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
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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 -