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<p><b>Abstract</b>—We present a careful analysis of elliptic curve point multiplication methods that use the point halving technique of Knudsen and Schroeppel and compare these methods to traditional algorithms that use point doubling. The performance advantage of halving methods is clearest in the case of point multiplication <tmath>kP</tmath>, where <tmath>P</tmath> is not known in advance and smaller field inversion to multiplication ratios generally favor halving. Although halving essentially operates on affine coordinate representations, we adapt an algorithm of Knuth to allow efficient use of projective coordinates with halving-based windowing methods for point multiplication.</p>
Public key cryptosystems, computer arithmetic, efficiency.

J. L?pez, A. Menezes, D. Hankerson and K. Fong, "Field Inversion and Point Halving Revisited," in IEEE Transactions on Computers, vol. 53, no. , pp. 1047-1059, 2004.
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