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 -