Parallelizing GF (p) montgomery elliptic curve crypto-system operations to improve security and performance.
The elliptic curve crypto-system (ECC) performs two levels of computations, lower point operations, and upper scalar multiplication levels. The use of usual serial design and affine coordinates to apply ECC computations increases the time delay and weaken the security of the crypto-system against si...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Book Section |
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Trans Tech Publications
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/29990/ |
| _version_ | 1848846551941644288 |
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| author | Alkhatib, Mohammad Jaafar, Azmi Md Said, Mohamad Rushdan Ahmad Zulkarnain, Zuriati |
| author2 | Sivakumar, R. |
| author_facet | Sivakumar, R. Alkhatib, Mohammad Jaafar, Azmi Md Said, Mohamad Rushdan Ahmad Zulkarnain, Zuriati |
| author_sort | Alkhatib, Mohammad |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The elliptic curve crypto-system (ECC) performs two levels of computations, lower point operations, and upper scalar multiplication levels. The use of usual serial design and affine coordinates to apply ECC computations increases the time delay and weaken the security of the crypto-system against simple power attack (SPA). This work combines the inherited parallelism in both computation levels for GF (p) Montgomery ECC to improve performance and enhance the immunity of the ECC against SPA. Moreover, projective coordinates were used to apply ECC operations to eliminate the time-consuming inversion operation. In order to increase the speed even further, this paper proposes to use known NAF algorithm for scalar multiplication, as well as Montgomery multiplier to perform multiplication operations. Hardware implementations with target FPGA for GF (p) Montgomery ECC are also presented. The best performance level was achieved when parallelizing Montgomery ECC computations to eight parallel multipliers (PM) using homogeneous coordinates. Such strategy, although it requires extra resources, is worth considering due to its attractive security and performance conclusions. |
| first_indexed | 2025-11-15T09:04:31Z |
| format | Book Section |
| id | upm-29990 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T09:04:31Z |
| publishDate | 2013 |
| publisher | Trans Tech Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-299902014-05-30T00:51:57Z http://psasir.upm.edu.my/id/eprint/29990/ Parallelizing GF (p) montgomery elliptic curve crypto-system operations to improve security and performance. Alkhatib, Mohammad Jaafar, Azmi Md Said, Mohamad Rushdan Ahmad Zulkarnain, Zuriati The elliptic curve crypto-system (ECC) performs two levels of computations, lower point operations, and upper scalar multiplication levels. The use of usual serial design and affine coordinates to apply ECC computations increases the time delay and weaken the security of the crypto-system against simple power attack (SPA). This work combines the inherited parallelism in both computation levels for GF (p) Montgomery ECC to improve performance and enhance the immunity of the ECC against SPA. Moreover, projective coordinates were used to apply ECC operations to eliminate the time-consuming inversion operation. In order to increase the speed even further, this paper proposes to use known NAF algorithm for scalar multiplication, as well as Montgomery multiplier to perform multiplication operations. Hardware implementations with target FPGA for GF (p) Montgomery ECC are also presented. The best performance level was achieved when parallelizing Montgomery ECC computations to eight parallel multipliers (PM) using homogeneous coordinates. Such strategy, although it requires extra resources, is worth considering due to its attractive security and performance conclusions. Trans Tech Publications Sivakumar, R. 2013 Book Section PeerReviewed Alkhatib, Mohammad and Jaafar, Azmi and Md Said, Mohamad Rushdan and Ahmad Zulkarnain, Zuriati (2013) Parallelizing GF (p) montgomery elliptic curve crypto-system operations to improve security and performance. In: Manufacturing Science and Technology. Advanced Materials Research, 3 (622-623). Trans Tech Publications, Switzerland, pp. 1906-1911. ISBN 9783037855638 http://www.scientific.net/AMR.622-623/38 10.4028/www.scientific.net/AMR.622-623.1906 |
| spellingShingle | Alkhatib, Mohammad Jaafar, Azmi Md Said, Mohamad Rushdan Ahmad Zulkarnain, Zuriati Parallelizing GF (p) montgomery elliptic curve crypto-system operations to improve security and performance. |
| title | Parallelizing GF (p) montgomery elliptic curve crypto-system operations to improve security and performance. |
| title_full | Parallelizing GF (p) montgomery elliptic curve crypto-system operations to improve security and performance. |
| title_fullStr | Parallelizing GF (p) montgomery elliptic curve crypto-system operations to improve security and performance. |
| title_full_unstemmed | Parallelizing GF (p) montgomery elliptic curve crypto-system operations to improve security and performance. |
| title_short | Parallelizing GF (p) montgomery elliptic curve crypto-system operations to improve security and performance. |
| title_sort | parallelizing gf (p) montgomery elliptic curve crypto-system operations to improve security and performance. |
| url | http://psasir.upm.edu.my/id/eprint/29990/ http://psasir.upm.edu.my/id/eprint/29990/ http://psasir.upm.edu.my/id/eprint/29990/ |