## Cryptology ePrint Archive: Report 2004/303

**Efficient Tate Pairing Computation for Supersingular Elliptic Curves over Binary Fields**

*Soonhak Kwon*

**Abstract: **We present a closed formula for the Tate pairing computation for
supersingular elliptic curves defined over the binary field F_{2^m} of odd dimension. There are exactly three isomorphism classes of supersingular elliptic curves over F_{2^m} for odd m and our result is applicable to all these curves. Moreover we show that our algorithm and also the Duursma-Lee algorithm can be modified to another algorithm which does not need any inverse Frobenius operation (square root or cube root extractions) without sacrificing any of the computational merits of the original algorithm. Since the computation of the inverse Frobenius map is not at all trivial in a polynomial basis and since a polynomial basis is still a preferred choice for the Tate pairing computation in many situations, this new algorithm avoiding the inverse Frobenius operation has some advantage over the existing algorithms.

**Category / Keywords: **public-key cryptography / Tate pairing, elliptic curve

**Date: **received 14 Nov 2004, last revised 20 Nov 2004

**Contact author: **shkwon at skku edu

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

**Version: **20041121:050329 (All versions of this report)

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