Width-3 joint sparse form

Katsuyuki Okeya, Hidehiro Kato, Yasuyuki Nogami

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 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 languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages67-84
Number of pages18
Volume6047 LNCS
DOIs
Publication statusPublished - 2010
Event6th International Conference on Information Security Practice and Experience, ISPEC 2010 - Seoul, Korea, Republic of
Duration: May 12 2010May 13 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6047 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other6th International Conference on Information Security Practice and Experience, ISPEC 2010
CountryKorea, Republic of
CitySeoul
Period5/12/105/13/10

Fingerprint

Cryptography
Elliptic Curve Cryptosystem
Scalar multiplication
Integer
Digit
Data storage equipment
Enhancement
Costs
Hamming Weight
Form
Computational Cost
Optimality
Uniqueness

Keywords

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

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Okeya, K., Kato, H., & Nogami, Y. (2010). Width-3 joint sparse form. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6047 LNCS, 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.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6047 LNCS 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 proceedingConference contribution

Okeya, K, Kato, H & Nogami, Y 2010, Width-3 joint sparse form. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 6047 LNCS, 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
Okeya K, Kato H, Nogami Y. Width-3 joint sparse form. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6047 LNCS. 2010. p. 67-84. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-12827-1_6
Okeya, Katsuyuki ; Kato, Hidehiro ; Nogami, Yasuyuki. / Width-3 joint sparse form. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6047 LNCS 2010. pp. 67-84 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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