I implemented below algorithm in hardware and it works fine with first point addition.

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However, when I continue to perform back-to-back addition, I got the wrong result. The part that I'm not sure here is,

  1. The original calculated X3 and Y3 are still in Jacobian coordinate and I do not want to convert them back to affine coordinate due to expensive cost for doing multiplicative inverse for Z-1.

  2. But I'm not sure how should I carry forward the calculated X3 and Y3 I got in 1st addition into the next addition without performing affine coordinate conversion?

  3. I'm ignoring the calculated Z3 as no conversion is needed in intermediate (I assume). But I am not sure is this something that important to be carried forward to next addition?

  • $\begingroup$ It appear like that formula I apply won't work for back-to-back addition without converting back affine coordinate because the Z3 is not 1. Appreciate if someone can help to enlighten me? $\endgroup$
    – Pi-Turn
    Apr 23, 2023 at 9:50


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