TY - GEN
T1 - Efficient scalar multiplication for ate based pairing over kss curve of embedding degree 18
AU - Khandaker, Md Al Amin
AU - Nogami, Yasuyuki
AU - Seo, Hwajeong
AU - Duquesne, Sylvain
N1 - Funding Information:
This work was partially supported by the Strategic Information and Communications R&D Promotion Programme (SCOPE) of Ministry of Internal Affairs and Communications, Japan.
Publisher Copyright:
© Springer International Publishing AG 2017.
PY - 2017
Y1 - 2017
N2 - Efficiency of the next generation pairing based security protocols rely not only on the faster pairing calculation but also on efficient scalar multiplication on higher degree rational points. In this paper we proposed a scalar multiplication technique in the context of Ate based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curves with embedding degree k = 18 at the 192-bit security level. From the systematically obtained characteristics p, order r and Frobenious trace t of KSS curve, which is given by certain integer z also known as mother parameter, we exploit the relation #E(F p) = p+1−t mod r by applying Frobenius mapping with rational point to enhance the scalar multiplication. In addition we proposed z-adic representation of scalar s. In combination of Frobenious mapping with multi-scalar multiplication technique we efficiently calculate scalar multiplication by s. Our proposed method can achieve 3 times or more than 3 times faster scalar multiplication compared to binary scalar multiplication, sliding-window and non-adjacent form method.
AB - Efficiency of the next generation pairing based security protocols rely not only on the faster pairing calculation but also on efficient scalar multiplication on higher degree rational points. In this paper we proposed a scalar multiplication technique in the context of Ate based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curves with embedding degree k = 18 at the 192-bit security level. From the systematically obtained characteristics p, order r and Frobenious trace t of KSS curve, which is given by certain integer z also known as mother parameter, we exploit the relation #E(F p) = p+1−t mod r by applying Frobenius mapping with rational point to enhance the scalar multiplication. In addition we proposed z-adic representation of scalar s. In combination of Frobenious mapping with multi-scalar multiplication technique we efficiently calculate scalar multiplication by s. Our proposed method can achieve 3 times or more than 3 times faster scalar multiplication compared to binary scalar multiplication, sliding-window and non-adjacent form method.
KW - Frobenius mapping
KW - KSS curve
KW - Scalar multiplication
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U2 - 10.1007/978-3-319-56549-1_19
DO - 10.1007/978-3-319-56549-1_19
M3 - Conference contribution
AN - SCOPUS:85017607789
SN - 9783319565484
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 221
EP - 232
BT - Information Security Applications - 17th International Workshop, WISA 2016, Revised Selected Papers
A2 - Choi, Dooho
A2 - Guilley , Sylvain
PB - Springer Verlag
T2 - 17th International Workshop on Information Security Applications, WISA 2016
Y2 - 25 August 2016 through 25 August 2016
ER -