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FPGA and ASIC implementations of the ηT pairing in characteristic three
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Reduction optimal trinomials for efficient software implementation of the ηT pairing
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In this paper, we present a closed formula for the Tate pairing computation for supersingular elliptic curves defined over the binary field $\mathbb F_{2^m}$ of odd dimension. There are exactly three isomorphism classes of supersingular elliptic curves over $\mathbb F_{2^m}$ for odd m and our result is applicable to all these curves.