{0, 1, 3}-NAF representation and algorithms for lightweight elliptic curve cryptosystem in Lopez Dahab model
Elliptic curve scalar multiplications is the most time-consuming and costly operation in elliptic curve cryptosystem. The scalar multiplication involves computation of Q = kP where k is a scalar multiplier, and P and Q are points on an elliptic curve. This computation can be improved by reducing the...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Praise Worthy Prize
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/36116/1/0.pdf |
| _version_ | 1825948779241537536 |
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| author | Md. Yasin, Sharifah Nor, Rozi Nor Haizan Din, Jamilah Muda, Zaiton |
| author_facet | Md. Yasin, Sharifah Nor, Rozi Nor Haizan Din, Jamilah Muda, Zaiton |
| author_sort | Md. Yasin, Sharifah |
| collection | UPM |
| description | Elliptic curve scalar multiplications is the most time-consuming and costly operation in elliptic curve cryptosystem. The scalar multiplication involves computation of Q = kP where k is a scalar multiplier, and P and Q are points on an elliptic curve. This computation can be improved by reducing the Hamming weight of the scalar multiplier k. The Hamming weight of k represents the number of nonzero digits in the scalar multiplier. This paper proposes a new scalar representation in non-adjacent form (NAF) using the digits 0, 1 and 3. This paper also proposes an algorithm for converting from a binary to {0,1,3}-NAF representation. Comparative analysis between the proposed NAF and the traditional NAF with digit {-1,0,1} is carried out. At average case, the proposes {0,1,3}-NAF representation has a lower Hamming weight than the traditional NAF. In our analysis, we use the {0,1,3}-NAF representation in the scalar multiplication operation. The average number of point addition operations in the scalar multiplication is considerably reduced compared to the addition-subtraction scalar multiplication algorithm. |
| first_indexed | 2024-03-06T08:34:22Z |
| format | Article |
| id | upm.eprints-36116 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:34:22Z |
| publishDate | 2014 |
| publisher | Praise Worthy Prize |
| record_format | dspace |
| spelling | upm.eprints-361162015-10-06T04:18:35Z http://psasir.upm.edu.my/id/eprint/36116/ {0, 1, 3}-NAF representation and algorithms for lightweight elliptic curve cryptosystem in Lopez Dahab model Md. Yasin, Sharifah Nor, Rozi Nor Haizan Din, Jamilah Muda, Zaiton Elliptic curve scalar multiplications is the most time-consuming and costly operation in elliptic curve cryptosystem. The scalar multiplication involves computation of Q = kP where k is a scalar multiplier, and P and Q are points on an elliptic curve. This computation can be improved by reducing the Hamming weight of the scalar multiplier k. The Hamming weight of k represents the number of nonzero digits in the scalar multiplier. This paper proposes a new scalar representation in non-adjacent form (NAF) using the digits 0, 1 and 3. This paper also proposes an algorithm for converting from a binary to {0,1,3}-NAF representation. Comparative analysis between the proposed NAF and the traditional NAF with digit {-1,0,1} is carried out. At average case, the proposes {0,1,3}-NAF representation has a lower Hamming weight than the traditional NAF. In our analysis, we use the {0,1,3}-NAF representation in the scalar multiplication operation. The average number of point addition operations in the scalar multiplication is considerably reduced compared to the addition-subtraction scalar multiplication algorithm. Praise Worthy Prize 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/36116/1/0.pdf Md. Yasin, Sharifah and Nor, Rozi Nor Haizan and Din, Jamilah and Muda, Zaiton (2014) {0, 1, 3}-NAF representation and algorithms for lightweight elliptic curve cryptosystem in Lopez Dahab model. International Review on Computers and Software, 9 (9). pp. 1541-1547. ISSN 1828-6003; ESSN: 1828-6011 |
| spellingShingle | Md. Yasin, Sharifah Nor, Rozi Nor Haizan Din, Jamilah Muda, Zaiton {0, 1, 3}-NAF representation and algorithms for lightweight elliptic curve cryptosystem in Lopez Dahab model |
| title | {0, 1, 3}-NAF representation and algorithms for lightweight elliptic curve cryptosystem in Lopez Dahab model |
| title_full | {0, 1, 3}-NAF representation and algorithms for lightweight elliptic curve cryptosystem in Lopez Dahab model |
| title_fullStr | {0, 1, 3}-NAF representation and algorithms for lightweight elliptic curve cryptosystem in Lopez Dahab model |
| title_full_unstemmed | {0, 1, 3}-NAF representation and algorithms for lightweight elliptic curve cryptosystem in Lopez Dahab model |
| title_short | {0, 1, 3}-NAF representation and algorithms for lightweight elliptic curve cryptosystem in Lopez Dahab model |
| title_sort | 0 1 3 naf representation and algorithms for lightweight elliptic curve cryptosystem in lopez dahab model |
| url | http://psasir.upm.edu.my/id/eprint/36116/1/0.pdf |
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