## Cryptology ePrint Archive: Report 2005/112

On the relationship between squared pairings and plain pairings

Bo Gyeong Kang and Je Hong Park

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 arbitrary chosen point can be transformed into a plain pairing for the trace zero point which has a special form to compute them more efficiently. This transformation requires only a cost of some Frobenius actions. Additionally, we show that the squared Weil pairing can be computed more efficiently for trace zero point and derive an explicit formula for the 4th powered Weil pairing as an optimized version of the Weil pairing.

Category / Keywords: Weil/Tate pairing, Squared pairing

Date: received 14 Apr 2005, last revised 13 May 2005

Contact author: jhpark at etri re kr

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Short URL: ia.cr/2005/112

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