### Abstract

Scalar multiplication is the most computational intensive operation in elliptic curve cryptosystem (ECC). Improving the performance of this operation can be achieved by using recoding technique which aims at minimizing the density of nonzero digits in the scalar, also known as its Hamming weight. We proposed XTract recoding technique that alters the representation of scalar from binary digit to {-1,0,1,3} digit set in non-adjacent form (NAF). The recoding algorithm can be expressed both mathematically and logically and reduces the Hamming weight of the scalar to 41% in average for 163-bit scalar with balanced bit. X-Tract Recoding algorithm reads every three adjacent bits overlapped by one bit from left-to-right in the input binary scalar to produce each new output digit. We use ANOVA analysis to show that the new recoding technique produces significantly better output with less Hamming weight compared to its counterparts.

Original language | English |
---|---|

Pages (from-to) | 109-114 |

Number of pages | 6 |

Journal | Journal of Theoretical and Applied Information Technology |

Volume | 75 |

Issue number | 1 |

Publication status | Published - 10 May 2015 |

### Fingerprint

### Keywords

- Elliptic curve cryptosystem
- Hamming weight
- Non-adjacent form
- Recoding
- Scalar multiplication

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Journal of Theoretical and Applied Information Technology*,

*75*(1), 109-114.

**X-Tract recoding algorithm for minimal hamming weight digit set conversion.** / Ahmad, Miza Mumtaz; Yasin, Sharifah Md; Mahmod, Ramlan; Mohamed, Mohamad Afendee.

Research output: Contribution to journal › Article

*Journal of Theoretical and Applied Information Technology*, vol. 75, no. 1, pp. 109-114.

}

TY - JOUR

T1 - X-Tract recoding algorithm for minimal hamming weight digit set conversion

AU - Ahmad, Miza Mumtaz

AU - Yasin, Sharifah Md

AU - Mahmod, Ramlan

AU - Mohamed, Mohamad Afendee

PY - 2015/5/10

Y1 - 2015/5/10

N2 - Scalar multiplication is the most computational intensive operation in elliptic curve cryptosystem (ECC). Improving the performance of this operation can be achieved by using recoding technique which aims at minimizing the density of nonzero digits in the scalar, also known as its Hamming weight. We proposed XTract recoding technique that alters the representation of scalar from binary digit to {-1,0,1,3} digit set in non-adjacent form (NAF). The recoding algorithm can be expressed both mathematically and logically and reduces the Hamming weight of the scalar to 41% in average for 163-bit scalar with balanced bit. X-Tract Recoding algorithm reads every three adjacent bits overlapped by one bit from left-to-right in the input binary scalar to produce each new output digit. We use ANOVA analysis to show that the new recoding technique produces significantly better output with less Hamming weight compared to its counterparts.

AB - Scalar multiplication is the most computational intensive operation in elliptic curve cryptosystem (ECC). Improving the performance of this operation can be achieved by using recoding technique which aims at minimizing the density of nonzero digits in the scalar, also known as its Hamming weight. We proposed XTract recoding technique that alters the representation of scalar from binary digit to {-1,0,1,3} digit set in non-adjacent form (NAF). The recoding algorithm can be expressed both mathematically and logically and reduces the Hamming weight of the scalar to 41% in average for 163-bit scalar with balanced bit. X-Tract Recoding algorithm reads every three adjacent bits overlapped by one bit from left-to-right in the input binary scalar to produce each new output digit. We use ANOVA analysis to show that the new recoding technique produces significantly better output with less Hamming weight compared to its counterparts.

KW - Elliptic curve cryptosystem

KW - Hamming weight

KW - Non-adjacent form

KW - Recoding

KW - Scalar multiplication

UR - http://www.scopus.com/inward/record.url?scp=84929074396&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929074396&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84929074396

VL - 75

SP - 109

EP - 114

JO - Journal of Theoretical and Applied Information Technology

JF - Journal of Theoretical and Applied Information Technology

SN - 1992-8645

IS - 1

ER -