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Paper 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.

Metadata
Available format(s)
PDF PS
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Tate pairingelliptic curve
Contact author(s)
shkwon @ skku edu
History
2004-11-21: last of 2 revisions
2004-11-15: received
See all versions
Short URL
https://ia.cr/2004/303
License
Creative Commons Attribution
CC BY
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