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A New Addition Formula for Elliptic Curves over GF(2^n)
August 2002 (vol. 51 no. 8)
pp. 972-975

In this paper, we propose a new addition formula in projective coordinates for elliptic curves over GF(2^n). The new formula speeds up the elliptic curve scalar multiplication by reducing the number of field multiplications. This was achieved by rewriting the elliptic curve addition formula. The complexity analysis shows that the new addition formula speeds up the addition in projective coordinates by about 10-2 percent, which leads to enhanced scalar multiplication methods for random and Koblitz curves.

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Index Terms:
Public-key cryptography, elliptic curves, point addition, projective coordinates, scalar multiplication.
Essame Al-Daoud, Ramlan Mahmod, Mohammad Rushdan, Adem Kilicman, "A New Addition Formula for Elliptic Curves over GF(2^n)," IEEE Transactions on Computers, vol. 51, no. 8, pp. 972-975, Aug. 2002, doi:10.1109/TC.2002.1024743
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