A Comparative Implementation of GLV Technique on KSS-16 Curve

Md Al Amin Khandaker; Yuki Nanjo; Takuya Kusaka; Yasuyuki Nogami

doi:10.1109/CANDAR.2018.00021

A Comparative Implementation of GLV Technique on KSS-16 Curve

Md Al Amin Khandaker, Yuki Nanjo, Takuya Kusaka, Yasuyuki Nogami

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

Abstract

Pairing-based protocols are getting popular in many cryptographic applications. Pairing algorithms involve computations on elements in all three pairing groups, G ₁ , G ₂ and G ₃ ; however, most protocols usually require additional scalar multiplication and exponentiation in any of these three groups. The Gallant-Lambert-Vanstone (GLV) method is an elegant technique to accelerate the scalar multiplication which can reduce the number of elliptic curve doubling by using Straus-Shamir simultaneous multi-scalar multiplication technique. However, efficiently computable endomorphisms are required to apply GLV for the elliptic curves. This paper shows the GLV technique by deriving efficiently computable endomorphism for Kachisa-Schaefer-Scott (KSS) curve defined over degree 16 extension field. In addition, the authors show explicit formulas to compute the GLV method together with Straus-Shamir simultaneous multi-scalar multiplication technique for 2, 4 and 8 dimensions in G ₂ group. The comparative implementation shows that dimension 4 gives faster computational time than dimension 8 and 2.

Original language	English
Title of host publication	Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	106-112
Number of pages	7
ISBN (Electronic)	9781538691823
DOIs	https://doi.org/10.1109/CANDAR.2018.00021
Publication status	Published - Dec 27 2018
Event	6th International Symposium on Computing and Networking, CANDAR 2018 - Takayama, Japan Duration: Nov 27 2018 → Nov 30 2018

Publication series

Name	Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018

Conference

Conference	6th International Symposium on Computing and Networking, CANDAR 2018
Country	Japan
City	Takayama
Period	11/27/18 → 11/30/18

Keywords

GLV method
KSS-16 curve
pairing-based cryptography
scalar multiplication

ASJC Scopus subject areas

Hardware and Architecture
Computer Networks and Communications
Software
Safety, Risk, Reliability and Quality

Access to Document

10.1109/CANDAR.2018.00021

Cite this

Khandaker, M. A. A., Nanjo, Y., Kusaka, T., & Nogami, Y. (2018). A Comparative Implementation of GLV Technique on KSS-16 Curve. In Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018 (pp. 106-112). [8594750] (Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CANDAR.2018.00021

A Comparative Implementation of GLV Technique on KSS-16 Curve. / Khandaker, Md Al Amin; Nanjo, Yuki; Kusaka, Takuya ; Nogami, Yasuyuki.

Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 106-112 8594750 (Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018).

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

Khandaker, MAA, Nanjo, Y, Kusaka, T & Nogami, Y 2018, A Comparative Implementation of GLV Technique on KSS-16 Curve. in Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018., 8594750, Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018, Institute of Electrical and Electronics Engineers Inc., pp. 106-112, 6th International Symposium on Computing and Networking, CANDAR 2018, Takayama, Japan, 11/27/18. https://doi.org/10.1109/CANDAR.2018.00021

Khandaker MAA, Nanjo Y, Kusaka T , Nogami Y. A Comparative Implementation of GLV Technique on KSS-16 Curve. In Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 106-112. 8594750. (Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018). https://doi.org/10.1109/CANDAR.2018.00021

Khandaker, Md Al Amin ; Nanjo, Yuki ; Kusaka, Takuya ; Nogami, Yasuyuki. / A Comparative Implementation of GLV Technique on KSS-16 Curve. Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 106-112 (Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018).

