TY - GEN
T1 - A Technique for Fast Miller's Algorithm of Ate Pairings on Elliptic Curves with Embedding Degrees of Multiple of Three
AU - Nanjo, Yuki
AU - Shirase, Masaaki
AU - Kusaka, Takuya
AU - Nogami, Yasuyuki
N1 - Funding Information:
This research was supported by JSPS KAKENHI Grant Numbers 19J2108612 and 19K11966. The authors would like to thank Dr. Tadanori Teruya from National Institute of Ad- vanced Industrial Science and Technology Koto-ku, Tokyo, Japan for his helpful advices.
Funding Information:
This research was supported by JSPS KAKENHI Grant Numbers 19J2108612 and 19K11966. The authors would like to thank Dr. Tadanori Teruya from National Institute of Advanced Industrial Science and Technology Koto-ku, Tokyo, Japan for his helpful advices.
Publisher Copyright:
© 2020 IEICE.
PY - 2020/7
Y1 - 2020/7
N2 - Bilinear pairings are widely used for innovative protocols such as ID-based encryption and group signature authentication. According to the current research of the pairings, not only families of pairing-friendly elliptic curves with embedding degrees of multiple of four or six but also that of multiple of three can realize efficient pairings. However, the range of the practical choices of the elliptic curves with embedding degrees of multiple of three is more restricted than that of even embedding degrees by an efficiency reason for the computation of Miller's algorithm with a signed binary representation of a loop parameter. To ease the restriction, the authors propose to compute the Miller's algorithm by swapping the sign of the loop parameter without performance degradation for the ate pairing on such the elliptic curves.
AB - Bilinear pairings are widely used for innovative protocols such as ID-based encryption and group signature authentication. According to the current research of the pairings, not only families of pairing-friendly elliptic curves with embedding degrees of multiple of four or six but also that of multiple of three can realize efficient pairings. However, the range of the practical choices of the elliptic curves with embedding degrees of multiple of three is more restricted than that of even embedding degrees by an efficiency reason for the computation of Miller's algorithm with a signed binary representation of a loop parameter. To ease the restriction, the authors propose to compute the Miller's algorithm by swapping the sign of the loop parameter without performance degradation for the ate pairing on such the elliptic curves.
KW - Divisors
KW - Miller's algorithm
KW - Pairing-based cryptography
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M3 - Conference contribution
AN - SCOPUS:85091464988
T3 - ITC-CSCC 2020 - 35th International Technical Conference on Circuits/Systems, Computers and Communications
SP - 283
EP - 287
BT - ITC-CSCC 2020 - 35th International Technical Conference on Circuits/Systems, Computers and Communications
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 35th International Technical Conference on Circuits/Systems, Computers and Communications, ITC-CSCC 2020
Y2 - 3 July 2020 through 6 July 2020
ER -