TY - GEN
T1 - A Construction Method of Final Exponentiation for a Specific Cyclotomic Family of Pairing-Friendly Elliptic Curves with Prime Embedding Degrees
AU - Nanjo, Yuki
AU - Shirase, Masaaki
AU - Kodera, Yuta
AU - Kusaka, Takuya
AU - Nogami, Yasuyuki
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - Pairings on elliptic curves which are carried out by the Miller loop and final exponentiation are used for innovative protocols such as ID-based encryption and group signature authentication. As the recent progress of attacks for finite fields in which pairings are defined, the importance of the use of the curves with prime embedding degrees k has been increased. In this manuscript, the authors provide a method for providing efficient final exponentiation algorithms for a specific cyclotomic family of curves with arbitrary prime k of k\equiv 1(\text{mod}\ 6). Applying the proposed method for several curves such as k=7, 13, and 19, it is found that the proposed method gives rise to the same algorithms as the previous state-of-The-Art ones by the lattice-based method.
AB - Pairings on elliptic curves which are carried out by the Miller loop and final exponentiation are used for innovative protocols such as ID-based encryption and group signature authentication. As the recent progress of attacks for finite fields in which pairings are defined, the importance of the use of the curves with prime embedding degrees k has been increased. In this manuscript, the authors provide a method for providing efficient final exponentiation algorithms for a specific cyclotomic family of curves with arbitrary prime k of k\equiv 1(\text{mod}\ 6). Applying the proposed method for several curves such as k=7, 13, and 19, it is found that the proposed method gives rise to the same algorithms as the previous state-of-The-Art ones by the lattice-based method.
KW - elliptic curve
KW - final exponentiation
KW - Pairing-based cryptography
UR - http://www.scopus.com/inward/record.url?scp=85124136218&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85124136218&partnerID=8YFLogxK
U2 - 10.1109/CANDAR53791.2021.00028
DO - 10.1109/CANDAR53791.2021.00028
M3 - Conference contribution
AN - SCOPUS:85124136218
T3 - Proceedings - 2021 9th International Symposium on Computing and Networking, CANDAR 2021
SP - 148
EP - 154
BT - Proceedings - 2021 9th International Symposium on Computing and Networking, CANDAR 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 9th International Symposium on Computing and Networking, CANDAR 2021
Y2 - 23 November 2021 through 26 November 2021
ER -