and imaginary parts of the discrete Fourier transform (DFT) of a real even-length signal are separated, which allows translating the complex-number calculations to real-number calculations. The operations of the algorithm are replaced in order to preserve symmetry in the real or imaginary parts of the multidigit numbers, which allows the use of DCT and DST of lower length N / 2 + 1 and increases the possibility of parallelizing in multidigit multiplication. multidigit multiplication multidigit arithmetic asymmetric cryptography discrete cosine transform discrete sine transform discrete Fourier transform fast Fourier algorithm Tereshchenko, A. M. aut Enthalten in Cybernetics and systems analysis Springer US, 1992 58(2022), 4 vom: Juli, Seite 619-639 (DE-627)131081225 (DE-600)1112963-3 (DE-576)029167868 1060-0396 nnns volume:58 year:2022 number:4 month:07 pages:619-639 https://doi.org/10.1007/s10559-022-00495-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 58 2022 4 07 619-639 |
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10.1007/s10559-022-00495-6 doi (DE-627)OLC2079835807 (DE-He213)s10559-022-00495-6-p DE-627 ger DE-627 rakwb eng 000 VZ Zadiraka, V. K. verfasserin aut Optimization of Multidigit Multiplication Based on Discrete (Fourier, Cosine, Sine) Transforms in the Parallel Computing Model 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract The authors consider the multidigit multiplication operation, on whose speed the speed of asymmetric cryptographic software and hardware depends. Algorithms for implementing the multiplication of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are proposed. Due to the use of DCT and DST, the calculations for the real and imaginary parts of the discrete Fourier transform (DFT) of a real even-length signal are separated, which allows translating the complex-number calculations to real-number calculations. The operations of the algorithm are replaced in order to preserve symmetry in the real or imaginary parts of the multidigit numbers, which allows the use of DCT and DST of lower length N / 2 + 1 and increases the possibility of parallelizing in multidigit multiplication. multidigit multiplication multidigit arithmetic asymmetric cryptography discrete cosine transform discrete sine transform discrete Fourier transform fast Fourier algorithm Tereshchenko, A. M. aut Enthalten in Cybernetics and systems analysis Springer US, 1992 58(2022), 4 vom: Juli, Seite 619-639 (DE-627)131081225 (DE-600)1112963-3 (DE-576)029167868 1060-0396 nnns volume:58 year:2022 number:4 month:07 pages:619-639 https://doi.org/10.1007/s10559-022-00495-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 58 2022 4 07 619-639 |
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Optimization of Multidigit Multiplication Based on Discrete (Fourier, Cosine, Sine) Transforms in the Parallel Computing Model |
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Abstract The authors consider the multidigit multiplication operation, on whose speed the speed of asymmetric cryptographic software and hardware depends. Algorithms for implementing the multiplication of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are proposed. Due to the use of DCT and DST, the calculations for the real and imaginary parts of the discrete Fourier transform (DFT) of a real even-length signal are separated, which allows translating the complex-number calculations to real-number calculations. The operations of the algorithm are replaced in order to preserve symmetry in the real or imaginary parts of the multidigit numbers, which allows the use of DCT and DST of lower length N / 2 + 1 and increases the possibility of parallelizing in multidigit multiplication. © Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract The authors consider the multidigit multiplication operation, on whose speed the speed of asymmetric cryptographic software and hardware depends. Algorithms for implementing the multiplication of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are proposed. Due to the use of DCT and DST, the calculations for the real and imaginary parts of the discrete Fourier transform (DFT) of a real even-length signal are separated, which allows translating the complex-number calculations to real-number calculations. The operations of the algorithm are replaced in order to preserve symmetry in the real or imaginary parts of the multidigit numbers, which allows the use of DCT and DST of lower length N / 2 + 1 and increases the possibility of parallelizing in multidigit multiplication. © Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract The authors consider the multidigit multiplication operation, on whose speed the speed of asymmetric cryptographic software and hardware depends. Algorithms for implementing the multiplication of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are proposed. Due to the use of DCT and DST, the calculations for the real and imaginary parts of the discrete Fourier transform (DFT) of a real even-length signal are separated, which allows translating the complex-number calculations to real-number calculations. The operations of the algorithm are replaced in order to preserve symmetry in the real or imaginary parts of the multidigit numbers, which allows the use of DCT and DST of lower length N / 2 + 1 and increases the possibility of parallelizing in multidigit multiplication. © Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| title_short |
Optimization of Multidigit Multiplication Based on Discrete (Fourier, Cosine, Sine) Transforms in the Parallel Computing Model |
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https://doi.org/10.1007/s10559-022-00495-6 |
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Tereshchenko, A. M. |
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