@inproceedings{ef56075005d148b7a888a3bab56d6c19,

title = "A Comparative Implementation of GLV Technique on KSS-16 Curve",

abstract = " Pairing-based protocols are getting popular in many cryptographic applications. Pairing algorithms involve computations on elements in all three pairing groups, G 1 , G 2 and G 3 ; however, most protocols usually require additional scalar multiplication and exponentiation in any of these three groups. The Gallant-Lambert-Vanstone (GLV) method is an elegant technique to accelerate the scalar multiplication which can reduce the number of elliptic curve doubling by using Straus-Shamir simultaneous multi-scalar multiplication technique. However, efficiently computable endomorphisms are required to apply GLV for the elliptic curves. This paper shows the GLV technique by deriving efficiently computable endomorphism for Kachisa-Schaefer-Scott (KSS) curve defined over degree 16 extension field. In addition, the authors show explicit formulas to compute the GLV method together with Straus-Shamir simultaneous multi-scalar multiplication technique for 2, 4 and 8 dimensions in G 2 group. The comparative implementation shows that dimension 4 gives faster computational time than dimension 8 and 2. ",

keywords = "GLV method, KSS-16 curve, pairing-based cryptography, scalar multiplication",

author = "Khandaker, {Md Al Amin} and Yuki Nanjo and Takuya Kusaka and Yasuyuki Nogami",

year = "2018",

month = dec,

day = "27",

doi = "10.1109/CANDAR.2018.00021",

language = "English",

series = "Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "106--112",

booktitle = "Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018",

note = "6th International Symposium on Computing and Networking, CANDAR 2018 ; Conference date: 27-11-2018 Through 30-11-2018",

}

TY - GEN

T1 - A Comparative Implementation of GLV Technique on KSS-16 Curve

AU - Khandaker, Md Al Amin

AU - Nanjo, Yuki

AU - Kusaka, Takuya

AU - Nogami, Yasuyuki

PY - 2018/12/27

Y1 - 2018/12/27

N2 - Pairing-based protocols are getting popular in many cryptographic applications. Pairing algorithms involve computations on elements in all three pairing groups, G 1 , G 2 and G 3 ; however, most protocols usually require additional scalar multiplication and exponentiation in any of these three groups. The Gallant-Lambert-Vanstone (GLV) method is an elegant technique to accelerate the scalar multiplication which can reduce the number of elliptic curve doubling by using Straus-Shamir simultaneous multi-scalar multiplication technique. However, efficiently computable endomorphisms are required to apply GLV for the elliptic curves. This paper shows the GLV technique by deriving efficiently computable endomorphism for Kachisa-Schaefer-Scott (KSS) curve defined over degree 16 extension field. In addition, the authors show explicit formulas to compute the GLV method together with Straus-Shamir simultaneous multi-scalar multiplication technique for 2, 4 and 8 dimensions in G 2 group. The comparative implementation shows that dimension 4 gives faster computational time than dimension 8 and 2.

AB - Pairing-based protocols are getting popular in many cryptographic applications. Pairing algorithms involve computations on elements in all three pairing groups, G 1 , G 2 and G 3 ; however, most protocols usually require additional scalar multiplication and exponentiation in any of these three groups. The Gallant-Lambert-Vanstone (GLV) method is an elegant technique to accelerate the scalar multiplication which can reduce the number of elliptic curve doubling by using Straus-Shamir simultaneous multi-scalar multiplication technique. However, efficiently computable endomorphisms are required to apply GLV for the elliptic curves. This paper shows the GLV technique by deriving efficiently computable endomorphism for Kachisa-Schaefer-Scott (KSS) curve defined over degree 16 extension field. In addition, the authors show explicit formulas to compute the GLV method together with Straus-Shamir simultaneous multi-scalar multiplication technique for 2, 4 and 8 dimensions in G 2 group. The comparative implementation shows that dimension 4 gives faster computational time than dimension 8 and 2.

KW - GLV method

KW - KSS-16 curve

KW - pairing-based cryptography

KW - scalar multiplication

UR - http://www.scopus.com/inward/record.url?scp=85061507883&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061507883&partnerID=8YFLogxK

U2 - 10.1109/CANDAR.2018.00021

DO - 10.1109/CANDAR.2018.00021

M3 - Conference contribution

AN - SCOPUS:85061507883

T3 - Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018

SP - 106

EP - 112

BT - Proceedings - 2018 6th International Symposium on Computing and Networking, CANDAR 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 6th International Symposium on Computing and Networking, CANDAR 2018

Y2 - 27 November 2018 through 30 November 2018

ER -