Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography Implementation
<p class="Abstract"><span lang="EN-US">Implementing a secure cryptosystem requires operations involving hundreds of bits. One of the most recommended algorithm is Elliptic Curve Cryptography (ECC). The complexity of elliptic curve algorithms and parameters with hundre...
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| Format: | Article |
| Language: | English |
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ITB Journal Publisher
2013-09-01
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| Series: | Journal of ICT Research and Applications |
| Online Access: | http://journals.itb.ac.id/index.php/jictra/article/view/221 |
| _version_ | 1828196252633792512 |
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| author | Marisa W. Paryasto Budi Rahardjo Fajar Yuliawan Intan Muchtadi Alamsyah Kuspriyanto Kuspriyanto |
| author_facet | Marisa W. Paryasto Budi Rahardjo Fajar Yuliawan Intan Muchtadi Alamsyah Kuspriyanto Kuspriyanto |
| author_sort | Marisa W. Paryasto |
| collection | DOAJ |
| description | <p class="Abstract"><span lang="EN-US">Implementing a secure cryptosystem requires operations involving hundreds of bits. One of the most recommended algorithm is Elliptic Curve Cryptography (ECC). The complexity of elliptic curve algorithms and parameters with hundreds of bits requires specific design and implementation strategy. The design architecture must be customized according to security requirement, available resources and parameter choices. In this work we propose the use of composite field to implement finite field multiplication for ECC implementation. We use 299-bit keylength represented in GF((2<sup>13</sup>)<sup>23</sup>) instead of in GF(2<sup>299</sup>). Composite field multiplier can be implemented using different multiplier for ground-field and for extension field. In this paper, LUT is used for multiplication in the ground-field and classic multiplieris used for the extension field multiplication. A generic architecture for the multiplier is presented. Implementation is done with VHDL with the target device Altera DE2. The work in this paper uses the simplest algorithm to confirm the idea that by dividing field into composite, use different multiplier for base and extension field would give better trade-off for time and area. This work will be the beginning of our more advanced further research that implements composite-field using Mastrovito Hybrid, KOA and LUT.</span></p> |
| first_indexed | 2024-04-12T09:58:17Z |
| format | Article |
| id | doaj.art-15455fa8cda74752ba038ed39cd1387a |
| institution | Directory Open Access Journal |
| issn | 2337-5787 2338-5499 |
| language | English |
| last_indexed | 2024-04-12T09:58:17Z |
| publishDate | 2013-09-01 |
| publisher | ITB Journal Publisher |
| record_format | Article |
| series | Journal of ICT Research and Applications |
| spelling | doaj.art-15455fa8cda74752ba038ed39cd1387a2022-12-22T03:37:37ZengITB Journal PublisherJournal of ICT Research and Applications2337-57872338-54992013-09-01616381222Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography ImplementationMarisa W. Paryasto0Budi Rahardjo1Fajar Yuliawan2Intan Muchtadi Alamsyah3Kuspriyanto Kuspriyanto4School of Electrical Engineering and Informatics, Institut Teknologi Bandung Jl. Ganesha No. 10 Bandung 40132 – IndonesiaSchool of Electrical Engineering and Informatics, Institut Teknologi Bandung Jl. Ganesha No. 10 Bandung 40132 – IndonesiaAlgebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha No. 10 Bandung 40132 – IndonesiaAlgebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha No. 10 Bandung 40132 – IndonesiaSchool of Electrical Engineering and Informatics, Institut Teknologi Bandung Jl. Ganesha No. 10 Bandung 40132 – Indonesia<p class="Abstract"><span lang="EN-US">Implementing a secure cryptosystem requires operations involving hundreds of bits. One of the most recommended algorithm is Elliptic Curve Cryptography (ECC). The complexity of elliptic curve algorithms and parameters with hundreds of bits requires specific design and implementation strategy. The design architecture must be customized according to security requirement, available resources and parameter choices. In this work we propose the use of composite field to implement finite field multiplication for ECC implementation. We use 299-bit keylength represented in GF((2<sup>13</sup>)<sup>23</sup>) instead of in GF(2<sup>299</sup>). Composite field multiplier can be implemented using different multiplier for ground-field and for extension field. In this paper, LUT is used for multiplication in the ground-field and classic multiplieris used for the extension field multiplication. A generic architecture for the multiplier is presented. Implementation is done with VHDL with the target device Altera DE2. The work in this paper uses the simplest algorithm to confirm the idea that by dividing field into composite, use different multiplier for base and extension field would give better trade-off for time and area. This work will be the beginning of our more advanced further research that implements composite-field using Mastrovito Hybrid, KOA and LUT.</span></p>http://journals.itb.ac.id/index.php/jictra/article/view/221 |
| spellingShingle | Marisa W. Paryasto Budi Rahardjo Fajar Yuliawan Intan Muchtadi Alamsyah Kuspriyanto Kuspriyanto Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography Implementation Journal of ICT Research and Applications |
| title | Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography Implementation |
| title_full | Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography Implementation |
| title_fullStr | Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography Implementation |
| title_full_unstemmed | Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography Implementation |
| title_short | Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography Implementation |
| title_sort | composite field multiplier based on look up table for elliptic curve cryptography implementation |
| url | http://journals.itb.ac.id/index.php/jictra/article/view/221 |
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