Width-3 joint sparse form

Katsuyuki Okeya; Hidehiro Kato; Yasuyuki Nogami

doi:10.1007/978-3-642-12827-1_6

Width-3 joint sparse form

Katsuyuki Okeya, Hidehiro Kato, Yasuyuki Nogami

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (Scopus)

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
Title of host publication	Information Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings
Pages	67-84
Number of pages	18
DOIs	https://doi.org/10.1007/978-3-642-12827-1_6
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)
Volume	6047 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	6th International Conference on Information Security Practice and Experience, ISPEC 2010
Country/Territory	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)

Access to Document

10.1007/978-3-642-12827-1_6

Cite this

Okeya, K., Kato, H., & Nogami, Y. (2010). Width-3 joint sparse form. In 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

Width-3 joint sparse form. / Okeya, Katsuyuki; Kato, Hidehiro; Nogami, Yasuyuki.
Information Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings. 2010. p. 67-84 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6047 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Okeya, K, Kato, H & Nogami, Y 2010, Width-3 joint sparse form. in Information Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6047 LNCS, pp. 67-84, 6th International Conference on Information Security Practice and Experience, ISPEC 2010, Seoul, Korea, Republic of, 5/12/10. https://doi.org/10.1007/978-3-642-12827-1_6

@inproceedings{80237de99298440485fd89a1c63cb3ac,

title = "Width-3 joint sparse form",

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).",

keywords = "Joint sparse form (JSF), Ulliptic curve cryptosystem, Uulti-scalar multiplication",

author = "Katsuyuki Okeya and Hidehiro Kato and Yasuyuki Nogami",

year = "2010",

month = dec,

day = "23",

doi = "10.1007/978-3-642-12827-1_6",

language = "English",

isbn = "3642128262",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "67--84",

booktitle = "Information Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings",

note = "6th International Conference on Information Security Practice and Experience, ISPEC 2010 ; Conference date: 12-05-2010 Through 13-05-2010",

}

TY - GEN

T1 - Width-3 joint sparse form

AU - Okeya, Katsuyuki

AU - Kato, Hidehiro

AU - Nogami, Yasuyuki

PY - 2010/12/23

Y1 - 2010/12/23

N2 - 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).

AB - 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).

KW - Joint sparse form (JSF)

KW - Ulliptic curve cryptosystem

KW - Uulti-scalar multiplication

UR - http://www.scopus.com/inward/record.url?scp=78650271070&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650271070&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-12827-1_6

DO - 10.1007/978-3-642-12827-1_6

M3 - Conference contribution

AN - SCOPUS:78650271070

SN - 3642128262

SN - 9783642128264

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 67

EP - 84

BT - Information Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings

T2 - 6th International Conference on Information Security Practice and Experience, ISPEC 2010

Y2 - 12 May 2010 through 13 May 2010

ER -

Width-3 joint sparse form

Abstract

Publication series

Other

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this