### Abstract

The joint sparse form (JSF) is a representation of a pair of integers, which is famous for accelerating a multi-scalar multiplication in elliptic curve cryptosystems. Solinas' original paper showed three unsolved problems on the enhancement of JSF. Whereas two of them have been solved, the other still remains to be done. The remaining unsolved problem is as follows: To design a representation of a pair of integers using a larger digit set such as a set involving ±3, while the original JSF utilizes the digit set that consists of 0,±1 for representing a pair of integers. This paper puts an end to the problem; width-3 JSF. The proposed enhancement satisfies properties that are similar to that of the original. For example, the enhanced representation is defined as a representation that satisfies some rules. Some other properties are the existence, the uniqueness of such a representation, and the optimality of the Hamming weight. The non-zero density of the width-3 JSF is 563/1574(= 0.3577) and this is ideal. The conversion algorithm to the enhanced representation takes O(log n) memory and O(n) computational cost, which is very efficient, where n stands for the bit length of the integers. Keywords: elliptic curve cryptosystem, multi-scalar multiplication, joint sparse form (JSF).

Original language | English |
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Title of host publication | Information Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings |

Pages | 67-84 |

Number of pages | 18 |

DOIs | |

Publication status | Published - Dec 23 2010 |

Event | 6th International Conference on Information Security Practice and Experience, ISPEC 2010 - Seoul, Korea, Republic of Duration: May 12 2010 → May 13 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6047 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 6th International Conference on Information Security Practice and Experience, ISPEC 2010 |
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Country | Korea, Republic of |

City | Seoul |

Period | 5/12/10 → 5/13/10 |

### Keywords

- Joint sparse form (JSF)
- Ulliptic curve cryptosystem
- Uulti-scalar multiplication

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Information Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings*(pp. 67-84). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6047 LNCS). https://doi.org/10.1007/978-3-642-12827-1_6