A new addition formula for elliptic curves over GF(2/sup n/)
In this paper, we propose a new addition formula in projective coordinates for elliptic curves over GF(2n). The new formula speeds up the elliptic curve scalar multiplication by reducing the number of field multiplications. This was achieved by rewriting the elliptic curve addition formula. The comp...
| Main Authors: | , , , |
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| Format: | Article |
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Institute of Electrical and Electronics Engineers
2002
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| Online Access: | http://psasir.upm.edu.my/id/eprint/112493/ |
| _version_ | 1848865957353619456 |
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| author | Al-Daoud, E. Mahmod, R. Rushdan, M. Kilicman, A. |
| author_facet | Al-Daoud, E. Mahmod, R. Rushdan, M. Kilicman, A. |
| author_sort | Al-Daoud, E. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, we propose a new addition formula in projective coordinates for elliptic curves over GF(2n). The new formula speeds up the elliptic curve scalar multiplication by reducing the number of field multiplications. This was achieved by rewriting the elliptic curve addition formula. The complexity analysis shows that the new addition formula speeds up the addition in projective coordinates by about 10-2 percent, which leads to enhanced scalar multiplication methods for random and Koblitz curves. |
| first_indexed | 2025-11-15T14:12:57Z |
| format | Article |
| id | upm-112493 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T14:12:57Z |
| publishDate | 2002 |
| publisher | Institute of Electrical and Electronics Engineers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1124932025-02-19T00:07:40Z http://psasir.upm.edu.my/id/eprint/112493/ A new addition formula for elliptic curves over GF(2/sup n/) Al-Daoud, E. Mahmod, R. Rushdan, M. Kilicman, A. In this paper, we propose a new addition formula in projective coordinates for elliptic curves over GF(2n). The new formula speeds up the elliptic curve scalar multiplication by reducing the number of field multiplications. This was achieved by rewriting the elliptic curve addition formula. The complexity analysis shows that the new addition formula speeds up the addition in projective coordinates by about 10-2 percent, which leads to enhanced scalar multiplication methods for random and Koblitz curves. Institute of Electrical and Electronics Engineers 2002 Article PeerReviewed Al-Daoud, E. and Mahmod, R. and Rushdan, M. and Kilicman, A. (2002) A new addition formula for elliptic curves over GF(2/sup n/). IEEE Transactions on Computers, 51 (8). pp. 972-975. ISSN 0018-9340; eISSN: 1557-9956 https://ieeexplore.ieee.org/document/1024743/ 10.1109/tc.2002.1024743 |
| spellingShingle | Al-Daoud, E. Mahmod, R. Rushdan, M. Kilicman, A. A new addition formula for elliptic curves over GF(2/sup n/) |
| title | A new addition formula for elliptic curves over GF(2/sup n/) |
| title_full | A new addition formula for elliptic curves over GF(2/sup n/) |
| title_fullStr | A new addition formula for elliptic curves over GF(2/sup n/) |
| title_full_unstemmed | A new addition formula for elliptic curves over GF(2/sup n/) |
| title_short | A new addition formula for elliptic curves over GF(2/sup n/) |
| title_sort | new addition formula for elliptic curves over gf(2/sup n/) |
| url | http://psasir.upm.edu.my/id/eprint/112493/ http://psasir.upm.edu.my/id/eprint/112493/ http://psasir.upm.edu.my/id/eprint/112493/ |