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 -