Signed decomposition method for scalar multiplication in elliptic curve cryptography
Addition chain is the solution to computability constraint of the problematic large number arithmetic. In elliptic curve cryptography, a point arithmetic on elliptic curve can be reduced to repetitive addition and doubling operations. Based on this idea, various methods were proposed, lately a decom...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
American Institute of Physics
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57287/1/Signed%20decomposition%20method%20for%20scalar%20multiplication%20in%20elliptic%20curve%20cryptography.pdf |
| _version_ | 1825931582572068864 |
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| author | Md. Said, Mohamad Rushdan Mohamed, M. A. Mohd Atan, Kamel Ariffin Ahmad Zukarnain, Zuriati |
| author_facet | Md. Said, Mohamad Rushdan Mohamed, M. A. Mohd Atan, Kamel Ariffin Ahmad Zukarnain, Zuriati |
| author_sort | Md. Said, Mohamad Rushdan |
| collection | UPM |
| description | Addition chain is the solution to computability constraint of the problematic large number arithmetic. In elliptic curve cryptography, a point arithmetic on elliptic curve can be reduced to repetitive addition and doubling operations. Based on this idea, various methods were proposed, lately a decomposition method based on prime decomposition was put forward. This method uses a pre‐generated set of rules to calculate an addition chain for n. Though the method shows it own advantage over others in some cases, but some improvements is still avail. We develop an enhancement version called signed decomposition method which takes rule from decomposition method as an input. We also generalize the idea of a prime rule to an integer rule. An improvement is done to the original add rule in decomposition method by allowing subtraction operation to terms. In so doing, we optimize the original form of add rule. The result shows not only an improvement over decomposition method but also become an all time superior compare to preceeding methods. Furthermore, having secret key in a form of rule will put up extra security to the message under communication. |
| first_indexed | 2024-03-06T09:28:56Z |
| format | Conference or Workshop Item |
| id | upm.eprints-57287 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:28:56Z |
| publishDate | 2010 |
| publisher | American Institute of Physics |
| record_format | dspace |
| spelling | upm.eprints-572872017-09-26T03:58:54Z http://psasir.upm.edu.my/id/eprint/57287/ Signed decomposition method for scalar multiplication in elliptic curve cryptography Md. Said, Mohamad Rushdan Mohamed, M. A. Mohd Atan, Kamel Ariffin Ahmad Zukarnain, Zuriati Addition chain is the solution to computability constraint of the problematic large number arithmetic. In elliptic curve cryptography, a point arithmetic on elliptic curve can be reduced to repetitive addition and doubling operations. Based on this idea, various methods were proposed, lately a decomposition method based on prime decomposition was put forward. This method uses a pre‐generated set of rules to calculate an addition chain for n. Though the method shows it own advantage over others in some cases, but some improvements is still avail. We develop an enhancement version called signed decomposition method which takes rule from decomposition method as an input. We also generalize the idea of a prime rule to an integer rule. An improvement is done to the original add rule in decomposition method by allowing subtraction operation to terms. In so doing, we optimize the original form of add rule. The result shows not only an improvement over decomposition method but also become an all time superior compare to preceeding methods. Furthermore, having secret key in a form of rule will put up extra security to the message under communication. American Institute of Physics 2010 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57287/1/Signed%20decomposition%20method%20for%20scalar%20multiplication%20in%20elliptic%20curve%20cryptography.pdf Md. Said, Mohamad Rushdan and Mohamed, M. A. and Mohd Atan, Kamel Ariffin and Ahmad Zukarnain, Zuriati (2010) Signed decomposition method for scalar multiplication in elliptic curve cryptography. In: International Conference on Mathematical Science (ICMS), 23-27 Nov. 2010, Bolu, Turkey. (pp. 805-813). 10.1063/1.3525209 |
| spellingShingle | Md. Said, Mohamad Rushdan Mohamed, M. A. Mohd Atan, Kamel Ariffin Ahmad Zukarnain, Zuriati Signed decomposition method for scalar multiplication in elliptic curve cryptography |
| title | Signed decomposition method for scalar multiplication in elliptic curve cryptography |
| title_full | Signed decomposition method for scalar multiplication in elliptic curve cryptography |
| title_fullStr | Signed decomposition method for scalar multiplication in elliptic curve cryptography |
| title_full_unstemmed | Signed decomposition method for scalar multiplication in elliptic curve cryptography |
| title_short | Signed decomposition method for scalar multiplication in elliptic curve cryptography |
| title_sort | signed decomposition method for scalar multiplication in elliptic curve cryptography |
| url | http://psasir.upm.edu.my/id/eprint/57287/1/Signed%20decomposition%20method%20for%20scalar%20multiplication%20in%20elliptic%20curve%20cryptography.pdf |
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