On the relationship between squared pairings and plain pairings

Authors:
Bo Gyeong Kang;Je Hong Park
Affiliations:
Department of Mathematics, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea;National Security Research Institute, 161 Gajeong-dong, Yuseong-gu, Daejeon 305-350, Republic of Korea
Venue:
Information Processing Letters
Year:
2006

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Abstract

In this paper, we investigate the relationship between the squared Weil/Tate pairing and the plain Weil/Tate pairing. Along these lines, we first show that the squared pairing for an arbitrary chosen point can be transformed into the plain pairing for a trace zero point which has a special form to compute them more efficiently. Then the optimizations made for computing squared pairings are combined with the computation of pairings on these trace zero points, to achieve even better performance for the computation of the 4th powered Weil pairing.